%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET967+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:44 AM UTC 2025
% Result : Theorem 6.63s 6.84s
% Output : Proof 6.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET967+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:52:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 6.63/6.84 % SZS status Theorem
% 6.63/6.84 % SZS output start Proof
% 6.63/6.84 tff(in_type, type, (
% 6.63/6.84 in: ( $i * $i ) > $o)).
% 6.63/6.84 tff(set_union2_type, type, (
% 6.63/6.84 set_union2: ( $i * $i ) > $i)).
% 6.63/6.84 tff(tptp_fun_A_11_type, type, (
% 6.63/6.84 tptp_fun_A_11: $i)).
% 6.63/6.84 tff(tptp_fun_B_10_type, type, (
% 6.63/6.84 tptp_fun_B_10: $i)).
% 6.63/6.84 tff(tptp_fun_D_4_type, type, (
% 6.63/6.84 tptp_fun_D_4: $i > $i)).
% 6.63/6.84 tff(tptp_fun_D_0_type, type, (
% 6.63/6.84 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 6.63/6.84 tff(cartesian_product2_type, type, (
% 6.63/6.84 cartesian_product2: ( $i * $i ) > $i)).
% 6.63/6.84 tff(tptp_fun_C_9_type, type, (
% 6.63/6.84 tptp_fun_C_9: $i)).
% 6.63/6.84 tff(tptp_fun_E_3_type, type, (
% 6.63/6.84 tptp_fun_E_3: $i > $i)).
% 6.63/6.84 tff(ordered_pair_type, type, (
% 6.63/6.84 ordered_pair: ( $i * $i ) > $i)).
% 6.63/6.84 tff(unordered_pair_type, type, (
% 6.63/6.84 unordered_pair: ( $i * $i ) > $i)).
% 6.63/6.84 tff(singleton_type, type, (
% 6.63/6.84 singleton: $i > $i)).
% 6.63/6.84 tff(1,assumption,(~(set_union2(B!10, A!11) = set_union2(A!11, B!10))), introduced(assumption)).
% 6.63/6.84 tff(2,plain,
% 6.63/6.84 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 6.63/6.84 inference(bind,[status(th)],[])).
% 6.63/6.84 tff(3,plain,
% 6.63/6.84 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 6.63/6.84 inference(quant_intro,[status(thm)],[2])).
% 6.63/6.84 tff(4,plain,
% 6.63/6.84 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 6.63/6.84 inference(rewrite,[status(thm)],[])).
% 6.63/6.84 tff(5,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 6.63/6.84 tff(6,plain,
% 6.63/6.84 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 6.63/6.84 inference(modus_ponens,[status(thm)],[5, 4])).
% 6.63/6.84 tff(7,plain,(
% 6.63/6.84 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 6.63/6.84 inference(skolemize,[status(sab)],[6])).
% 6.63/6.84 tff(8,plain,
% 6.63/6.84 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 6.63/6.84 inference(modus_ponens,[status(thm)],[7, 3])).
% 6.63/6.84 tff(9,plain,
% 6.63/6.84 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(B!10, A!11) = set_union2(A!11, B!10))),
% 6.63/6.84 inference(quant_inst,[status(thm)],[])).
% 6.63/6.84 tff(10,plain,
% 6.63/6.84 ($false),
% 6.63/6.84 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 6.63/6.84 tff(11,plain,(set_union2(B!10, A!11) = set_union2(A!11, B!10)), inference(lemma,lemma(discharge,[]))).
% 6.63/6.84 tff(12,plain,
% 6.63/6.84 (set_union2(A!11, B!10) = set_union2(B!10, A!11)),
% 6.63/6.84 inference(symmetry,[status(thm)],[11])).
% 6.63/6.84 tff(13,plain,
% 6.63/6.84 (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10)) <=> in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11))),
% 6.63/6.84 inference(monotonicity,[status(thm)],[12])).
% 6.63/6.84 tff(14,plain,
% 6.63/6.84 ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) <=> (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)))),
% 6.63/6.84 inference(monotonicity,[status(thm)],[13])).
% 6.63/6.84 tff(15,plain,
% 6.63/6.84 (^[A: $i, B: $i, C: $i, D: $i] : refl((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))),
% 6.63/6.84 inference(bind,[status(th)],[])).
% 6.63/6.84 tff(16,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 6.63/6.84 inference(quant_intro,[status(thm)],[15])).
% 6.63/6.84 tff(17,plain,
% 6.63/6.84 (^[A: $i, B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((in(A, C) & in(B, D)) <=> (~((~in(A, C)) | (~in(B, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))), rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))), rewrite((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))))),
% 6.63/6.84 inference(bind,[status(th)],[])).
% 6.63/6.84 tff(18,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 6.63/6.84 inference(quant_intro,[status(thm)],[17])).
% 6.63/6.84 tff(19,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 6.63/6.84 inference(rewrite,[status(thm)],[])).
% 6.63/6.84 tff(20,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l55_zfmisc_1')).
% 6.63/6.84 tff(21,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 6.63/6.84 inference(modus_ponens,[status(thm)],[20, 19])).
% 6.63/6.84 tff(22,plain,(
% 6.63/6.84 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 6.63/6.84 inference(skolemize,[status(sab)],[21])).
% 6.63/6.84 tff(23,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 6.63/6.84 inference(modus_ponens,[status(thm)],[22, 18])).
% 6.63/6.84 tff(24,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 6.63/6.84 inference(modus_ponens,[status(thm)],[23, 16])).
% 6.63/6.84 tff(25,plain,
% 6.63/6.84 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(set_union2(A!11, B!10), C!9))))),
% 6.63/6.84 inference(quant_inst,[status(thm)],[])).
% 6.63/6.84 tff(26,plain,
% 6.63/6.84 (~(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(set_union2(A!11, B!10), C!9)))),
% 6.63/6.84 inference(unit_resolution,[status(thm)],[25, 24])).
% 6.63/6.84 tff(27,assumption,(~(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), introduced(assumption)).
% 6.63/6.84 tff(28,plain,
% 6.63/6.84 (^[A: $i, B: $i, C: $i] : refl(((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A)) <=> ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A)))),
% 6.63/6.84 inference(bind,[status(th)],[])).
% 6.63/6.84 tff(29,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A)) <=> ![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))),
% 6.63/6.84 inference(quant_intro,[status(thm)],[28])).
% 6.63/6.84 tff(30,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : (~(in(A, cartesian_product2(B, C)) & ![D: $i, E: $i] : (~(ordered_pair(D, E) = A)))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, cartesian_product2(B, C)) & ![D: $i, E: $i] : (~(ordered_pair(D, E) = A))))),
% 6.63/6.84 inference(rewrite,[status(thm)],[])).
% 6.63/6.84 tff(31,axiom,(![A: $i, B: $i, C: $i] : (~(in(A, cartesian_product2(B, C)) & ![D: $i, E: $i] : (~(ordered_pair(D, E) = A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t102_zfmisc_1')).
% 6.63/6.84 tff(32,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : (~(in(A, cartesian_product2(B, C)) & ![D: $i, E: $i] : (~(ordered_pair(D, E) = A))))),
% 6.63/6.84 inference(modus_ponens,[status(thm)],[31, 30])).
% 6.63/6.84 tff(33,plain,(
% 6.63/6.84 ![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))),
% 6.63/6.84 inference(skolemize,[status(sab)],[32])).
% 6.63/6.84 tff(34,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))),
% 6.63/6.84 inference(modus_ponens,[status(thm)],[33, 29])).
% 6.63/6.84 tff(35,plain,
% 6.63/6.84 (((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | ((~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))))),
% 6.63/6.84 inference(rewrite,[status(thm)],[])).
% 6.63/6.84 tff(36,plain,
% 6.63/6.84 ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | ((~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))))),
% 6.63/6.84 inference(quant_inst,[status(thm)],[])).
% 6.63/6.84 tff(37,plain,
% 6.63/6.84 ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))),
% 6.63/6.84 inference(modus_ponens,[status(thm)],[36, 35])).
% 6.63/6.84 tff(38,plain,
% 6.63/6.84 ((~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))),
% 6.63/6.84 inference(unit_resolution,[status(thm)],[37, 34])).
% 6.63/6.84 tff(39,plain,
% 6.63/6.84 (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9))),
% 6.63/6.84 inference(unit_resolution,[status(thm)],[38, 27])).
% 6.63/6.84 tff(40,plain,
% 6.63/6.84 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 6.63/6.84 inference(bind,[status(th)],[])).
% 6.63/6.84 tff(41,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 6.63/6.84 inference(quant_intro,[status(thm)],[40])).
% 6.63/6.84 tff(42,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 6.63/6.84 inference(pull_quant,[status(thm)],[])).
% 6.63/6.84 tff(43,plain,
% 6.63/6.84 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))))),
% 6.63/6.84 inference(bind,[status(th)],[])).
% 6.63/6.84 tff(44,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 6.63/6.84 inference(quant_intro,[status(thm)],[43])).
% 6.63/6.84 tff(45,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 6.63/6.84 inference(transitivity,[status(thm)],[44, 42])).
% 6.63/6.84 tff(46,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 6.63/6.84 inference(transitivity,[status(thm)],[45, 41])).
% 6.63/6.84 tff(47,plain,
% 6.63/6.84 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 6.63/6.84 inference(bind,[status(th)],[])).
% 6.63/6.84 tff(48,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 6.63/6.84 inference(quant_intro,[status(thm)],[47])).
% 6.63/6.84 tff(49,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 6.63/6.84 inference(transitivity,[status(thm)],[48, 46])).
% 6.63/6.84 tff(50,plain,
% 6.63/6.84 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))) <=> (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), rewrite(((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))))),
% 6.63/6.84 inference(bind,[status(th)],[])).
% 6.63/6.84 tff(51,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 6.63/6.84 inference(quant_intro,[status(thm)],[50])).
% 6.63/6.84 tff(52,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 6.63/6.84 inference(rewrite,[status(thm)],[])).
% 6.63/6.84 tff(53,plain,
% 6.63/6.84 (^[A: $i, B: $i, C: $i] : rewrite(((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))))),
% 6.63/6.84 inference(bind,[status(th)],[])).
% 6.63/6.84 tff(54,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 6.63/6.84 inference(quant_intro,[status(thm)],[53])).
% 6.63/6.84 tff(55,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_xboole_0')).
% 6.63/6.84 tff(56,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 6.63/6.84 inference(modus_ponens,[status(thm)],[55, 54])).
% 6.63/6.84 tff(57,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 6.63/6.84 inference(modus_ponens,[status(thm)],[56, 52])).
% 6.63/6.84 tff(58,plain,(
% 6.63/6.84 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))),
% 6.63/6.84 inference(skolemize,[status(sab)],[57])).
% 6.63/6.84 tff(59,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 6.63/6.84 inference(modus_ponens,[status(thm)],[58, 51])).
% 6.63/6.84 tff(60,plain,
% 6.63/6.84 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 6.63/6.84 inference(modus_ponens,[status(thm)],[59, 49])).
% 6.63/6.84 tff(61,plain,
% 6.63/6.84 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~((~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))) | (cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~((~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))) | (cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))))))),
% 6.63/6.84 inference(rewrite,[status(thm)],[])).
% 6.63/6.84 tff(62,plain,
% 6.63/6.84 ((~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))))))) <=> (~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~((~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))) | (cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))))))),
% 6.63/6.84 inference(rewrite,[status(thm)],[])).
% 6.63/6.84 tff(63,plain,
% 6.63/6.84 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~((~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))) | (cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))))))),
% 6.63/6.85 inference(monotonicity,[status(thm)],[62])).
% 6.63/6.85 tff(64,plain,
% 6.63/6.85 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~((~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))) | (cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))))))),
% 6.63/6.85 inference(transitivity,[status(thm)],[63, 61])).
% 6.63/6.85 tff(65,plain,
% 6.63/6.85 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9)))))))))),
% 6.63/6.85 inference(quant_inst,[status(thm)],[])).
% 6.63/6.85 tff(66,plain,
% 6.63/6.85 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~((~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))) | (cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))))))),
% 6.63/6.85 inference(modus_ponens,[status(thm)],[65, 64])).
% 6.63/6.85 tff(67,plain,
% 6.63/6.85 (~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~((~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))) | (cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))))),
% 6.63/6.85 inference(unit_resolution,[status(thm)],[66, 60])).
% 6.63/6.85 tff(68,plain,
% 6.63/6.85 (((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~((~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))) | (cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))))) | ((~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))) | (cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))),
% 6.63/6.85 inference(tautology,[status(thm)],[])).
% 6.63/6.85 tff(69,plain,
% 6.63/6.85 ((~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))) | (cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))),
% 6.63/6.85 inference(unit_resolution,[status(thm)],[68, 67])).
% 6.63/6.85 tff(70,plain,
% 6.63/6.85 (((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~((~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))) | (cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))))) | ((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))),
% 6.63/6.85 inference(tautology,[status(thm)],[])).
% 6.63/6.85 tff(71,plain,
% 6.63/6.85 ((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9))))),
% 6.63/6.85 inference(unit_resolution,[status(thm)],[70, 67])).
% 6.63/6.85 tff(72,plain,
% 6.63/6.85 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9))))))) | (~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(A!11, C!9)) | in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(B!10, C!9))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9))))))) | (~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(A!11, C!9)) | in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(B!10, C!9)))))))))),
% 6.63/6.85 inference(rewrite,[status(thm)],[])).
% 6.63/6.85 tff(73,plain,
% 6.63/6.85 ((~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(B!10, C!9)) | in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(A!11, C!9)))))) | (~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9))))))))) <=> (~((~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9))))))) | (~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(A!11, C!9)) | in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(B!10, C!9))))))))),
% 6.63/6.85 inference(rewrite,[status(thm)],[])).
% 6.63/6.85 tff(74,plain,
% 6.63/6.85 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(B!10, C!9)) | in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(A!11, C!9)))))) | (~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9))))))) | (~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(A!11, C!9)) | in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(B!10, C!9)))))))))),
% 6.63/6.86 inference(monotonicity,[status(thm)],[73])).
% 6.63/6.86 tff(75,plain,
% 6.63/6.86 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(B!10, C!9)) | in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(A!11, C!9)))))) | (~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9))))))) | (~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(A!11, C!9)) | in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(B!10, C!9)))))))))),
% 6.63/6.86 inference(transitivity,[status(thm)],[74, 72])).
% 6.63/6.86 tff(76,plain,
% 6.63/6.86 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(B!10, C!9)) | in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(A!11, C!9)))))) | (~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)))))))))),
% 6.63/6.86 inference(quant_inst,[status(thm)],[])).
% 6.63/6.86 tff(77,plain,
% 6.63/6.86 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9))))))) | (~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(A!11, C!9)) | in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(B!10, C!9))))))))),
% 6.63/6.86 inference(modus_ponens,[status(thm)],[76, 75])).
% 6.63/6.86 tff(78,plain,
% 6.63/6.86 (~((~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9))))))) | (~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(A!11, C!9)) | in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(B!10, C!9)))))))),
% 6.63/6.86 inference(unit_resolution,[status(thm)],[77, 60])).
% 6.63/6.86 tff(79,plain,
% 6.63/6.86 (((~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9))))))) | (~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(A!11, C!9)) | in(unordered_pair(unordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))), singleton(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))), cartesian_product2(B!10, C!9))))))) | ((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9))))))),
% 6.63/6.86 inference(tautology,[status(thm)],[])).
% 6.63/6.86 tff(80,plain,
% 6.63/6.86 ((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))),
% 6.63/6.86 inference(unit_resolution,[status(thm)],[79, 78])).
% 6.63/6.86 tff(81,plain,
% 6.63/6.86 (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(A!11, B!10)) <=> in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11))),
% 6.63/6.86 inference(monotonicity,[status(thm)],[12])).
% 6.63/6.86 tff(82,plain,
% 6.63/6.86 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(A!11, B!10)))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(A!11, B!10)))))),
% 6.63/6.86 inference(quant_inst,[status(thm)],[])).
% 6.63/6.86 tff(83,plain,
% 6.63/6.86 (~(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(A!11, B!10)))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(A!11, B!10))))),
% 6.63/6.86 inference(unit_resolution,[status(thm)],[82, 24])).
% 6.63/6.86 tff(84,assumption,(~(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))))), introduced(assumption)).
% 6.63/6.86 tff(85,assumption,(~(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), introduced(assumption)).
% 6.63/6.86 tff(86,plain,
% 6.63/6.86 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!11, B!10) = set_union2(B!10, A!11))),
% 6.63/6.86 inference(quant_inst,[status(thm)],[])).
% 6.63/6.86 tff(87,plain,
% 6.63/6.86 (set_union2(A!11, B!10) = set_union2(B!10, A!11)),
% 6.63/6.86 inference(unit_resolution,[status(thm)],[86, 8])).
% 6.63/6.86 tff(88,plain,
% 6.63/6.86 (set_union2(B!10, A!11) = set_union2(A!11, B!10)),
% 6.63/6.86 inference(symmetry,[status(thm)],[87])).
% 6.63/6.86 tff(89,plain,
% 6.63/6.86 (cartesian_product2(C!9, set_union2(B!10, A!11)) = cartesian_product2(C!9, set_union2(A!11, B!10))),
% 6.63/6.86 inference(monotonicity,[status(thm)],[88])).
% 6.63/6.86 tff(90,plain,
% 6.63/6.86 (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(B!10, A!11))) <=> in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10)))),
% 6.63/6.86 inference(monotonicity,[status(thm)],[89])).
% 6.63/6.86 tff(91,plain,
% 6.63/6.86 ((~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(B!10, A!11)))) <=> (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))))),
% 6.63/6.86 inference(monotonicity,[status(thm)],[90])).
% 6.63/6.86 tff(92,plain,
% 6.63/6.86 (((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | ((~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(B!10, A!11)))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(B!10, A!11)))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))))),
% 6.63/6.86 inference(rewrite,[status(thm)],[])).
% 6.63/6.86 tff(93,plain,
% 6.63/6.86 ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | ((~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(B!10, A!11)))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))))),
% 6.63/6.87 inference(quant_inst,[status(thm)],[])).
% 6.63/6.87 tff(94,plain,
% 6.63/6.87 ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(B!10, A!11)))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))),
% 6.63/6.87 inference(modus_ponens,[status(thm)],[93, 92])).
% 6.63/6.87 tff(95,plain,
% 6.63/6.87 ((~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(B!10, A!11)))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[94, 34])).
% 6.63/6.87 tff(96,plain,
% 6.63/6.87 (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(B!10, A!11)))),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[95, 85])).
% 6.63/6.87 tff(97,plain,
% 6.63/6.87 (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10)))),
% 6.63/6.87 inference(modus_ponens,[status(thm)],[96, 91])).
% 6.63/6.87 tff(98,plain,
% 6.63/6.87 ((in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) | (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))),
% 6.63/6.87 inference(tautology,[status(thm)],[])).
% 6.63/6.87 tff(99,plain,
% 6.63/6.87 (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[98, 97, 84])).
% 6.63/6.87 tff(100,assumption,(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))), introduced(assumption)).
% 6.63/6.87 tff(101,plain,
% 6.63/6.87 (((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | ((~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))))),
% 6.63/6.87 inference(rewrite,[status(thm)],[])).
% 6.63/6.87 tff(102,plain,
% 6.63/6.87 ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | ((~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))))),
% 6.63/6.87 inference(quant_inst,[status(thm)],[])).
% 6.63/6.87 tff(103,plain,
% 6.63/6.87 ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))),
% 6.63/6.87 inference(modus_ponens,[status(thm)],[102, 101])).
% 6.63/6.87 tff(104,plain,
% 6.63/6.87 ($false),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[103, 34, 100, 85])).
% 6.63/6.87 tff(105,plain,((~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), inference(lemma,lemma(discharge,[]))).
% 6.63/6.87 tff(106,plain,
% 6.63/6.87 (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[105, 85])).
% 6.63/6.87 tff(107,plain,
% 6.63/6.87 ((~(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))),
% 6.63/6.87 inference(tautology,[status(thm)],[])).
% 6.63/6.87 tff(108,plain,
% 6.63/6.87 (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10))),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[107, 106, 99])).
% 6.63/6.87 tff(109,plain,
% 6.63/6.87 (((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | ((~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))))),
% 6.63/6.87 inference(rewrite,[status(thm)],[])).
% 6.63/6.87 tff(110,plain,
% 6.63/6.87 ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | ((~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))))),
% 6.63/6.87 inference(quant_inst,[status(thm)],[])).
% 6.63/6.87 tff(111,plain,
% 6.63/6.87 ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))),
% 6.63/6.87 inference(modus_ponens,[status(thm)],[110, 109])).
% 6.63/6.87 tff(112,plain,
% 6.63/6.87 ($false),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[111, 34, 108, 85])).
% 6.63/6.87 tff(113,plain,((ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))) | (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))))), inference(lemma,lemma(discharge,[]))).
% 6.63/6.87 tff(114,plain,
% 6.63/6.87 (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[113, 84])).
% 6.63/6.87 tff(115,plain,
% 6.63/6.87 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10)))),
% 6.63/6.87 inference(monotonicity,[status(thm)],[114])).
% 6.63/6.87 tff(116,plain,
% 6.63/6.87 (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(A!11, B!10)))),
% 6.63/6.87 inference(symmetry,[status(thm)],[115])).
% 6.63/6.87 tff(117,plain,
% 6.63/6.87 (set_union2(B!10, A!11) = set_union2(A!11, B!10)),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[9, 8])).
% 6.63/6.87 tff(118,assumption,((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))))), introduced(assumption)).
% 6.63/6.87 tff(119,plain,
% 6.63/6.87 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))))))))),
% 6.63/6.87 inference(rewrite,[status(thm)],[])).
% 6.63/6.87 tff(120,plain,
% 6.63/6.87 ((~((~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))))) | (~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))))) <=> (~((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))))))),
% 6.63/6.87 inference(rewrite,[status(thm)],[])).
% 6.63/6.87 tff(121,plain,
% 6.63/6.87 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))))) | (~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))))))))),
% 6.63/6.87 inference(monotonicity,[status(thm)],[120])).
% 6.63/6.87 tff(122,plain,
% 6.63/6.87 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))))) | (~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))))))))),
% 6.63/6.87 inference(transitivity,[status(thm)],[121, 119])).
% 6.63/6.87 tff(123,plain,
% 6.63/6.87 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))))) | (~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11))))))))),
% 6.63/6.87 inference(quant_inst,[status(thm)],[])).
% 6.63/6.87 tff(124,plain,
% 6.63/6.87 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))))))),
% 6.63/6.87 inference(modus_ponens,[status(thm)],[123, 122])).
% 6.63/6.87 tff(125,plain,
% 6.63/6.87 ($false),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[124, 60, 118])).
% 6.63/6.87 tff(126,plain,(~((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))))))), inference(lemma,lemma(discharge,[]))).
% 6.63/6.87 tff(127,plain,
% 6.63/6.87 (((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))))) | ((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))))),
% 6.63/6.87 inference(tautology,[status(thm)],[])).
% 6.63/6.87 tff(128,plain,
% 6.63/6.87 ((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[127, 126])).
% 6.63/6.88 tff(129,plain,
% 6.63/6.88 ((~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))))) | (~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))),
% 6.63/6.88 inference(tautology,[status(thm)],[])).
% 6.63/6.88 tff(130,plain,
% 6.63/6.88 ((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[129, 128])).
% 6.63/6.88 tff(131,plain,
% 6.63/6.88 (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[130, 117])).
% 6.63/6.88 tff(132,plain,
% 6.63/6.88 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(B!10, A!11)))))),
% 6.63/6.88 inference(quant_inst,[status(thm)],[])).
% 6.63/6.88 tff(133,plain,
% 6.63/6.88 (~(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(B!10, A!11))))),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[132, 24])).
% 6.63/6.88 tff(134,assumption,(~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10)))), introduced(assumption)).
% 6.63/6.88 tff(135,assumption,(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), introduced(assumption)).
% 6.63/6.88 tff(136,plain,
% 6.63/6.88 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(B!10, A!11))) <=> in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10)))),
% 6.63/6.88 inference(monotonicity,[status(thm)],[135, 89])).
% 6.63/6.88 tff(137,plain,
% 6.63/6.88 (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(B!10, A!11)))),
% 6.63/6.88 inference(symmetry,[status(thm)],[136])).
% 6.63/6.88 tff(138,plain,
% 6.63/6.88 ((~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10)))) <=> (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(B!10, A!11))))),
% 6.63/6.88 inference(monotonicity,[status(thm)],[137])).
% 6.63/6.88 tff(139,plain,
% 6.63/6.88 (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(B!10, A!11)))),
% 6.63/6.88 inference(modus_ponens,[status(thm)],[134, 138])).
% 6.63/6.88 tff(140,assumption,(in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(B!10, A!11)))), introduced(assumption)).
% 6.63/6.88 tff(141,plain,
% 6.63/6.88 ($false),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[140, 139])).
% 6.63/6.88 tff(142,plain,((~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(B!10, A!11)))) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) | (~(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))))), inference(lemma,lemma(discharge,[]))).
% 6.63/6.88 tff(143,plain,
% 6.63/6.88 (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(B!10, A!11)))),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[142, 114, 134])).
% 6.63/6.88 tff(144,plain,
% 6.63/6.88 ((((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(B!10, A!11)))) | ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(B!10, A!11)))),
% 6.63/6.88 inference(tautology,[status(thm)],[])).
% 6.63/6.88 tff(145,plain,
% 6.63/6.88 ((((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(B!10, A!11)))) | ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11))))),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[144, 143])).
% 6.63/6.88 tff(146,plain,
% 6.63/6.88 ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)))),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[145, 133])).
% 6.63/6.88 tff(147,plain,
% 6.63/6.88 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10))))),
% 6.63/6.88 inference(quant_inst,[status(thm)],[])).
% 6.63/6.88 tff(148,plain,
% 6.63/6.88 (~(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10)))),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[147, 24])).
% 6.63/6.88 tff(149,plain,
% 6.63/6.88 (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[98, 84, 134])).
% 6.63/6.88 tff(150,plain,
% 6.63/6.88 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, A!11)) <=> in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))),
% 6.63/6.88 inference(monotonicity,[status(thm)],[114])).
% 6.63/6.88 tff(151,plain,
% 6.63/6.88 ((~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, A!11))) <=> (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))),
% 6.63/6.88 inference(monotonicity,[status(thm)],[150])).
% 6.63/6.88 tff(152,plain,
% 6.63/6.88 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, A!11))))),
% 6.63/6.88 inference(quant_inst,[status(thm)],[])).
% 6.63/6.88 tff(153,plain,
% 6.63/6.88 (~(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, A!11)))),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[152, 24])).
% 6.63/6.88 tff(154,assumption,((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)))), introduced(assumption)).
% 6.63/6.88 tff(155,assumption,(~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11)))), introduced(assumption)).
% 6.63/6.88 tff(156,plain,
% 6.63/6.88 (((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)),
% 6.63/6.88 inference(tautology,[status(thm)],[])).
% 6.63/6.88 tff(157,plain,
% 6.63/6.88 (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[156, 155])).
% 6.63/6.88 tff(158,plain,
% 6.63/6.88 ((~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11))))) | (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)))),
% 6.63/6.88 inference(tautology,[status(thm)],[])).
% 6.63/6.88 tff(159,plain,
% 6.63/6.88 (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11))),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[158, 157, 154])).
% 6.63/6.88 tff(160,plain,
% 6.63/6.88 (((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11)),
% 6.63/6.88 inference(tautology,[status(thm)],[])).
% 6.63/6.88 tff(161,plain,
% 6.63/6.88 (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11)),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[160, 155])).
% 6.63/6.88 tff(162,plain,
% 6.63/6.88 ((in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))),
% 6.63/6.88 inference(tautology,[status(thm)],[])).
% 6.63/6.88 tff(163,plain,
% 6.63/6.88 (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[162, 161])).
% 6.63/6.88 tff(164,plain,
% 6.63/6.88 ((~(in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) | (~(in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))),
% 6.63/6.88 inference(tautology,[status(thm)],[])).
% 6.63/6.88 tff(165,plain,
% 6.63/6.88 ($false),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[164, 163, 159, 131])).
% 6.63/6.88 tff(166,plain,(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))) | (~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)))))), inference(lemma,lemma(discharge,[]))).
% 6.63/6.88 tff(167,plain,
% 6.63/6.88 ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))),
% 6.63/6.88 inference(unit_resolution,[status(thm)],[166, 146])).
% 6.63/6.88 tff(168,plain,
% 6.63/6.88 ((((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, A!11))) | (~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11)))) | (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, A!11)))),
% 6.63/6.88 inference(tautology,[status(thm)],[])).
% 6.63/6.88 tff(169,plain,
% 6.63/6.88 (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, A!11))),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[168, 167, 153])).
% 6.63/6.89 tff(170,plain,
% 6.63/6.89 (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))),
% 6.63/6.89 inference(modus_ponens,[status(thm)],[169, 151])).
% 6.63/6.89 tff(171,plain,
% 6.63/6.89 (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10))),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[107, 170, 149])).
% 6.63/6.89 tff(172,plain,
% 6.63/6.89 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10)) <=> in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10))),
% 6.63/6.89 inference(monotonicity,[status(thm)],[135])).
% 6.63/6.89 tff(173,plain,
% 6.63/6.89 (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10))),
% 6.63/6.89 inference(symmetry,[status(thm)],[172])).
% 6.63/6.89 tff(174,assumption,(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10))), introduced(assumption)).
% 6.63/6.89 tff(175,plain,
% 6.63/6.89 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10))),
% 6.63/6.89 inference(modus_ponens,[status(thm)],[174, 173])).
% 6.63/6.89 tff(176,assumption,(~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10))), introduced(assumption)).
% 6.63/6.89 tff(177,plain,
% 6.63/6.89 ($false),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[176, 175])).
% 6.63/6.89 tff(178,plain,(in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10)) | (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10))) | (~(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))) = tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))))), inference(lemma,lemma(discharge,[]))).
% 6.63/6.89 tff(179,plain,
% 6.63/6.89 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10))),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[178, 171, 114])).
% 6.63/6.89 tff(180,plain,
% 6.63/6.89 ((((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10))) | (~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))) | (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10)))),
% 6.63/6.89 inference(tautology,[status(thm)],[])).
% 6.63/6.89 tff(181,plain,
% 6.63/6.89 (~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[180, 179, 148])).
% 6.63/6.89 tff(182,plain,
% 6.63/6.89 (((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)),
% 6.63/6.89 inference(tautology,[status(thm)],[])).
% 6.63/6.89 tff(183,plain,
% 6.63/6.89 (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[182, 181])).
% 6.63/6.89 tff(184,plain,
% 6.63/6.89 (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11))),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[158, 183, 146])).
% 6.63/6.89 tff(185,plain,
% 6.63/6.89 (((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)),
% 6.63/6.89 inference(tautology,[status(thm)],[])).
% 6.63/6.89 tff(186,plain,
% 6.63/6.89 (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[185, 181])).
% 6.63/6.89 tff(187,plain,
% 6.63/6.89 ((in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))),
% 6.63/6.89 inference(tautology,[status(thm)],[])).
% 6.63/6.89 tff(188,plain,
% 6.63/6.89 (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[187, 186])).
% 6.63/6.89 tff(189,plain,
% 6.63/6.89 ($false),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[164, 188, 184, 131])).
% 6.63/6.89 tff(190,plain,((in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10)))), inference(lemma,lemma(discharge,[]))).
% 6.63/6.89 tff(191,plain,
% 6.63/6.89 (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10)))),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[190, 84])).
% 6.63/6.89 tff(192,plain,
% 6.63/6.89 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(A!11, B!10)))),
% 6.63/6.89 inference(modus_ponens,[status(thm)],[191, 116])).
% 6.63/6.89 tff(193,plain,
% 6.63/6.89 ((((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(A!11, B!10)))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(A!11, B!10)))) | (~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(A!11, B!10))))) | (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, set_union2(A!11, B!10))))),
% 6.63/6.89 inference(tautology,[status(thm)],[])).
% 6.63/6.89 tff(194,plain,
% 6.63/6.89 (~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(A!11, B!10))))),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[193, 192, 83])).
% 6.63/6.89 tff(195,plain,
% 6.63/6.89 (((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(A!11, B!10)))) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(A!11, B!10))),
% 6.63/6.89 inference(tautology,[status(thm)],[])).
% 6.63/6.89 tff(196,plain,
% 6.63/6.89 (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(A!11, B!10))),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[195, 194])).
% 6.63/6.89 tff(197,plain,
% 6.63/6.89 (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11))),
% 6.63/6.89 inference(modus_ponens,[status(thm)],[196, 81])).
% 6.63/6.89 tff(198,plain,
% 6.63/6.89 (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, A!11))),
% 6.63/6.89 inference(symmetry,[status(thm)],[150])).
% 6.63/6.89 tff(199,plain,
% 6.63/6.89 ((~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))) <=> (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, A!11)))),
% 6.63/6.89 inference(monotonicity,[status(thm)],[198])).
% 6.63/6.89 tff(200,plain,
% 6.63/6.89 ((in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))) | (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10)))) | (~(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))))),
% 6.63/6.89 inference(tautology,[status(thm)],[])).
% 6.63/6.89 tff(201,plain,
% 6.63/6.89 (~(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[200, 191, 84])).
% 6.63/6.89 tff(202,plain,
% 6.63/6.89 ((in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))) | (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))),
% 6.63/6.89 inference(tautology,[status(thm)],[])).
% 6.63/6.89 tff(203,plain,
% 6.63/6.89 (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[202, 201])).
% 6.63/6.89 tff(204,plain,
% 6.63/6.89 (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, A!11))),
% 6.63/6.89 inference(modus_ponens,[status(thm)],[203, 199])).
% 6.63/6.89 tff(205,plain,
% 6.63/6.89 ((((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, A!11))) | ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, A!11))),
% 6.63/6.89 inference(tautology,[status(thm)],[])).
% 6.63/6.89 tff(206,plain,
% 6.63/6.89 ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[205, 204, 153])).
% 6.63/6.89 tff(207,plain,
% 6.63/6.89 (((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(A!11, B!10)))) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)),
% 6.63/6.89 inference(tautology,[status(thm)],[])).
% 6.63/6.89 tff(208,plain,
% 6.63/6.89 (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[207, 194])).
% 6.63/6.89 tff(209,plain,
% 6.63/6.89 ((~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11)))) | (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11))),
% 6.63/6.89 inference(tautology,[status(thm)],[])).
% 6.63/6.89 tff(210,plain,
% 6.63/6.89 (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11)),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[209, 208, 206])).
% 6.63/6.89 tff(211,plain,
% 6.63/6.89 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10)) <=> in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10))),
% 6.63/6.89 inference(monotonicity,[status(thm)],[114])).
% 6.63/6.89 tff(212,plain,
% 6.63/6.89 (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10))),
% 6.63/6.89 inference(symmetry,[status(thm)],[211])).
% 6.63/6.89 tff(213,plain,
% 6.63/6.89 ((~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10))) <=> (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10)))),
% 6.63/6.89 inference(monotonicity,[status(thm)],[212])).
% 6.63/6.89 tff(214,plain,
% 6.63/6.89 ((in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))) | (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)))),
% 6.63/6.89 inference(tautology,[status(thm)],[])).
% 6.63/6.89 tff(215,plain,
% 6.63/6.89 (~in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10))),
% 6.63/6.89 inference(unit_resolution,[status(thm)],[214, 201])).
% 6.63/6.89 tff(216,plain,
% 6.63/6.89 (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10))),
% 6.63/6.89 inference(modus_ponens,[status(thm)],[215, 213])).
% 6.63/6.89 tff(217,plain,
% 6.63/6.89 ((((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10))) | ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10))),
% 6.63/6.89 inference(tautology,[status(thm)],[])).
% 6.63/6.89 tff(218,plain,
% 6.63/6.89 ((((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)))), cartesian_product2(C!9, B!10))) | ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[217, 216])).
% 6.72/6.90 tff(219,plain,
% 6.72/6.90 ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[218, 148])).
% 6.72/6.90 tff(220,plain,
% 6.72/6.90 ((~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))) | (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), C!9)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))),
% 6.72/6.90 inference(tautology,[status(thm)],[])).
% 6.72/6.90 tff(221,plain,
% 6.72/6.90 (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[220, 208, 219])).
% 6.72/6.90 tff(222,plain,
% 6.72/6.90 ((~(in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)),
% 6.72/6.90 inference(tautology,[status(thm)],[])).
% 6.72/6.90 tff(223,plain,
% 6.72/6.90 (~(in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[222, 221, 210])).
% 6.72/6.90 tff(224,plain,
% 6.72/6.90 (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[130, 11])).
% 6.72/6.90 tff(225,plain,
% 6.72/6.90 ((~(in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11)) <=> (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10)))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))),
% 6.72/6.90 inference(tautology,[status(thm)],[])).
% 6.72/6.90 tff(226,plain,
% 6.72/6.90 ((~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11))) | (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), A!11) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), B!10))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[225, 224])).
% 6.72/6.90 tff(227,plain,
% 6.72/6.90 (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11))), set_union2(B!10, A!11))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[226, 223])).
% 6.72/6.90 tff(228,plain,
% 6.72/6.90 ($false),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[227, 197])).
% 6.72/6.90 tff(229,plain,(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))), inference(lemma,lemma(discharge,[]))).
% 6.72/6.90 tff(230,assumption,((~((~(cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10)))) | (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))))) | (~((cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))) | (~(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))))))), introduced(assumption)).
% 6.72/6.90 tff(231,plain,
% 6.72/6.90 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10)))) | (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))))) | (~((cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))) | (~(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))))))))),
% 6.72/6.90 inference(quant_inst,[status(thm)],[])).
% 6.72/6.90 tff(232,plain,
% 6.72/6.90 ($false),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[231, 60, 230])).
% 6.72/6.90 tff(233,plain,(~((~((~(cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10)))) | (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))))) | (~((cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))) | (~(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))))))))), inference(lemma,lemma(discharge,[]))).
% 6.72/6.90 tff(234,plain,
% 6.72/6.90 (((~((~(cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10)))) | (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))))) | (~((cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))) | (~(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))))))) | ((cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))) | (~(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))))))),
% 6.72/6.90 inference(tautology,[status(thm)],[])).
% 6.72/6.90 tff(235,plain,
% 6.72/6.90 ((cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))) | (~(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[234, 233])).
% 6.72/6.90 tff(236,plain,
% 6.72/6.90 ((~((cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))) | (~(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11))))))) | (cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))) | (~(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))))),
% 6.72/6.90 inference(tautology,[status(thm)],[])).
% 6.72/6.90 tff(237,plain,
% 6.72/6.90 ((cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))) | (~(in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, set_union2(A!11, B!10))) <=> (in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, B!10)) | in(tptp_fun_D_0(cartesian_product2(C!9, set_union2(A!11, B!10)), cartesian_product2(C!9, B!10), cartesian_product2(C!9, A!11)), cartesian_product2(C!9, A!11)))))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[236, 235])).
% 6.72/6.90 tff(238,plain,
% 6.72/6.90 (cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[237, 229])).
% 6.72/6.90 tff(239,plain,
% 6.72/6.90 ((~(~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (~(cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))))))) <=> ((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (~(cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10)))))),
% 6.72/6.90 inference(rewrite,[status(thm)],[])).
% 6.72/6.90 tff(240,plain,
% 6.72/6.90 (((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) & (cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10)))) <=> (~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (~(cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))))))),
% 6.72/6.90 inference(rewrite,[status(thm)],[])).
% 6.72/6.90 tff(241,plain,
% 6.72/6.90 ((~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) & (cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))))) <=> (~(~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (~(cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10)))))))),
% 6.72/6.90 inference(monotonicity,[status(thm)],[240])).
% 6.72/6.90 tff(242,plain,
% 6.72/6.90 ((~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) & (cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))))) <=> ((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (~(cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10)))))),
% 6.72/6.90 inference(transitivity,[status(thm)],[241, 239])).
% 6.72/6.90 tff(243,plain,
% 6.72/6.90 ((~![A: $i, B: $i, C: $i] : ((cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C))) & (cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))) <=> (~![A: $i, B: $i, C: $i] : ((cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C))) & (cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B)))))),
% 6.72/6.90 inference(rewrite,[status(thm)],[])).
% 6.72/6.90 tff(244,axiom,(~![A: $i, B: $i, C: $i] : ((cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C))) & (cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t120_zfmisc_1')).
% 6.72/6.90 tff(245,plain,
% 6.72/6.90 (~![A: $i, B: $i, C: $i] : ((cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C))) & (cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 6.72/6.90 inference(modus_ponens,[status(thm)],[244, 243])).
% 6.72/6.90 tff(246,plain,
% 6.72/6.90 (~![A: $i, B: $i, C: $i] : ((cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C))) & (cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 6.72/6.90 inference(modus_ponens,[status(thm)],[245, 243])).
% 6.72/6.90 tff(247,plain,
% 6.72/6.90 (~![A: $i, B: $i, C: $i] : ((cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C))) & (cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 6.72/6.90 inference(modus_ponens,[status(thm)],[246, 243])).
% 6.72/6.90 tff(248,plain,
% 6.72/6.90 (~![A: $i, B: $i, C: $i] : ((cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C))) & (cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 6.72/6.90 inference(modus_ponens,[status(thm)],[247, 243])).
% 6.72/6.90 tff(249,plain,(
% 6.72/6.90 ~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) & (cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))))),
% 6.72/6.90 inference(skolemize,[status(sab)],[248])).
% 6.72/6.90 tff(250,plain,
% 6.72/6.90 ((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) | (~(cartesian_product2(C!9, set_union2(A!11, B!10)) = set_union2(cartesian_product2(C!9, A!11), cartesian_product2(C!9, B!10))))),
% 6.72/6.90 inference(modus_ponens,[status(thm)],[249, 242])).
% 6.72/6.90 tff(251,plain,
% 6.72/6.90 (~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[250, 238])).
% 6.72/6.90 tff(252,plain,
% 6.72/6.90 ((~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9))))))) | (cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))),
% 6.72/6.90 inference(tautology,[status(thm)],[])).
% 6.72/6.90 tff(253,plain,
% 6.72/6.90 ((~((cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9))))))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[252, 251])).
% 6.72/6.90 tff(254,plain,
% 6.72/6.90 (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9))))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[253, 80])).
% 6.72/6.90 tff(255,plain,
% 6.72/6.90 ((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9))))),
% 6.72/6.90 inference(tautology,[status(thm)],[])).
% 6.72/6.90 tff(256,plain,
% 6.72/6.90 ((~((~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)), cartesian_product2(B!10, C!9)))))) | (~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[255, 254])).
% 6.72/6.90 tff(257,plain,
% 6.72/6.90 (~(cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[256, 71])).
% 6.72/6.90 tff(258,plain,
% 6.72/6.90 ((~((~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))) | (cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9))))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))) | (cartesian_product2(set_union2(A!11, B!10), C!9) = set_union2(cartesian_product2(B!10, C!9), cartesian_product2(A!11, C!9)))),
% 6.72/6.90 inference(tautology,[status(thm)],[])).
% 6.72/6.90 tff(259,plain,
% 6.72/6.90 (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))),
% 6.72/6.90 inference(unit_resolution,[status(thm)],[258, 257, 69])).
% 6.72/6.90 tff(260,plain,
% 6.72/6.90 ((in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9)))) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9)))),
% 6.72/6.91 inference(tautology,[status(thm)],[])).
% 6.72/6.91 tff(261,plain,
% 6.72/6.91 (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) | (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9)))),
% 6.72/6.91 inference(unit_resolution,[status(thm)],[260, 259])).
% 6.72/6.91 tff(262,plain,
% 6.72/6.91 (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))),
% 6.72/6.91 inference(unit_resolution,[status(thm)],[261, 39])).
% 6.72/6.91 tff(263,assumption,(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))), introduced(assumption)).
% 6.72/6.91 tff(264,plain,
% 6.72/6.91 (((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | ((~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))))),
% 6.72/6.91 inference(rewrite,[status(thm)],[])).
% 6.72/6.91 tff(265,plain,
% 6.72/6.91 ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | ((~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))))),
% 6.72/6.91 inference(quant_inst,[status(thm)],[])).
% 6.72/6.91 tff(266,plain,
% 6.72/6.91 ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))),
% 6.72/6.91 inference(modus_ponens,[status(thm)],[265, 264])).
% 6.72/6.91 tff(267,plain,
% 6.72/6.91 ($false),
% 6.72/6.91 inference(unit_resolution,[status(thm)],[266, 34, 27, 263])).
% 6.72/6.91 tff(268,plain,((~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), inference(lemma,lemma(discharge,[]))).
% 6.72/6.91 tff(269,plain,
% 6.72/6.91 (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))),
% 6.72/6.91 inference(unit_resolution,[status(thm)],[268, 27])).
% 6.72/6.91 tff(270,plain,
% 6.72/6.91 ((~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9)))) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))),
% 6.72/6.91 inference(tautology,[status(thm)],[])).
% 6.72/6.91 tff(271,plain,
% 6.72/6.91 (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9))),
% 6.72/6.91 inference(unit_resolution,[status(thm)],[270, 269, 262])).
% 6.72/6.91 tff(272,plain,
% 6.72/6.91 (((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | ((~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))))),
% 6.72/6.91 inference(rewrite,[status(thm)],[])).
% 6.72/6.91 tff(273,plain,
% 6.72/6.91 ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | ((~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))))),
% 6.72/6.91 inference(quant_inst,[status(thm)],[])).
% 6.72/6.91 tff(274,plain,
% 6.72/6.91 ((~![A: $i, B: $i, C: $i] : ((~in(A, cartesian_product2(B, C))) | (ordered_pair(tptp_fun_D_4(A), tptp_fun_E_3(A)) = A))) | (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9))) | (ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))),
% 6.72/6.91 inference(modus_ponens,[status(thm)],[273, 272])).
% 6.72/6.91 tff(275,plain,
% 6.72/6.91 ($false),
% 6.72/6.91 inference(unit_resolution,[status(thm)],[274, 34, 27, 271])).
% 6.72/6.91 tff(276,plain,(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))) = tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), inference(lemma,lemma(discharge,[]))).
% 6.72/6.91 tff(277,plain,
% 6.72/6.91 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9))),
% 6.72/6.91 inference(monotonicity,[status(thm)],[276])).
% 6.72/6.91 tff(278,plain,
% 6.72/6.91 (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(set_union2(A!11, B!10), C!9))),
% 6.72/6.91 inference(symmetry,[status(thm)],[277])).
% 6.72/6.91 tff(279,plain,
% 6.72/6.91 ((~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9))) <=> (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(set_union2(A!11, B!10), C!9)))),
% 6.72/6.91 inference(monotonicity,[status(thm)],[278])).
% 6.72/6.91 tff(280,assumption,(~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9)))), introduced(assumption)).
% 6.72/6.91 tff(281,plain,
% 6.72/6.91 (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9))),
% 6.72/6.91 inference(unit_resolution,[status(thm)],[261, 280])).
% 6.72/6.91 tff(282,plain,
% 6.72/6.91 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(set_union2(A!11, B!10), C!9))),
% 6.72/6.91 inference(modus_ponens,[status(thm)],[281, 278])).
% 6.72/6.91 tff(283,plain,
% 6.72/6.91 ((((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(set_union2(A!11, B!10), C!9))) | (~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)))) | (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(set_union2(A!11, B!10), C!9)))),
% 6.72/6.91 inference(tautology,[status(thm)],[])).
% 6.72/6.91 tff(284,plain,
% 6.72/6.91 (~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)))),
% 6.72/6.91 inference(unit_resolution,[status(thm)],[283, 282, 26])).
% 6.72/6.91 tff(285,plain,
% 6.72/6.91 ((in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))) | (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9)))),
% 6.72/6.91 inference(tautology,[status(thm)],[])).
% 6.72/6.91 tff(286,plain,
% 6.72/6.91 (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))),
% 6.72/6.91 inference(unit_resolution,[status(thm)],[285, 263])).
% 6.72/6.91 tff(287,plain,
% 6.72/6.91 ((in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9)) <=> (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9)))) | (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))),
% 6.72/6.91 inference(tautology,[status(thm)],[])).
% 6.72/6.91 tff(288,plain,
% 6.72/6.91 ((~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9))) | (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))))),
% 6.72/6.91 inference(unit_resolution,[status(thm)],[287, 259])).
% 6.72/6.91 tff(289,plain,
% 6.72/6.91 (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9))),
% 6.72/6.91 inference(unit_resolution,[status(thm)],[288, 286])).
% 6.72/6.91 tff(290,plain,
% 6.72/6.91 (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(set_union2(A!11, B!10), C!9))),
% 6.72/6.91 inference(modus_ponens,[status(thm)],[289, 279])).
% 6.72/6.91 tff(291,plain,
% 6.72/6.91 ((((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(set_union2(A!11, B!10), C!9))) | ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(set_union2(A!11, B!10), C!9))),
% 6.72/6.91 inference(tautology,[status(thm)],[])).
% 6.72/6.91 tff(292,plain,
% 6.72/6.91 ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))),
% 6.72/6.91 inference(unit_resolution,[status(thm)],[291, 290, 26])).
% 6.72/6.91 tff(293,plain,
% 6.72/6.91 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(B!10, C!9))))),
% 6.72/6.91 inference(quant_inst,[status(thm)],[])).
% 6.72/6.91 tff(294,plain,
% 6.72/6.91 (~(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(B!10, C!9)))),
% 6.72/6.91 inference(unit_resolution,[status(thm)],[293, 24])).
% 6.72/6.91 tff(295,plain,
% 6.72/6.91 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(B!10, C!9)) <=> in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))),
% 6.72/6.91 inference(monotonicity,[status(thm)],[276])).
% 6.72/6.91 tff(296,plain,
% 6.72/6.91 (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9)) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(B!10, C!9))),
% 6.72/6.91 inference(symmetry,[status(thm)],[295])).
% 6.72/6.91 tff(297,plain,
% 6.72/6.91 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(B!10, C!9))),
% 6.72/6.91 inference(modus_ponens,[status(thm)],[263, 296])).
% 6.72/6.91 tff(298,plain,
% 6.72/6.91 ((((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)))) | (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(B!10, C!9)))),
% 6.72/6.92 inference(tautology,[status(thm)],[])).
% 6.72/6.92 tff(299,plain,
% 6.72/6.92 (~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)))),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[298, 297, 294])).
% 6.72/6.92 tff(300,plain,
% 6.72/6.92 (((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)),
% 6.72/6.92 inference(tautology,[status(thm)],[])).
% 6.72/6.92 tff(301,plain,
% 6.72/6.92 (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[300, 299])).
% 6.72/6.92 tff(302,plain,
% 6.72/6.92 ((~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)))) | (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))),
% 6.72/6.92 inference(tautology,[status(thm)],[])).
% 6.72/6.92 tff(303,plain,
% 6.72/6.92 (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[302, 301, 292])).
% 6.72/6.92 tff(304,plain,
% 6.72/6.92 (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11))),
% 6.72/6.92 inference(modus_ponens,[status(thm)],[303, 14])).
% 6.72/6.92 tff(305,plain,
% 6.72/6.92 (((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)),
% 6.72/6.92 inference(tautology,[status(thm)],[])).
% 6.72/6.92 tff(306,plain,
% 6.72/6.92 (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[305, 299])).
% 6.72/6.92 tff(307,plain,
% 6.72/6.92 ((in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)) | (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10))),
% 6.72/6.92 inference(tautology,[status(thm)],[])).
% 6.72/6.92 tff(308,plain,
% 6.72/6.92 (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[307, 306])).
% 6.72/6.92 tff(309,assumption,((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)))))), introduced(assumption)).
% 6.72/6.92 tff(310,plain,
% 6.72/6.92 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10))))))))),
% 6.72/6.92 inference(rewrite,[status(thm)],[])).
% 6.72/6.92 tff(311,plain,
% 6.72/6.92 ((~((~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11))))) | (~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))))) <=> (~((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)))))))),
% 6.72/6.92 inference(rewrite,[status(thm)],[])).
% 6.72/6.92 tff(312,plain,
% 6.72/6.92 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11))))) | (~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10))))))))),
% 6.72/6.92 inference(monotonicity,[status(thm)],[311])).
% 6.72/6.92 tff(313,plain,
% 6.72/6.92 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11))))) | (~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10))))))))),
% 6.72/6.92 inference(transitivity,[status(thm)],[312, 310])).
% 6.72/6.92 tff(314,plain,
% 6.72/6.92 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11))))) | (~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11))))))))),
% 6.72/6.92 inference(quant_inst,[status(thm)],[])).
% 6.72/6.92 tff(315,plain,
% 6.72/6.92 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)))))))),
% 6.72/6.92 inference(modus_ponens,[status(thm)],[314, 313])).
% 6.72/6.92 tff(316,plain,
% 6.72/6.92 ($false),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[315, 60, 309])).
% 6.72/6.92 tff(317,plain,(~((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10))))))), inference(lemma,lemma(discharge,[]))).
% 6.72/6.92 tff(318,plain,
% 6.72/6.92 (((~((set_union2(B!10, A!11) = set_union2(A!11, B!10)) | (~(in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), B!10) | in(tptp_fun_D_0(set_union2(B!10, A!11), B!10, A!11), A!11)))))) | (~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)))))) | ((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10))))),
% 6.72/6.92 inference(tautology,[status(thm)],[])).
% 6.72/6.92 tff(319,plain,
% 6.72/6.92 ((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)))),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[318, 317])).
% 6.72/6.92 tff(320,plain,
% 6.72/6.92 ((~((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10))))) | (~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)))),
% 6.72/6.92 inference(tautology,[status(thm)],[])).
% 6.72/6.92 tff(321,plain,
% 6.72/6.92 ((~(set_union2(B!10, A!11) = set_union2(A!11, B!10))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)))),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[320, 319])).
% 6.72/6.92 tff(322,plain,
% 6.72/6.92 (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10))),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[321, 11])).
% 6.72/6.92 tff(323,plain,
% 6.72/6.92 ((~(in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)))) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) | (~(in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)))),
% 6.72/6.92 inference(tautology,[status(thm)],[])).
% 6.72/6.92 tff(324,plain,
% 6.72/6.92 (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) | (~(in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)))),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[323, 322])).
% 6.72/6.92 tff(325,plain,
% 6.72/6.92 (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11))),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[324, 308])).
% 6.72/6.92 tff(326,plain,
% 6.72/6.92 ($false),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[325, 304])).
% 6.72/6.92 tff(327,plain,(~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))), inference(lemma,lemma(discharge,[]))).
% 6.72/6.92 tff(328,plain,
% 6.72/6.92 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(A!11, C!9)) <=> in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9))),
% 6.72/6.92 inference(monotonicity,[status(thm)],[276])).
% 6.72/6.92 tff(329,plain,
% 6.72/6.92 ((~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(A!11, C!9))) <=> (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)))),
% 6.72/6.92 inference(monotonicity,[status(thm)],[328])).
% 6.72/6.92 tff(330,plain,
% 6.72/6.92 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(A!11, C!9))))),
% 6.72/6.92 inference(quant_inst,[status(thm)],[])).
% 6.72/6.92 tff(331,plain,
% 6.72/6.92 (~(((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(A!11, C!9)))),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[330, 24])).
% 6.72/6.92 tff(332,assumption,(~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)), introduced(assumption)).
% 6.72/6.92 tff(333,plain,
% 6.72/6.92 (((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)),
% 6.72/6.92 inference(tautology,[status(thm)],[])).
% 6.72/6.92 tff(334,plain,
% 6.72/6.92 ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[333, 332])).
% 6.72/6.92 tff(335,plain,
% 6.72/6.92 ((((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(A!11, C!9))) | (~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)))) | (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(A!11, C!9)))),
% 6.72/6.92 inference(tautology,[status(thm)],[])).
% 6.72/6.92 tff(336,plain,
% 6.72/6.92 (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(A!11, C!9))),
% 6.72/6.92 inference(unit_resolution,[status(thm)],[335, 334, 331])).
% 6.72/6.92 tff(337,plain,
% 6.72/6.92 (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9))),
% 6.72/6.92 inference(modus_ponens,[status(thm)],[336, 329])).
% 6.72/6.92 tff(338,assumption,(~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))), introduced(assumption)).
% 6.72/6.93 tff(339,plain,
% 6.72/6.93 (~(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9)))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[270, 338, 337])).
% 6.72/6.93 tff(340,plain,
% 6.72/6.93 (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[261, 339])).
% 6.72/6.93 tff(341,plain,
% 6.72/6.93 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(set_union2(A!11, B!10), C!9))),
% 6.72/6.93 inference(modus_ponens,[status(thm)],[340, 278])).
% 6.72/6.93 tff(342,plain,
% 6.72/6.93 (~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[283, 341, 26])).
% 6.72/6.93 tff(343,plain,
% 6.72/6.93 (((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))),
% 6.72/6.93 inference(tautology,[status(thm)],[])).
% 6.72/6.93 tff(344,plain,
% 6.72/6.93 (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[343, 342])).
% 6.72/6.93 tff(345,plain,
% 6.72/6.93 (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11))),
% 6.72/6.93 inference(modus_ponens,[status(thm)],[344, 13])).
% 6.72/6.93 tff(346,plain,
% 6.72/6.93 ((~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))) <=> (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(B!10, C!9)))),
% 6.72/6.93 inference(monotonicity,[status(thm)],[296])).
% 6.72/6.93 tff(347,plain,
% 6.72/6.93 (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(B!10, C!9))),
% 6.72/6.93 inference(modus_ponens,[status(thm)],[338, 346])).
% 6.72/6.93 tff(348,plain,
% 6.72/6.93 ((((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(B!10, C!9))) | ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(B!10, C!9))),
% 6.72/6.93 inference(tautology,[status(thm)],[])).
% 6.72/6.93 tff(349,plain,
% 6.72/6.93 ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[348, 347, 294])).
% 6.72/6.93 tff(350,plain,
% 6.72/6.93 (((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)),
% 6.72/6.93 inference(tautology,[status(thm)],[])).
% 6.72/6.93 tff(351,plain,
% 6.72/6.93 (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[350, 342])).
% 6.72/6.93 tff(352,plain,
% 6.72/6.93 ((~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)))) | (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))),
% 6.72/6.93 inference(tautology,[status(thm)],[])).
% 6.72/6.93 tff(353,plain,
% 6.72/6.93 (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[352, 351, 349])).
% 6.72/6.93 tff(354,plain,
% 6.72/6.93 ((~(in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10))) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)),
% 6.72/6.93 inference(tautology,[status(thm)],[])).
% 6.72/6.93 tff(355,plain,
% 6.72/6.93 (~(in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[354, 353, 332])).
% 6.72/6.93 tff(356,plain,
% 6.72/6.93 ((~(in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11)) <=> (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)))) | (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10))),
% 6.72/6.93 inference(tautology,[status(thm)],[])).
% 6.72/6.93 tff(357,plain,
% 6.72/6.93 ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11))) | (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[356, 322])).
% 6.72/6.93 tff(358,plain,
% 6.72/6.93 (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[357, 355])).
% 6.72/6.93 tff(359,plain,
% 6.72/6.93 ($false),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[358, 345])).
% 6.72/6.93 tff(360,plain,(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9)) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)), inference(lemma,lemma(discharge,[]))).
% 6.72/6.93 tff(361,plain,
% 6.72/6.93 (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[360, 327])).
% 6.72/6.93 tff(362,plain,
% 6.72/6.93 (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(A!11, C!9))),
% 6.72/6.93 inference(symmetry,[status(thm)],[328])).
% 6.72/6.93 tff(363,plain,
% 6.72/6.93 ((~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9))) <=> (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(A!11, C!9)))),
% 6.72/6.93 inference(monotonicity,[status(thm)],[362])).
% 6.72/6.93 tff(364,plain,
% 6.72/6.93 ((in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))) | (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)))),
% 6.72/6.93 inference(tautology,[status(thm)],[])).
% 6.72/6.93 tff(365,plain,
% 6.72/6.93 (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[364, 280])).
% 6.72/6.93 tff(366,plain,
% 6.72/6.93 (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(A!11, C!9))),
% 6.72/6.93 inference(modus_ponens,[status(thm)],[365, 363])).
% 6.72/6.93 tff(367,plain,
% 6.72/6.93 ((((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(A!11, C!9))) | ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(A!11, C!9))),
% 6.72/6.93 inference(tautology,[status(thm)],[])).
% 6.72/6.93 tff(368,plain,
% 6.72/6.93 ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[367, 366, 331])).
% 6.72/6.93 tff(369,plain,
% 6.72/6.93 ((~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)))) | (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))),
% 6.72/6.93 inference(tautology,[status(thm)],[])).
% 6.72/6.93 tff(370,plain,
% 6.72/6.93 (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[369, 368, 361])).
% 6.72/6.93 tff(371,plain,
% 6.72/6.93 ($false),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[350, 370, 284])).
% 6.72/6.93 tff(372,plain,(in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9)) | in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(B!10, C!9))), inference(lemma,lemma(discharge,[]))).
% 6.72/6.93 tff(373,plain,
% 6.72/6.93 (~in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(set_union2(A!11, B!10), C!9))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[288, 372])).
% 6.72/6.93 tff(374,plain,
% 6.72/6.93 (~in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(set_union2(A!11, B!10), C!9))),
% 6.72/6.93 inference(modus_ponens,[status(thm)],[373, 279])).
% 6.72/6.93 tff(375,plain,
% 6.72/6.93 ((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[291, 374, 26])).
% 6.72/6.93 tff(376,plain,
% 6.72/6.93 (in(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)), cartesian_product2(A!11, C!9))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[270, 372, 327])).
% 6.72/6.93 tff(377,plain,
% 6.72/6.93 (in(ordered_pair(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9)))), cartesian_product2(A!11, C!9))),
% 6.72/6.93 inference(modus_ponens,[status(thm)],[376, 362])).
% 6.72/6.93 tff(378,plain,
% 6.72/6.93 (~((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[335, 377, 331])).
% 6.72/6.93 tff(379,plain,
% 6.72/6.93 (((~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11)) | (~in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9))) | in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)),
% 6.72/6.93 inference(tautology,[status(thm)],[])).
% 6.72/6.93 tff(380,plain,
% 6.72/6.93 (in(tptp_fun_E_3(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), C!9)),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[379, 378])).
% 6.72/6.93 tff(381,plain,
% 6.72/6.93 (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(A!11, B!10))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[302, 380, 375])).
% 6.72/6.93 tff(382,plain,
% 6.72/6.93 (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11))),
% 6.72/6.93 inference(modus_ponens,[status(thm)],[381, 14])).
% 6.72/6.93 tff(383,plain,
% 6.72/6.93 ((in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)) | (~in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11))),
% 6.72/6.93 inference(tautology,[status(thm)],[])).
% 6.72/6.93 tff(384,plain,
% 6.72/6.93 (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), A!11) | in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), B!10)),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[383, 361])).
% 6.72/6.93 tff(385,plain,
% 6.72/6.93 (in(tptp_fun_D_4(tptp_fun_D_0(cartesian_product2(set_union2(A!11, B!10), C!9), cartesian_product2(A!11, C!9), cartesian_product2(B!10, C!9))), set_union2(B!10, A!11))),
% 6.72/6.93 inference(unit_resolution,[status(thm)],[324, 384])).
% 6.72/6.94 tff(386,plain,
% 6.72/6.94 ($false),
% 6.72/6.94 inference(unit_resolution,[status(thm)],[385, 382])).
% 6.72/6.94 % SZS output end Proof
% 6.72/6.94 % E exiting
%------------------------------------------------------------------------------