%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU105+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:26:54 AM UTC 2025
% Result : Theorem 3.15s 3.34s
% Output : Proof 3.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU105+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:04:56 EDT 2025
% 0.13/0.36 % CPUTime :
% 3.15/3.34 % SZS status Theorem
% 3.15/3.34 % SZS output start Proof
% 3.15/3.34 tff(in_type, type, (
% 3.15/3.34 in: ( $i * $i ) > $o)).
% 3.15/3.34 tff(tptp_fun_A_11_type, type, (
% 3.15/3.34 tptp_fun_A_11: $i)).
% 3.15/3.34 tff(symmetric_difference_type, type, (
% 3.15/3.34 symmetric_difference: ( $i * $i ) > $i)).
% 3.15/3.34 tff(set_union2_type, type, (
% 3.15/3.34 set_union2: ( $i * $i ) > $i)).
% 3.15/3.34 tff(set_difference_type, type, (
% 3.15/3.34 set_difference: ( $i * $i ) > $i)).
% 3.15/3.34 tff(tptp_fun_B_10_type, type, (
% 3.15/3.34 tptp_fun_B_10: $i > $i)).
% 3.15/3.34 tff(tptp_fun_C_9_type, type, (
% 3.15/3.34 tptp_fun_C_9: $i > $i)).
% 3.15/3.34 tff(set_intersection2_type, type, (
% 3.15/3.34 set_intersection2: ( $i * $i ) > $i)).
% 3.15/3.34 tff(preboolean_type, type, (
% 3.15/3.34 preboolean: $i > $o)).
% 3.15/3.34 tff(element_type, type, (
% 3.15/3.34 element: ( $i * $i ) > $o)).
% 3.15/3.34 tff(empty_type, type, (
% 3.15/3.34 empty: $i > $o)).
% 3.15/3.34 tff(1,plain,
% 3.15/3.34 (^[A: $i, B: $i] : refl((set_union2(A, B) = symmetric_difference(symmetric_difference(A, B), set_intersection2(A, B))) <=> (set_union2(A, B) = symmetric_difference(symmetric_difference(A, B), set_intersection2(A, B))))),
% 3.15/3.34 inference(bind,[status(th)],[])).
% 3.15/3.34 tff(2,plain,
% 3.15/3.34 (![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(symmetric_difference(A, B), set_intersection2(A, B))) <=> ![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(symmetric_difference(A, B), set_intersection2(A, B)))),
% 3.15/3.34 inference(quant_intro,[status(thm)],[1])).
% 3.15/3.34 tff(3,plain,
% 3.15/3.34 (![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(symmetric_difference(A, B), set_intersection2(A, B))) <=> ![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(symmetric_difference(A, B), set_intersection2(A, B)))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(4,axiom,(![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(symmetric_difference(A, B), set_intersection2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t94_xboole_1')).
% 3.15/3.34 tff(5,plain,
% 3.15/3.34 (![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(symmetric_difference(A, B), set_intersection2(A, B)))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.15/3.34 tff(6,plain,(
% 3.15/3.34 ![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(symmetric_difference(A, B), set_intersection2(A, B)))),
% 3.15/3.34 inference(skolemize,[status(sab)],[5])).
% 3.15/3.34 tff(7,plain,
% 3.15/3.34 (![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(symmetric_difference(A, B), set_intersection2(A, B)))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.15/3.34 tff(8,plain,
% 3.15/3.34 ((~![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(symmetric_difference(A, B), set_intersection2(A, B)))) | (set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)) = symmetric_difference(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))))),
% 3.15/3.34 inference(quant_inst,[status(thm)],[])).
% 3.15/3.34 tff(9,plain,
% 3.15/3.34 (set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)) = symmetric_difference(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[8, 7])).
% 3.15/3.34 tff(10,plain,
% 3.15/3.34 (symmetric_difference(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))) = set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))),
% 3.15/3.34 inference(symmetry,[status(thm)],[9])).
% 3.15/3.34 tff(11,plain,
% 3.15/3.34 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 3.15/3.34 inference(bind,[status(th)],[])).
% 3.15/3.34 tff(12,plain,
% 3.15/3.34 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 3.15/3.34 inference(quant_intro,[status(thm)],[11])).
% 3.15/3.34 tff(13,plain,
% 3.15/3.34 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(14,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 3.15/3.34 tff(15,plain,
% 3.15/3.34 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[14, 13])).
% 3.15/3.34 tff(16,plain,(
% 3.15/3.34 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 3.15/3.34 inference(skolemize,[status(sab)],[15])).
% 3.15/3.34 tff(17,plain,
% 3.15/3.34 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[16, 12])).
% 3.15/3.34 tff(18,plain,
% 3.15/3.34 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)) = set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))),
% 3.15/3.34 inference(quant_inst,[status(thm)],[])).
% 3.15/3.34 tff(19,plain,
% 3.15/3.34 (set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)) = set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[18, 17])).
% 3.15/3.34 tff(20,plain,
% 3.15/3.34 (set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)) = set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))),
% 3.15/3.34 inference(symmetry,[status(thm)],[19])).
% 3.15/3.34 tff(21,plain,
% 3.15/3.34 (^[A: $i, B: $i] : refl((symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A))) <=> (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A))))),
% 3.15/3.34 inference(bind,[status(th)],[])).
% 3.15/3.34 tff(22,plain,
% 3.15/3.34 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A))) <=> ![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 3.15/3.34 inference(quant_intro,[status(thm)],[21])).
% 3.15/3.34 tff(23,plain,
% 3.15/3.34 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A))) <=> ![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(24,axiom,(![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_xboole_0')).
% 3.15/3.34 tff(25,plain,
% 3.15/3.34 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[24, 23])).
% 3.15/3.34 tff(26,plain,(
% 3.15/3.34 ![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 3.15/3.34 inference(skolemize,[status(sab)],[25])).
% 3.15/3.34 tff(27,plain,
% 3.15/3.34 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[26, 22])).
% 3.15/3.34 tff(28,plain,
% 3.15/3.34 ((~![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))) | (symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)) = set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))))),
% 3.15/3.34 inference(quant_inst,[status(thm)],[])).
% 3.15/3.34 tff(29,plain,
% 3.15/3.34 (symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)) = set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[28, 27])).
% 3.15/3.34 tff(30,plain,
% 3.15/3.34 (set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))) = symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))),
% 3.15/3.34 inference(symmetry,[status(thm)],[29])).
% 3.15/3.34 tff(31,plain,
% 3.15/3.34 (symmetric_difference(set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))) = symmetric_difference(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)))),
% 3.15/3.34 inference(monotonicity,[status(thm)],[30, 20])).
% 3.15/3.34 tff(32,plain,
% 3.15/3.34 (^[A: $i, B: $i] : refl((symmetric_difference(A, B) = symmetric_difference(B, A)) <=> (symmetric_difference(A, B) = symmetric_difference(B, A)))),
% 3.15/3.34 inference(bind,[status(th)],[])).
% 3.15/3.34 tff(33,plain,
% 3.15/3.34 (![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A)) <=> ![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A))),
% 3.15/3.34 inference(quant_intro,[status(thm)],[32])).
% 3.15/3.34 tff(34,plain,
% 3.15/3.34 (![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A)) <=> ![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(35,axiom,(![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k5_xboole_0')).
% 3.15/3.34 tff(36,plain,
% 3.15/3.34 (![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[35, 34])).
% 3.15/3.34 tff(37,plain,(
% 3.15/3.34 ![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A))),
% 3.15/3.34 inference(skolemize,[status(sab)],[36])).
% 3.15/3.34 tff(38,plain,
% 3.15/3.34 (![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[37, 33])).
% 3.15/3.34 tff(39,plain,
% 3.15/3.34 ((~![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A))) | (symmetric_difference(set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))) = symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))))),
% 3.15/3.34 inference(quant_inst,[status(thm)],[])).
% 3.15/3.34 tff(40,plain,
% 3.15/3.34 (symmetric_difference(set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))) = symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[39, 38])).
% 3.15/3.34 tff(41,plain,
% 3.15/3.34 (symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))) = symmetric_difference(set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))),
% 3.15/3.34 inference(symmetry,[status(thm)],[40])).
% 3.15/3.34 tff(42,plain,
% 3.15/3.34 (symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))) = set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))),
% 3.15/3.34 inference(transitivity,[status(thm)],[41, 31, 10])).
% 3.15/3.34 tff(43,plain,
% 3.15/3.34 (in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11) <=> in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 3.15/3.34 inference(monotonicity,[status(thm)],[42])).
% 3.15/3.34 tff(44,plain,
% 3.15/3.34 (in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11) <=> in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11)),
% 3.15/3.34 inference(symmetry,[status(thm)],[43])).
% 3.15/3.34 tff(45,plain,
% 3.15/3.34 ((~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) <=> (~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11))),
% 3.15/3.34 inference(monotonicity,[status(thm)],[44])).
% 3.15/3.34 tff(46,plain,
% 3.15/3.34 (^[A: $i] : refl((~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))) <=> (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))))),
% 3.15/3.34 inference(bind,[status(th)],[])).
% 3.15/3.34 tff(47,plain,
% 3.15/3.34 (![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))) <=> ![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))),
% 3.15/3.34 inference(quant_intro,[status(thm)],[46])).
% 3.15/3.34 tff(48,plain,
% 3.15/3.34 (^[A: $i] : rewrite((~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))) <=> (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))))),
% 3.15/3.34 inference(bind,[status(th)],[])).
% 3.15/3.34 tff(49,plain,
% 3.15/3.34 (![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))) <=> ![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))),
% 3.15/3.34 inference(quant_intro,[status(thm)],[48])).
% 3.15/3.34 tff(50,plain,
% 3.15/3.34 (![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))) <=> ![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))),
% 3.15/3.34 inference(transitivity,[status(thm)],[49, 47])).
% 3.15/3.34 tff(51,plain,
% 3.15/3.34 (^[A: $i] : trans(monotonicity(rewrite(((~preboolean(A)) | ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) <=> ((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))), rewrite((preboolean(A) | (~((~(in(tptp_fun_B_10(A), A) & in(tptp_fun_C_9(A), A))) | (in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A) & in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))) <=> (preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))), ((((~preboolean(A)) | ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) & (preboolean(A) | (~((~(in(tptp_fun_B_10(A), A) & in(tptp_fun_C_9(A), A))) | (in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A) & in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))) <=> (((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A)))))) & (preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))), rewrite((((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A)))))) & (preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))) <=> (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))), ((((~preboolean(A)) | ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) & (preboolean(A) | (~((~(in(tptp_fun_B_10(A), A) & in(tptp_fun_C_9(A), A))) | (in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A) & in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))) <=> (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))))),
% 3.15/3.34 inference(bind,[status(th)],[])).
% 3.15/3.34 tff(52,plain,
% 3.15/3.34 (![A: $i] : (((~preboolean(A)) | ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) & (preboolean(A) | (~((~(in(tptp_fun_B_10(A), A) & in(tptp_fun_C_9(A), A))) | (in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A) & in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))) <=> ![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))),
% 3.15/3.34 inference(quant_intro,[status(thm)],[51])).
% 3.15/3.34 tff(53,plain,
% 3.15/3.34 (![A: $i] : (preboolean(A) <=> ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) <=> ![A: $i] : (preboolean(A) <=> ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(54,plain,
% 3.15/3.34 (^[A: $i] : rewrite((preboolean(A) <=> ![B: $i, C: $i] : ((in(B, A) & in(C, A)) => (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) <=> (preboolean(A) <=> ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A)))))),
% 3.15/3.34 inference(bind,[status(th)],[])).
% 3.15/3.34 tff(55,plain,
% 3.15/3.34 (![A: $i] : (preboolean(A) <=> ![B: $i, C: $i] : ((in(B, A) & in(C, A)) => (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) <=> ![A: $i] : (preboolean(A) <=> ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A))))),
% 3.15/3.34 inference(quant_intro,[status(thm)],[54])).
% 3.15/3.34 tff(56,axiom,(![A: $i] : (preboolean(A) <=> ![B: $i, C: $i] : ((in(B, A) & in(C, A)) => (in(set_union2(B, C), A) & in(set_difference(B, C), A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t10_finsub_1')).
% 3.15/3.34 tff(57,plain,
% 3.15/3.34 (![A: $i] : (preboolean(A) <=> ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A))))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[56, 55])).
% 3.15/3.34 tff(58,plain,
% 3.15/3.34 (![A: $i] : (preboolean(A) <=> ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A))))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[57, 53])).
% 3.15/3.34 tff(59,plain,(
% 3.15/3.34 ![A: $i] : (((~preboolean(A)) | ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) & (preboolean(A) | (~((~(in(tptp_fun_B_10(A), A) & in(tptp_fun_C_9(A), A))) | (in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A) & in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))),
% 3.15/3.34 inference(skolemize,[status(sab)],[58])).
% 3.15/3.34 tff(60,plain,
% 3.15/3.34 (![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[59, 52])).
% 3.15/3.34 tff(61,plain,
% 3.15/3.34 (![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[60, 50])).
% 3.15/3.34 tff(62,plain,
% 3.15/3.34 (((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))))))) <=> ((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(63,plain,
% 3.15/3.34 ((~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))))) <=> (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(64,plain,
% 3.15/3.34 (((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))))))) <=> ((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))))))),
% 3.15/3.34 inference(monotonicity,[status(thm)],[63])).
% 3.15/3.34 tff(65,plain,
% 3.15/3.34 (((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))))))) <=> ((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))))))),
% 3.15/3.34 inference(transitivity,[status(thm)],[64, 62])).
% 3.15/3.34 tff(66,plain,
% 3.15/3.34 ((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))))))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(67,plain,
% 3.15/3.35 ((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[66, 65])).
% 3.15/3.35 tff(68,plain,
% 3.15/3.35 (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[67, 61])).
% 3.15/3.35 tff(69,plain,
% 3.15/3.35 (((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))))) | (preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))),
% 3.15/3.35 inference(tautology,[status(thm)],[])).
% 3.15/3.35 tff(70,plain,
% 3.15/3.35 (preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[69, 68])).
% 3.15/3.35 tff(71,plain,
% 3.15/3.35 (((~empty(A!11)) & (~preboolean(A!11)) & ![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_intersection2(B, C), A!11))))) <=> ((~empty(A!11)) & (~preboolean(A!11)) & ![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_intersection2(B, C), A!11)))))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(72,plain,
% 3.15/3.35 ((~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_intersection2(B, C), A))))))) <=> (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_intersection2(B, C), A)))))))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(73,plain,
% 3.15/3.35 ((~![A: $i] : ((~empty(A)) => (![B: $i] : (element(B, A) => ![C: $i] : (element(C, A) => (in(symmetric_difference(B, C), A) & in(set_intersection2(B, C), A)))) => preboolean(A)))) <=> (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_intersection2(B, C), A)))))))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(74,axiom,(~![A: $i] : ((~empty(A)) => (![B: $i] : (element(B, A) => ![C: $i] : (element(C, A) => (in(symmetric_difference(B, C), A) & in(set_intersection2(B, C), A)))) => preboolean(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t16_finsub_1')).
% 3.15/3.35 tff(75,plain,
% 3.15/3.35 (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_intersection2(B, C), A))))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[74, 73])).
% 3.15/3.35 tff(76,plain,
% 3.15/3.35 (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_intersection2(B, C), A))))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[75, 72])).
% 3.15/3.35 tff(77,plain,
% 3.15/3.35 (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_intersection2(B, C), A))))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[76, 72])).
% 3.15/3.35 tff(78,plain,
% 3.15/3.35 (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_intersection2(B, C), A))))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[77, 72])).
% 3.15/3.35 tff(79,plain,
% 3.15/3.35 ((~empty(A!11)) & (~preboolean(A!11)) & ![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_intersection2(B, C), A!11))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[78, 71])).
% 3.15/3.35 tff(80,plain,
% 3.15/3.35 (~preboolean(A!11)),
% 3.15/3.35 inference(and_elim,[status(thm)],[79])).
% 3.15/3.35 tff(81,plain,
% 3.15/3.35 ((~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))) | preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))),
% 3.15/3.35 inference(tautology,[status(thm)],[])).
% 3.15/3.35 tff(82,plain,
% 3.15/3.35 ((~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[81, 80])).
% 3.15/3.35 tff(83,plain,
% 3.15/3.35 (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[82, 70])).
% 3.15/3.35 tff(84,plain,
% 3.15/3.35 (((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))) | ((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))),
% 3.15/3.35 inference(tautology,[status(thm)],[])).
% 3.15/3.35 tff(85,plain,
% 3.15/3.35 ((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[84, 83])).
% 3.15/3.35 tff(86,plain,
% 3.15/3.35 (symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))) = symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))),
% 3.15/3.35 inference(monotonicity,[status(thm)],[19])).
% 3.15/3.35 tff(87,plain,
% 3.15/3.35 (^[A: $i, B: $i] : refl((set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B))) <=> (set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B))))),
% 3.15/3.35 inference(bind,[status(th)],[])).
% 3.15/3.35 tff(88,plain,
% 3.15/3.35 (![A: $i, B: $i] : (set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B))) <=> ![A: $i, B: $i] : (set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B)))),
% 3.15/3.35 inference(quant_intro,[status(thm)],[87])).
% 3.15/3.35 tff(89,plain,
% 3.15/3.35 (![A: $i, B: $i] : (set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B))) <=> ![A: $i, B: $i] : (set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B)))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(90,axiom,(![A: $i, B: $i] : (set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t100_xboole_1')).
% 3.15/3.35 tff(91,plain,
% 3.15/3.35 (![A: $i, B: $i] : (set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B)))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[90, 89])).
% 3.15/3.35 tff(92,plain,(
% 3.15/3.35 ![A: $i, B: $i] : (set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B)))),
% 3.15/3.35 inference(skolemize,[status(sab)],[91])).
% 3.15/3.35 tff(93,plain,
% 3.15/3.35 (![A: $i, B: $i] : (set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B)))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[92, 88])).
% 3.15/3.35 tff(94,plain,
% 3.15/3.35 ((~![A: $i, B: $i] : (set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B)))) | (set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)) = symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(95,plain,
% 3.15/3.35 (set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)) = symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[94, 93])).
% 3.15/3.35 tff(96,plain,
% 3.15/3.35 (set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)) = symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))),
% 3.15/3.35 inference(transitivity,[status(thm)],[95, 86])).
% 3.15/3.35 tff(97,plain,
% 3.15/3.35 (in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11) <=> in(symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)),
% 3.15/3.35 inference(monotonicity,[status(thm)],[96])).
% 3.15/3.35 tff(98,plain,
% 3.15/3.35 (in(symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11) <=> in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 3.15/3.35 inference(symmetry,[status(thm)],[97])).
% 3.15/3.35 tff(99,plain,
% 3.15/3.35 (((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))) | in(tptp_fun_C_9(A!11), A!11)),
% 3.15/3.35 inference(tautology,[status(thm)],[])).
% 3.15/3.35 tff(100,plain,
% 3.15/3.35 (in(tptp_fun_C_9(A!11), A!11)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[99, 83])).
% 3.15/3.35 tff(101,plain,
% 3.15/3.35 (^[A: $i, B: $i] : refl(((~in(A, B)) | element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 3.15/3.35 inference(bind,[status(th)],[])).
% 3.15/3.35 tff(102,plain,
% 3.15/3.35 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 3.15/3.35 inference(quant_intro,[status(thm)],[101])).
% 3.15/3.35 tff(103,plain,
% 3.15/3.35 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(104,plain,
% 3.15/3.35 (^[A: $i, B: $i] : rewrite((in(A, B) => element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 3.15/3.35 inference(bind,[status(th)],[])).
% 3.15/3.35 tff(105,plain,
% 3.15/3.35 (![A: $i, B: $i] : (in(A, B) => element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 3.15/3.35 inference(quant_intro,[status(thm)],[104])).
% 3.15/3.35 tff(106,axiom,(![A: $i, B: $i] : (in(A, B) => element(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_subset')).
% 3.15/3.35 tff(107,plain,
% 3.15/3.35 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[106, 105])).
% 3.15/3.35 tff(108,plain,
% 3.15/3.35 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[107, 103])).
% 3.15/3.35 tff(109,plain,(
% 3.15/3.35 ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 3.15/3.35 inference(skolemize,[status(sab)],[108])).
% 3.15/3.35 tff(110,plain,
% 3.15/3.35 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[109, 102])).
% 3.15/3.35 tff(111,plain,
% 3.15/3.35 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_C_9(A!11), A!11)) | element(tptp_fun_C_9(A!11), A!11))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_C_9(A!11), A!11)) | element(tptp_fun_C_9(A!11), A!11))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(112,plain,
% 3.15/3.35 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_C_9(A!11), A!11)) | element(tptp_fun_C_9(A!11), A!11))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(113,plain,
% 3.15/3.35 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_C_9(A!11), A!11)) | element(tptp_fun_C_9(A!11), A!11)),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[112, 111])).
% 3.15/3.35 tff(114,plain,
% 3.15/3.35 (element(tptp_fun_C_9(A!11), A!11)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[113, 110, 100])).
% 3.15/3.35 tff(115,plain,
% 3.15/3.35 (^[B: $i] : refl(((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11)))))) <=> ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11)))))))),
% 3.15/3.35 inference(bind,[status(th)],[])).
% 3.15/3.35 tff(116,plain,
% 3.15/3.35 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11)))))) <=> ![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))),
% 3.15/3.35 inference(quant_intro,[status(thm)],[115])).
% 3.15/3.35 tff(117,plain,
% 3.15/3.35 (^[B: $i] : rewrite(((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11)))))) <=> ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11)))))))),
% 3.15/3.35 inference(bind,[status(th)],[])).
% 3.15/3.35 tff(118,plain,
% 3.15/3.35 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11)))))) <=> ![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))),
% 3.15/3.35 inference(quant_intro,[status(thm)],[117])).
% 3.15/3.35 tff(119,plain,
% 3.15/3.35 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11)))))) <=> ![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))),
% 3.15/3.35 inference(transitivity,[status(thm)],[118, 116])).
% 3.15/3.35 tff(120,plain,
% 3.15/3.35 (^[B: $i] : rewrite(((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_intersection2(B, C), A!11)))) <=> ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11)))))))),
% 3.15/3.35 inference(bind,[status(th)],[])).
% 3.15/3.35 tff(121,plain,
% 3.15/3.35 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_intersection2(B, C), A!11)))) <=> ![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))),
% 3.15/3.35 inference(quant_intro,[status(thm)],[120])).
% 3.15/3.35 tff(122,plain,
% 3.15/3.35 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_intersection2(B, C), A!11))))),
% 3.15/3.35 inference(and_elim,[status(thm)],[79])).
% 3.15/3.35 tff(123,plain,
% 3.15/3.35 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[122, 121])).
% 3.15/3.35 tff(124,plain,
% 3.15/3.35 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[123, 119])).
% 3.15/3.35 tff(125,plain,
% 3.15/3.35 (((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))) | ((~element(tptp_fun_C_9(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), C), A!11))))))) <=> ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))) | (~element(tptp_fun_C_9(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), C), A!11))))))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(126,plain,
% 3.15/3.35 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))) | ((~element(tptp_fun_C_9(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), C), A!11))))))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(127,plain,
% 3.15/3.35 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))) | (~element(tptp_fun_C_9(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), C), A!11)))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[126, 125])).
% 3.15/3.35 tff(128,plain,
% 3.15/3.35 (![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), C), A!11)))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[127, 124, 114])).
% 3.15/3.35 tff(129,plain,
% 3.15/3.35 (((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))) | in(tptp_fun_B_10(A!11), A!11)),
% 3.15/3.35 inference(tautology,[status(thm)],[])).
% 3.15/3.35 tff(130,plain,
% 3.15/3.35 (in(tptp_fun_B_10(A!11), A!11)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[129, 83])).
% 3.15/3.35 tff(131,plain,
% 3.15/3.35 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_B_10(A!11), A!11)) | element(tptp_fun_B_10(A!11), A!11))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_B_10(A!11), A!11)) | element(tptp_fun_B_10(A!11), A!11))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(132,plain,
% 3.15/3.35 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_B_10(A!11), A!11)) | element(tptp_fun_B_10(A!11), A!11))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(133,plain,
% 3.15/3.35 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_B_10(A!11), A!11)) | element(tptp_fun_B_10(A!11), A!11)),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[132, 131])).
% 3.15/3.35 tff(134,plain,
% 3.15/3.35 (element(tptp_fun_B_10(A!11), A!11)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[133, 110, 130])).
% 3.15/3.35 tff(135,plain,
% 3.15/3.35 (((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), C), A!11)))))) | ((~element(tptp_fun_B_10(A!11), A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)))))) <=> ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), C), A!11)))))) | (~element(tptp_fun_B_10(A!11), A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)))))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(136,plain,
% 3.15/3.35 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), C), A!11)))))) | ((~element(tptp_fun_B_10(A!11), A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)))))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(137,plain,
% 3.15/3.35 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), C), A!11)))))) | (~element(tptp_fun_B_10(A!11), A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[136, 135])).
% 3.15/3.35 tff(138,plain,
% 3.15/3.35 (~((~in(symmetric_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[137, 134, 128])).
% 3.15/3.35 tff(139,plain,
% 3.15/3.35 (((~in(symmetric_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | (~in(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11))) | in(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)),
% 3.15/3.35 inference(tautology,[status(thm)],[])).
% 3.15/3.35 tff(140,plain,
% 3.15/3.35 (in(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[139, 138])).
% 3.15/3.35 tff(141,plain,
% 3.15/3.35 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | element(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | element(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(142,plain,
% 3.15/3.35 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | element(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(143,plain,
% 3.15/3.35 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | element(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[142, 141])).
% 3.15/3.35 tff(144,plain,
% 3.15/3.35 (element(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[143, 110, 140])).
% 3.15/3.35 tff(145,plain,
% 3.15/3.35 (((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))) | ((~element(tptp_fun_B_10(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), C), A!11))))))) <=> ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))) | (~element(tptp_fun_B_10(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), C), A!11))))))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(146,plain,
% 3.15/3.35 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))) | ((~element(tptp_fun_B_10(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), C), A!11))))))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(147,plain,
% 3.15/3.35 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))) | (~element(tptp_fun_B_10(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), C), A!11)))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[146, 145])).
% 3.15/3.35 tff(148,plain,
% 3.15/3.35 (![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), C), A!11)))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[147, 124, 134])).
% 3.15/3.35 tff(149,plain,
% 3.15/3.35 (((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), C), A!11)))))) | ((~element(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)))))) <=> ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), C), A!11)))))) | (~element(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)))))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(150,plain,
% 3.15/3.35 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), C), A!11)))))) | ((~element(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)))))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(151,plain,
% 3.15/3.35 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), C), A!11)))))) | (~element(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[150, 149])).
% 3.15/3.35 tff(152,plain,
% 3.15/3.35 (~((~in(symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[151, 148, 144])).
% 3.15/3.35 tff(153,plain,
% 3.15/3.35 (((~in(symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11))) | in(symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)),
% 3.15/3.35 inference(tautology,[status(thm)],[])).
% 3.15/3.35 tff(154,plain,
% 3.15/3.35 (in(symmetric_difference(tptp_fun_B_10(A!11), set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[153, 152])).
% 3.15/3.35 tff(155,plain,
% 3.15/3.35 (in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[154, 98])).
% 3.15/3.35 tff(156,plain,
% 3.15/3.35 ((~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))),
% 3.15/3.35 inference(tautology,[status(thm)],[])).
% 3.15/3.35 tff(157,plain,
% 3.15/3.35 (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[156, 155, 85])).
% 3.15/3.35 tff(158,plain,
% 3.15/3.35 (~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11)),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[157, 45])).
% 3.15/3.35 tff(159,plain,
% 3.15/3.35 (((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))) | ((~element(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11))))))) <=> ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))) | (~element(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11))))))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(160,plain,
% 3.15/3.35 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))) | ((~element(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11))))))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(161,plain,
% 3.15/3.35 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_intersection2(B, C), A!11))))))) | (~element(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[160, 159])).
% 3.15/3.35 tff(162,plain,
% 3.15/3.35 (![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[161, 124, 144])).
% 3.15/3.35 tff(163,plain,
% 3.15/3.35 (element(set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11) <=> element(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 3.15/3.35 inference(monotonicity,[status(thm)],[30])).
% 3.15/3.35 tff(164,plain,
% 3.15/3.35 (element(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11) <=> element(set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)),
% 3.15/3.35 inference(symmetry,[status(thm)],[163])).
% 3.15/3.35 tff(165,plain,
% 3.15/3.35 (((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), C), A!11)))))) | ((~element(tptp_fun_C_9(A!11), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))) <=> ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), C), A!11)))))) | (~element(tptp_fun_C_9(A!11), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(166,plain,
% 3.15/3.35 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), C), A!11)))))) | ((~element(tptp_fun_C_9(A!11), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(167,plain,
% 3.15/3.35 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), C), A!11)))))) | (~element(tptp_fun_C_9(A!11), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[166, 165])).
% 3.15/3.35 tff(168,plain,
% 3.15/3.35 (~((~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[167, 114, 148])).
% 3.15/3.35 tff(169,plain,
% 3.15/3.35 (((~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_intersection2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))) | in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 3.15/3.35 inference(tautology,[status(thm)],[])).
% 3.15/3.35 tff(170,plain,
% 3.15/3.35 (in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[169, 168])).
% 3.15/3.35 tff(171,plain,
% 3.15/3.35 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | element(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | element(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(172,plain,
% 3.15/3.35 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | element(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(173,plain,
% 3.15/3.35 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | element(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[172, 171])).
% 3.15/3.35 tff(174,plain,
% 3.15/3.35 (element(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[173, 110, 170])).
% 3.15/3.35 tff(175,plain,
% 3.15/3.35 (element(set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[174, 164])).
% 3.15/3.35 tff(176,plain,
% 3.15/3.35 (((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)))))) | ((~element(set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)) | (~((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11)))))) <=> ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)))))) | (~element(set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)) | (~((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11)))))),
% 3.15/3.36 inference(rewrite,[status(thm)],[])).
% 3.15/3.36 tff(177,plain,
% 3.15/3.36 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)))))) | ((~element(set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)) | (~((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11)))))),
% 3.15/3.36 inference(quant_inst,[status(thm)],[])).
% 3.15/3.36 tff(178,plain,
% 3.15/3.36 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)))))) | (~element(set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))), A!11)) | (~((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11))))),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[177, 176])).
% 3.15/3.36 tff(179,plain,
% 3.15/3.36 (~((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11)))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[178, 175, 162])).
% 3.15/3.36 tff(180,plain,
% 3.15/3.36 (((~in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11)) | (~in(set_intersection2(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11))) | in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11)),
% 3.15/3.36 inference(tautology,[status(thm)],[])).
% 3.15/3.36 tff(181,plain,
% 3.15/3.36 (in(symmetric_difference(set_intersection2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), set_union2(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))), A!11)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[180, 179])).
% 3.15/3.36 tff(182,plain,
% 3.15/3.36 ($false),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[181, 158])).
% 3.15/3.36 % SZS output end Proof
% 3.15/3.37 % E exiting
%------------------------------------------------------------------------------