%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU106+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 05:26:54 AM UTC 2025
% Result : Theorem 19.21s 19.40s
% Output : Proof 19.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU106+1 : TPTP v9.0.0. Released v3.2.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n012.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Fri Jun 20 06:03:40 EDT 2025
% 0.13/0.36 % CPUTime :
% 19.21/19.40 % SZS status Theorem
% 19.21/19.40 % SZS output start Proof
% 19.21/19.40 tff(in_type, type, (
% 19.21/19.40 in: ( $i * $i ) > $o)).
% 19.21/19.40 tff(tptp_fun_A_11_type, type, (
% 19.21/19.40 tptp_fun_A_11: $i)).
% 19.21/19.40 tff(symmetric_difference_type, type, (
% 19.21/19.40 symmetric_difference: ( $i * $i ) > $i)).
% 19.21/19.40 tff(set_union2_type, type, (
% 19.21/19.40 set_union2: ( $i * $i ) > $i)).
% 19.21/19.40 tff(tptp_fun_C_9_type, type, (
% 19.21/19.40 tptp_fun_C_9: $i > $i)).
% 19.21/19.40 tff(tptp_fun_B_10_type, type, (
% 19.21/19.40 tptp_fun_B_10: $i > $i)).
% 19.21/19.40 tff(set_difference_type, type, (
% 19.21/19.40 set_difference: ( $i * $i ) > $i)).
% 19.21/19.40 tff(element_type, type, (
% 19.21/19.40 element: ( $i * $i ) > $o)).
% 19.21/19.40 tff(preboolean_type, type, (
% 19.21/19.40 preboolean: $i > $o)).
% 19.21/19.40 tff(empty_type, type, (
% 19.21/19.40 empty: $i > $o)).
% 19.21/19.40 tff(set_intersection2_type, type, (
% 19.21/19.40 set_intersection2: ( $i * $i ) > $i)).
% 19.21/19.40 tff(1,plain,
% 19.21/19.40 (^[A: $i, B: $i] : refl((symmetric_difference(A, B) = symmetric_difference(B, A)) <=> (symmetric_difference(A, B) = symmetric_difference(B, A)))),
% 19.21/19.40 inference(bind,[status(th)],[])).
% 19.21/19.40 tff(2,plain,
% 19.21/19.40 (![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A)) <=> ![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A))),
% 19.21/19.40 inference(quant_intro,[status(thm)],[1])).
% 19.21/19.40 tff(3,plain,
% 19.21/19.40 (![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A)) <=> ![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A))),
% 19.21/19.40 inference(rewrite,[status(thm)],[])).
% 19.21/19.40 tff(4,axiom,(![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k5_xboole_0')).
% 19.21/19.40 tff(5,plain,
% 19.21/19.40 (![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 19.21/19.40 tff(6,plain,(
% 19.21/19.40 ![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A))),
% 19.21/19.40 inference(skolemize,[status(sab)],[5])).
% 19.21/19.40 tff(7,plain,
% 19.21/19.40 (![A: $i, B: $i] : (symmetric_difference(A, B) = symmetric_difference(B, A))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 19.21/19.40 tff(8,plain,
% 19.21/19.40 ((~![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_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))) = symmetric_difference(set_union2(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)))))),
% 19.21/19.40 inference(quant_inst,[status(thm)],[])).
% 19.21/19.40 tff(9,plain,
% 19.21/19.40 (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_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))) = symmetric_difference(set_union2(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))))),
% 19.21/19.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 19.21/19.40 tff(10,plain,
% 19.21/19.40 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 19.21/19.40 inference(bind,[status(th)],[])).
% 19.21/19.40 tff(11,plain,
% 19.21/19.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 19.21/19.40 inference(quant_intro,[status(thm)],[10])).
% 19.21/19.40 tff(12,plain,
% 19.21/19.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 19.21/19.40 inference(rewrite,[status(thm)],[])).
% 19.21/19.40 tff(13,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 19.21/19.40 tff(14,plain,
% 19.21/19.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 19.21/19.40 tff(15,plain,(
% 19.21/19.40 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 19.21/19.40 inference(skolemize,[status(sab)],[14])).
% 19.21/19.40 tff(16,plain,
% 19.21/19.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 19.21/19.40 tff(17,plain,
% 19.21/19.40 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)) = set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))),
% 19.21/19.40 inference(quant_inst,[status(thm)],[])).
% 19.21/19.40 tff(18,plain,
% 19.21/19.40 (set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)) = set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))),
% 19.21/19.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 19.21/19.40 tff(19,plain,
% 19.21/19.40 (set_union2(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))),
% 19.21/19.40 inference(symmetry,[status(thm)],[18])).
% 19.21/19.40 tff(20,plain,
% 19.21/19.40 (^[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))))),
% 19.21/19.40 inference(bind,[status(th)],[])).
% 19.21/19.40 tff(21,plain,
% 19.21/19.40 (![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)))),
% 19.21/19.40 inference(quant_intro,[status(thm)],[20])).
% 19.21/19.40 tff(22,plain,
% 19.21/19.40 (![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)))),
% 19.21/19.40 inference(rewrite,[status(thm)],[])).
% 19.21/19.40 tff(23,axiom,(![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_xboole_0')).
% 19.21/19.40 tff(24,plain,
% 19.21/19.40 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 19.21/19.40 tff(25,plain,(
% 19.21/19.40 ![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 19.21/19.40 inference(skolemize,[status(sab)],[24])).
% 19.21/19.40 tff(26,plain,
% 19.21/19.40 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 19.21/19.40 tff(27,plain,
% 19.21/19.40 ((~![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))))),
% 19.21/19.40 inference(quant_inst,[status(thm)],[])).
% 19.21/19.40 tff(28,plain,
% 19.21/19.40 (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)))),
% 19.21/19.40 inference(unit_resolution,[status(thm)],[27, 26])).
% 19.21/19.40 tff(29,plain,
% 19.21/19.40 (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))),
% 19.21/19.40 inference(symmetry,[status(thm)],[28])).
% 19.21/19.40 tff(30,plain,
% 19.21/19.40 (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_union2(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_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)))),
% 19.21/19.40 inference(monotonicity,[status(thm)],[29, 19])).
% 19.21/19.40 tff(31,plain,
% 19.21/19.40 (symmetric_difference(symmetric_difference(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))) = 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_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))),
% 19.21/19.40 inference(symmetry,[status(thm)],[30])).
% 19.21/19.40 tff(32,plain,
% 19.21/19.40 (symmetric_difference(symmetric_difference(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))) = symmetric_difference(set_union2(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))))),
% 19.21/19.40 inference(transitivity,[status(thm)],[31, 9])).
% 19.21/19.40 tff(33,plain,
% 19.21/19.40 (in(symmetric_difference(symmetric_difference(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))), A!11) <=> in(symmetric_difference(set_union2(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)),
% 19.21/19.40 inference(monotonicity,[status(thm)],[32])).
% 19.21/19.40 tff(34,plain,
% 19.21/19.40 (in(symmetric_difference(set_union2(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(symmetric_difference(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))), A!11)),
% 19.21/19.40 inference(symmetry,[status(thm)],[33])).
% 19.21/19.40 tff(35,plain,
% 19.21/19.40 (^[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)))))))))))),
% 19.21/19.40 inference(bind,[status(th)],[])).
% 19.21/19.40 tff(36,plain,
% 19.21/19.40 (![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))))))))))),
% 19.21/19.40 inference(quant_intro,[status(thm)],[35])).
% 19.21/19.40 tff(37,plain,
% 19.21/19.40 (^[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)))))))))))),
% 19.21/19.40 inference(bind,[status(th)],[])).
% 19.21/19.40 tff(38,plain,
% 19.21/19.40 (![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))))))))))),
% 19.21/19.40 inference(quant_intro,[status(thm)],[37])).
% 19.21/19.40 tff(39,plain,
% 19.21/19.40 (![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))))))))))),
% 19.21/19.40 inference(transitivity,[status(thm)],[38, 36])).
% 19.21/19.40 tff(40,plain,
% 19.21/19.40 (^[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))))))))))))),
% 19.21/19.40 inference(bind,[status(th)],[])).
% 19.21/19.40 tff(41,plain,
% 19.21/19.40 (![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))))))))))),
% 19.21/19.40 inference(quant_intro,[status(thm)],[40])).
% 19.21/19.40 tff(42,plain,
% 19.21/19.40 (![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))))),
% 19.21/19.40 inference(rewrite,[status(thm)],[])).
% 19.21/19.40 tff(43,plain,
% 19.21/19.40 (^[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)))))),
% 19.21/19.40 inference(bind,[status(th)],[])).
% 19.21/19.40 tff(44,plain,
% 19.21/19.40 (![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))))),
% 19.21/19.40 inference(quant_intro,[status(thm)],[43])).
% 19.21/19.40 tff(45,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/sandbox/benchmark/theBenchmark.p','t10_finsub_1')).
% 19.21/19.40 tff(46,plain,
% 19.21/19.40 (![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))))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 19.21/19.40 tff(47,plain,
% 19.21/19.40 (![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))))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 19.21/19.40 tff(48,plain,(
% 19.21/19.40 ![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))))))),
% 19.21/19.40 inference(skolemize,[status(sab)],[47])).
% 19.21/19.40 tff(49,plain,
% 19.21/19.40 (![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))))))))))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[48, 41])).
% 19.21/19.40 tff(50,plain,
% 19.21/19.40 (![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))))))))))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[49, 39])).
% 19.21/19.40 tff(51,plain,
% 19.21/19.40 (((~![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)))))))))))),
% 19.21/19.40 inference(rewrite,[status(thm)],[])).
% 19.21/19.40 tff(52,plain,
% 19.21/19.40 ((~((~((~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))))))))))),
% 19.21/19.40 inference(rewrite,[status(thm)],[])).
% 19.21/19.40 tff(53,plain,
% 19.21/19.40 (((~![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)))))))))))),
% 19.21/19.40 inference(monotonicity,[status(thm)],[52])).
% 19.21/19.40 tff(54,plain,
% 19.21/19.40 (((~![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)))))))))))),
% 19.21/19.40 inference(transitivity,[status(thm)],[53, 51])).
% 19.21/19.40 tff(55,plain,
% 19.21/19.40 ((~![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))))))))))),
% 19.21/19.40 inference(quant_inst,[status(thm)],[])).
% 19.21/19.40 tff(56,plain,
% 19.21/19.40 ((~![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))))))))))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 19.21/19.40 tff(57,plain,
% 19.21/19.40 (~((~((~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)))))))))),
% 19.21/19.40 inference(unit_resolution,[status(thm)],[56, 50])).
% 19.21/19.40 tff(58,plain,
% 19.21/19.40 (((~((~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)))))))),
% 19.21/19.40 inference(tautology,[status(thm)],[])).
% 19.21/19.40 tff(59,plain,
% 19.21/19.40 (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))))))),
% 19.21/19.40 inference(unit_resolution,[status(thm)],[58, 57])).
% 19.21/19.40 tff(60,plain,
% 19.21/19.40 (((~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_union2(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_union2(B, C), A!11)))))),
% 19.21/19.40 inference(rewrite,[status(thm)],[])).
% 19.21/19.40 tff(61,plain,
% 19.21/19.40 ((~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_union2(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_union2(B, C), A)))))))),
% 19.21/19.40 inference(rewrite,[status(thm)],[])).
% 19.21/19.40 tff(62,plain,
% 19.21/19.40 ((~![A: $i] : ((~empty(A)) => (![B: $i] : (element(B, A) => ![C: $i] : (element(C, A) => (in(symmetric_difference(B, C), A) & in(set_union2(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_union2(B, C), A)))))))),
% 19.21/19.40 inference(rewrite,[status(thm)],[])).
% 19.21/19.40 tff(63,axiom,(~![A: $i] : ((~empty(A)) => (![B: $i] : (element(B, A) => ![C: $i] : (element(C, A) => (in(symmetric_difference(B, C), A) & in(set_union2(B, C), A)))) => preboolean(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t17_finsub_1')).
% 19.21/19.40 tff(64,plain,
% 19.21/19.40 (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_union2(B, C), A))))))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 19.21/19.40 tff(65,plain,
% 19.21/19.40 (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_union2(B, C), A))))))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[64, 61])).
% 19.21/19.40 tff(66,plain,
% 19.21/19.40 (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_union2(B, C), A))))))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[65, 61])).
% 19.21/19.40 tff(67,plain,
% 19.21/19.40 (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_union2(B, C), A))))))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[66, 61])).
% 19.21/19.40 tff(68,plain,
% 19.21/19.40 ((~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_union2(B, C), A!11))))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[67, 60])).
% 19.21/19.40 tff(69,plain,
% 19.21/19.40 (~preboolean(A!11)),
% 19.21/19.40 inference(and_elim,[status(thm)],[68])).
% 19.21/19.40 tff(70,plain,
% 19.21/19.40 ((~(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))))))),
% 19.21/19.40 inference(tautology,[status(thm)],[])).
% 19.21/19.40 tff(71,plain,
% 19.21/19.40 ((~(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))))))),
% 19.21/19.40 inference(unit_resolution,[status(thm)],[70, 69])).
% 19.21/19.40 tff(72,plain,
% 19.21/19.40 (~((~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)))))),
% 19.21/19.40 inference(unit_resolution,[status(thm)],[71, 59])).
% 19.21/19.40 tff(73,plain,
% 19.21/19.40 (((~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)),
% 19.21/19.40 inference(tautology,[status(thm)],[])).
% 19.21/19.40 tff(74,plain,
% 19.21/19.40 (in(tptp_fun_C_9(A!11), A!11)),
% 19.21/19.40 inference(unit_resolution,[status(thm)],[73, 72])).
% 19.21/19.40 tff(75,plain,
% 19.21/19.40 (^[A: $i, B: $i] : refl(((~in(A, B)) | element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 19.21/19.40 inference(bind,[status(th)],[])).
% 19.21/19.40 tff(76,plain,
% 19.21/19.40 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 19.21/19.40 inference(quant_intro,[status(thm)],[75])).
% 19.21/19.40 tff(77,plain,
% 19.21/19.40 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 19.21/19.40 inference(rewrite,[status(thm)],[])).
% 19.21/19.40 tff(78,plain,
% 19.21/19.40 (^[A: $i, B: $i] : rewrite((in(A, B) => element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 19.21/19.40 inference(bind,[status(th)],[])).
% 19.21/19.40 tff(79,plain,
% 19.21/19.40 (![A: $i, B: $i] : (in(A, B) => element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 19.21/19.40 inference(quant_intro,[status(thm)],[78])).
% 19.21/19.40 tff(80,axiom,(![A: $i, B: $i] : (in(A, B) => element(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 19.21/19.40 tff(81,plain,
% 19.21/19.40 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 19.21/19.40 tff(82,plain,
% 19.21/19.40 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[81, 77])).
% 19.21/19.40 tff(83,plain,(
% 19.21/19.40 ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 19.21/19.40 inference(skolemize,[status(sab)],[82])).
% 19.21/19.40 tff(84,plain,
% 19.21/19.40 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[83, 76])).
% 19.21/19.40 tff(85,plain,
% 19.21/19.40 (((~![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))),
% 19.21/19.40 inference(rewrite,[status(thm)],[])).
% 19.21/19.40 tff(86,plain,
% 19.21/19.40 ((~![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))),
% 19.21/19.40 inference(quant_inst,[status(thm)],[])).
% 19.21/19.40 tff(87,plain,
% 19.21/19.40 ((~![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)),
% 19.21/19.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 19.21/19.40 tff(88,plain,
% 19.21/19.40 (element(tptp_fun_C_9(A!11), A!11)),
% 19.21/19.40 inference(unit_resolution,[status(thm)],[87, 84, 74])).
% 19.21/19.40 tff(89,plain,
% 19.21/19.40 (^[B: $i] : refl(((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11)))))) <=> ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11)))))))),
% 19.21/19.40 inference(bind,[status(th)],[])).
% 19.21/19.40 tff(90,plain,
% 19.21/19.40 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(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_union2(B, C), A!11))))))),
% 19.21/19.40 inference(quant_intro,[status(thm)],[89])).
% 19.21/19.40 tff(91,plain,
% 19.21/19.40 (^[B: $i] : rewrite(((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11)))))) <=> ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11)))))))),
% 19.21/19.40 inference(bind,[status(th)],[])).
% 19.21/19.40 tff(92,plain,
% 19.21/19.40 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(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_union2(B, C), A!11))))))),
% 19.21/19.40 inference(quant_intro,[status(thm)],[91])).
% 19.21/19.40 tff(93,plain,
% 19.21/19.40 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(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_union2(B, C), A!11))))))),
% 19.21/19.41 inference(transitivity,[status(thm)],[92, 90])).
% 19.21/19.41 tff(94,plain,
% 19.21/19.41 (^[B: $i] : rewrite(((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_union2(B, C), A!11)))) <=> ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11)))))))),
% 19.21/19.41 inference(bind,[status(th)],[])).
% 19.21/19.41 tff(95,plain,
% 19.21/19.41 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_union2(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_union2(B, C), A!11))))))),
% 19.21/19.41 inference(quant_intro,[status(thm)],[94])).
% 19.21/19.41 tff(96,plain,
% 19.21/19.41 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_union2(B, C), A!11))))),
% 19.21/19.41 inference(and_elim,[status(thm)],[68])).
% 19.21/19.41 tff(97,plain,
% 19.21/19.41 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11))))))),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 19.21/19.41 tff(98,plain,
% 19.21/19.41 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11))))))),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[97, 93])).
% 19.21/19.41 tff(99,plain,
% 19.21/19.41 (((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(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_union2(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_union2(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_union2(tptp_fun_C_9(A!11), C), A!11))))))),
% 19.21/19.41 inference(rewrite,[status(thm)],[])).
% 19.21/19.41 tff(100,plain,
% 19.21/19.41 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(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_union2(tptp_fun_C_9(A!11), C), A!11))))))),
% 19.21/19.41 inference(quant_inst,[status(thm)],[])).
% 19.21/19.41 tff(101,plain,
% 19.21/19.41 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(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_union2(tptp_fun_C_9(A!11), C), A!11)))))),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[100, 99])).
% 19.21/19.41 tff(102,plain,
% 19.21/19.41 (![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_union2(tptp_fun_C_9(A!11), C), A!11)))))),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[101, 98, 88])).
% 19.21/19.41 tff(103,plain,
% 19.21/19.41 (((~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)),
% 19.21/19.41 inference(tautology,[status(thm)],[])).
% 19.21/19.41 tff(104,plain,
% 19.21/19.41 (in(tptp_fun_B_10(A!11), A!11)),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[103, 72])).
% 19.21/19.41 tff(105,plain,
% 19.21/19.41 (((~![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))),
% 19.21/19.41 inference(rewrite,[status(thm)],[])).
% 19.21/19.41 tff(106,plain,
% 19.21/19.41 ((~![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))),
% 19.21/19.41 inference(quant_inst,[status(thm)],[])).
% 19.21/19.41 tff(107,plain,
% 19.21/19.41 ((~![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)),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[106, 105])).
% 19.21/19.41 tff(108,plain,
% 19.21/19.41 (element(tptp_fun_B_10(A!11), A!11)),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[107, 84, 104])).
% 19.21/19.41 tff(109,plain,
% 19.21/19.41 (((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_union2(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_union2(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_union2(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_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)))))),
% 19.21/19.41 inference(rewrite,[status(thm)],[])).
% 19.21/19.41 tff(110,plain,
% 19.21/19.41 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_union2(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_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)))))),
% 19.21/19.41 inference(quant_inst,[status(thm)],[])).
% 19.21/19.41 tff(111,plain,
% 19.21/19.41 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_union2(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_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11))))),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[110, 109])).
% 19.21/19.41 tff(112,plain,
% 19.21/19.41 (~((~in(symmetric_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | (~in(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)))),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[111, 108, 102])).
% 19.21/19.41 tff(113,plain,
% 19.21/19.41 (((~in(symmetric_difference(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | (~in(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11))) | in(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)),
% 19.21/19.41 inference(tautology,[status(thm)],[])).
% 19.21/19.41 tff(114,plain,
% 19.21/19.41 (in(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[113, 112])).
% 19.21/19.41 tff(115,plain,
% 19.21/19.41 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | element(set_union2(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_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | element(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11))),
% 19.21/19.41 inference(rewrite,[status(thm)],[])).
% 19.21/19.41 tff(116,plain,
% 19.21/19.41 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | element(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11))),
% 19.21/19.41 inference(quant_inst,[status(thm)],[])).
% 19.21/19.41 tff(117,plain,
% 19.21/19.41 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | element(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[116, 115])).
% 19.21/19.41 tff(118,plain,
% 19.21/19.41 (element(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[117, 84, 114])).
% 19.21/19.41 tff(119,plain,
% 19.21/19.41 (((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11))))))) | ((~element(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_union2(set_union2(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_union2(B, C), A!11))))))) | (~element(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_union2(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11))))))),
% 19.21/19.41 inference(rewrite,[status(thm)],[])).
% 19.21/19.41 tff(120,plain,
% 19.21/19.41 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11))))))) | ((~element(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_union2(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11))))))),
% 19.21/19.41 inference(quant_inst,[status(thm)],[])).
% 19.21/19.41 tff(121,plain,
% 19.21/19.41 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11))))))) | (~element(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_union2(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)))))),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[120, 119])).
% 19.21/19.41 tff(122,plain,
% 19.21/19.41 (![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_union2(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)))))),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[121, 98, 118])).
% 19.21/19.41 tff(123,plain,
% 19.21/19.41 (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)),
% 19.21/19.41 inference(monotonicity,[status(thm)],[29])).
% 19.21/19.41 tff(124,plain,
% 19.21/19.41 (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)),
% 19.21/19.41 inference(symmetry,[status(thm)],[123])).
% 19.21/19.41 tff(125,plain,
% 19.21/19.41 (((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(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_union2(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_union2(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_union2(tptp_fun_B_10(A!11), C), A!11))))))),
% 19.21/19.41 inference(rewrite,[status(thm)],[])).
% 19.21/19.41 tff(126,plain,
% 19.21/19.41 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(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_union2(tptp_fun_B_10(A!11), C), A!11))))))),
% 19.21/19.41 inference(quant_inst,[status(thm)],[])).
% 19.21/19.41 tff(127,plain,
% 19.21/19.41 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_union2(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_union2(tptp_fun_B_10(A!11), C), A!11)))))),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[126, 125])).
% 19.21/19.41 tff(128,plain,
% 19.21/19.41 (![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), C), A!11)))))),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[127, 98, 108])).
% 19.21/19.41 tff(129,plain,
% 19.21/19.41 (((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), C), A!11)))))) | ((~element(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(symmetric_difference(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_union2(tptp_fun_B_10(A!11), C), A!11)))))) | (~element(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(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))),
% 19.21/19.41 inference(rewrite,[status(thm)],[])).
% 19.21/19.41 tff(130,plain,
% 19.21/19.41 (((~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_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))) <=> ((~element(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(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))),
% 19.21/19.41 inference(rewrite,[status(thm)],[])).
% 19.21/19.41 tff(131,plain,
% 19.21/19.41 (((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_union2(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_union2(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_union2(tptp_fun_B_10(A!11), C), A!11)))))) | ((~element(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(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))),
% 19.21/19.41 inference(monotonicity,[status(thm)],[130])).
% 19.21/19.41 tff(132,plain,
% 19.21/19.41 (((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_union2(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_union2(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_union2(tptp_fun_B_10(A!11), C), A!11)))))) | (~element(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(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))),
% 19.21/19.41 inference(transitivity,[status(thm)],[131, 129])).
% 19.21/19.41 tff(133,plain,
% 19.21/19.41 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_union2(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_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))),
% 19.21/19.41 inference(quant_inst,[status(thm)],[])).
% 19.21/19.41 tff(134,plain,
% 19.21/19.41 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), C), A!11)))))) | (~element(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(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[133, 132])).
% 19.21/19.41 tff(135,plain,
% 19.21/19.41 (~((~in(set_union2(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)))),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[134, 88, 128])).
% 19.21/19.41 tff(136,plain,
% 19.21/19.41 (((~in(set_union2(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))) | in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 19.21/19.41 inference(tautology,[status(thm)],[])).
% 19.21/19.41 tff(137,plain,
% 19.21/19.41 (in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[136, 135])).
% 19.21/19.41 tff(138,plain,
% 19.21/19.41 (((~![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))),
% 19.21/19.41 inference(rewrite,[status(thm)],[])).
% 19.21/19.41 tff(139,plain,
% 19.21/19.41 ((~![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))),
% 19.21/19.41 inference(quant_inst,[status(thm)],[])).
% 19.21/19.41 tff(140,plain,
% 19.21/19.41 ((~![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)),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[139, 138])).
% 19.21/19.41 tff(141,plain,
% 19.21/19.41 (element(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[140, 84, 137])).
% 19.21/19.41 tff(142,plain,
% 19.21/19.41 (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)),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[141, 124])).
% 19.21/19.41 tff(143,plain,
% 19.21/19.41 (((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_union2(set_union2(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_union2(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(set_union2(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_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_union2(set_union2(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_union2(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(set_union2(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)))))),
% 19.21/19.41 inference(rewrite,[status(thm)],[])).
% 19.21/19.41 tff(144,plain,
% 19.21/19.41 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_union2(set_union2(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_union2(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(set_union2(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)))))),
% 19.21/19.41 inference(quant_inst,[status(thm)],[])).
% 19.21/19.41 tff(145,plain,
% 19.21/19.41 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)), C), A!11)) | (~in(set_union2(set_union2(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_union2(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(set_union2(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))))),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[144, 143])).
% 19.21/19.41 tff(146,plain,
% 19.21/19.41 (~((~in(symmetric_difference(set_union2(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(set_union2(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)))),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[145, 142, 122])).
% 19.21/19.41 tff(147,plain,
% 19.21/19.41 (((~in(symmetric_difference(set_union2(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(set_union2(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_union2(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)),
% 19.21/19.41 inference(tautology,[status(thm)],[])).
% 19.21/19.41 tff(148,plain,
% 19.21/19.41 (in(symmetric_difference(set_union2(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)),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[147, 146])).
% 19.21/19.41 tff(149,plain,
% 19.21/19.41 (in(symmetric_difference(symmetric_difference(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))), A!11)),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[148, 34])).
% 19.21/19.41 tff(150,plain,
% 19.21/19.41 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = symmetric_difference(symmetric_difference(A, B), set_union2(A, B))) <=> (set_intersection2(A, B) = symmetric_difference(symmetric_difference(A, B), set_union2(A, B))))),
% 19.21/19.41 inference(bind,[status(th)],[])).
% 19.21/19.41 tff(151,plain,
% 19.21/19.41 (![A: $i, B: $i] : (set_intersection2(A, B) = symmetric_difference(symmetric_difference(A, B), set_union2(A, B))) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = symmetric_difference(symmetric_difference(A, B), set_union2(A, B)))),
% 19.21/19.41 inference(quant_intro,[status(thm)],[150])).
% 19.21/19.41 tff(152,plain,
% 19.21/19.41 (![A: $i, B: $i] : (set_intersection2(A, B) = symmetric_difference(symmetric_difference(A, B), set_union2(A, B))) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = symmetric_difference(symmetric_difference(A, B), set_union2(A, B)))),
% 19.21/19.41 inference(rewrite,[status(thm)],[])).
% 19.21/19.41 tff(153,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = symmetric_difference(symmetric_difference(A, B), set_union2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t95_xboole_1')).
% 19.21/19.41 tff(154,plain,
% 19.21/19.41 (![A: $i, B: $i] : (set_intersection2(A, B) = symmetric_difference(symmetric_difference(A, B), set_union2(A, B)))),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[153, 152])).
% 19.21/19.41 tff(155,plain,(
% 19.21/19.41 ![A: $i, B: $i] : (set_intersection2(A, B) = symmetric_difference(symmetric_difference(A, B), set_union2(A, B)))),
% 19.21/19.41 inference(skolemize,[status(sab)],[154])).
% 19.21/19.41 tff(156,plain,
% 19.21/19.41 (![A: $i, B: $i] : (set_intersection2(A, B) = symmetric_difference(symmetric_difference(A, B), set_union2(A, B)))),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[155, 151])).
% 19.21/19.41 tff(157,plain,
% 19.21/19.41 ((~![A: $i, B: $i] : (set_intersection2(A, B) = symmetric_difference(symmetric_difference(A, B), set_union2(A, B)))) | (set_intersection2(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_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))))),
% 19.21/19.41 inference(quant_inst,[status(thm)],[])).
% 19.21/19.41 tff(158,plain,
% 19.21/19.41 (set_intersection2(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_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)))),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[157, 156])).
% 19.21/19.41 tff(159,plain,
% 19.21/19.41 (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), symmetric_difference(symmetric_difference(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))))),
% 19.21/19.41 inference(monotonicity,[status(thm)],[158])).
% 19.21/19.41 tff(160,plain,
% 19.21/19.41 (^[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))))),
% 19.21/19.41 inference(bind,[status(th)],[])).
% 19.21/19.41 tff(161,plain,
% 19.21/19.41 (![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)))),
% 19.21/19.41 inference(quant_intro,[status(thm)],[160])).
% 19.21/19.41 tff(162,plain,
% 19.21/19.41 (![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)))),
% 19.21/19.41 inference(rewrite,[status(thm)],[])).
% 19.21/19.41 tff(163,axiom,(![A: $i, B: $i] : (set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t100_xboole_1')).
% 19.21/19.41 tff(164,plain,
% 19.21/19.41 (![A: $i, B: $i] : (set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B)))),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[163, 162])).
% 19.21/19.41 tff(165,plain,(
% 19.21/19.41 ![A: $i, B: $i] : (set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B)))),
% 19.21/19.41 inference(skolemize,[status(sab)],[164])).
% 19.21/19.41 tff(166,plain,
% 19.21/19.41 (![A: $i, B: $i] : (set_difference(A, B) = symmetric_difference(A, set_intersection2(A, B)))),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[165, 161])).
% 19.21/19.41 tff(167,plain,
% 19.21/19.41 ((~![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))))),
% 19.21/19.41 inference(quant_inst,[status(thm)],[])).
% 19.21/19.41 tff(168,plain,
% 19.21/19.41 (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)))),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[167, 166])).
% 19.21/19.41 tff(169,plain,
% 19.21/19.41 (set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)) = symmetric_difference(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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))))),
% 19.21/19.41 inference(transitivity,[status(thm)],[168, 159])).
% 19.21/19.41 tff(170,plain,
% 19.21/19.41 (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), symmetric_difference(symmetric_difference(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)))), A!11)),
% 19.21/19.41 inference(monotonicity,[status(thm)],[169])).
% 19.21/19.41 tff(171,plain,
% 19.21/19.41 ((~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), symmetric_difference(symmetric_difference(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)))), A!11))),
% 19.21/19.41 inference(monotonicity,[status(thm)],[170])).
% 19.21/19.41 tff(172,plain,
% 19.21/19.41 (((~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)))),
% 19.21/19.41 inference(tautology,[status(thm)],[])).
% 19.21/19.41 tff(173,plain,
% 19.21/19.41 ((~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))),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[172, 72])).
% 19.21/19.41 tff(174,plain,
% 19.21/19.41 (((~in(set_union2(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))) | in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 19.21/19.41 inference(tautology,[status(thm)],[])).
% 19.21/19.41 tff(175,plain,
% 19.21/19.41 (in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[174, 135])).
% 19.21/19.41 tff(176,plain,
% 19.21/19.41 ((~((~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))),
% 19.21/19.41 inference(tautology,[status(thm)],[])).
% 19.21/19.41 tff(177,plain,
% 19.21/19.41 (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[176, 175, 173])).
% 19.21/19.41 tff(178,plain,
% 19.21/19.41 (~in(symmetric_difference(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11)),
% 19.21/19.41 inference(modus_ponens,[status(thm)],[177, 171])).
% 19.21/19.41 tff(179,plain,
% 19.21/19.41 (((~in(symmetric_difference(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11))) | in(symmetric_difference(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11)),
% 19.21/19.41 inference(tautology,[status(thm)],[])).
% 19.21/19.41 tff(180,plain,
% 19.21/19.41 ((~in(symmetric_difference(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11))),
% 19.21/19.41 inference(unit_resolution,[status(thm)],[179, 178])).
% 19.21/19.41 tff(181,plain,
% 19.21/19.41 (((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), C), A!11)))))) | ((~element(symmetric_difference(symmetric_difference(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))), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11)))))) <=> ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), C), A!11)))))) | (~element(symmetric_difference(symmetric_difference(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))), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11)))))),
% 19.21/19.42 inference(rewrite,[status(thm)],[])).
% 19.21/19.42 tff(182,plain,
% 19.21/19.42 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), C), A!11)))))) | ((~element(symmetric_difference(symmetric_difference(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))), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11)))))),
% 19.21/19.42 inference(quant_inst,[status(thm)],[])).
% 19.21/19.42 tff(183,plain,
% 19.21/19.42 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), C), A!11)))))) | (~element(symmetric_difference(symmetric_difference(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))), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11))))),
% 19.21/19.42 inference(modus_ponens,[status(thm)],[182, 181])).
% 19.21/19.42 tff(184,plain,
% 19.21/19.42 ((~element(symmetric_difference(symmetric_difference(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))), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), symmetric_difference(symmetric_difference(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)))), A!11))))),
% 19.21/19.42 inference(unit_resolution,[status(thm)],[183, 128])).
% 19.21/19.42 tff(185,plain,
% 19.21/19.42 (~element(symmetric_difference(symmetric_difference(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))), A!11)),
% 19.21/19.42 inference(unit_resolution,[status(thm)],[184, 180])).
% 19.21/19.42 tff(186,plain,
% 19.21/19.42 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(symmetric_difference(symmetric_difference(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))), A!11)) | element(symmetric_difference(symmetric_difference(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))), A!11))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(symmetric_difference(symmetric_difference(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))), A!11)) | element(symmetric_difference(symmetric_difference(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))), A!11))),
% 19.21/19.42 inference(rewrite,[status(thm)],[])).
% 19.21/19.42 tff(187,plain,
% 19.21/19.42 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(symmetric_difference(symmetric_difference(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))), A!11)) | element(symmetric_difference(symmetric_difference(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))), A!11))),
% 19.21/19.43 inference(quant_inst,[status(thm)],[])).
% 19.21/19.43 tff(188,plain,
% 19.21/19.43 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(symmetric_difference(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)) | element(symmetric_difference(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)),
% 19.21/19.43 inference(modus_ponens,[status(thm)],[187, 186])).
% 19.21/19.43 tff(189,plain,
% 19.21/19.43 (~in(symmetric_difference(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)),
% 19.21/19.43 inference(unit_resolution,[status(thm)],[188, 84, 185])).
% 19.21/19.43 tff(190,plain,
% 19.21/19.43 ($false),
% 19.21/19.43 inference(unit_resolution,[status(thm)],[189, 149])).
% 19.21/19.43 % SZS output end Proof
% 19.34/19.51 % E exiting
%------------------------------------------------------------------------------