%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU132+1 : TPTP v9.0.0. Released v3.3.0.
% 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 05:26:58 AM UTC 2025
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU132+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:07:11 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(in_type, type, (
% 0.21/0.44 in: ( $i * $i ) > $o)).
% 0.21/0.44 tff(tptp_fun_B_5_type, type, (
% 0.21/0.44 tptp_fun_B_5: $i)).
% 0.21/0.44 tff(tptp_fun_C_0_type, type, (
% 0.21/0.44 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.21/0.44 tff(set_difference_type, type, (
% 0.21/0.44 set_difference: ( $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_C_4_type, type, (
% 0.21/0.44 tptp_fun_C_4: $i)).
% 0.21/0.44 tff(tptp_fun_A_6_type, type, (
% 0.21/0.44 tptp_fun_A_6: $i)).
% 0.21/0.44 tff(tptp_fun_D_1_type, type, (
% 0.21/0.44 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(subset_type, type, (
% 0.21/0.44 subset: ( $i * $i ) > $o)).
% 0.21/0.44 tff(1,assumption,(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))), introduced(assumption)).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.44 inference(pull_quant,[status(thm)],[])).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(6,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[6, 4])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[7, 3])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[10, 8])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), rewrite(((C = set_difference(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B)))))) <=> ((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.44 tff(14,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(15,axiom,(![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_xboole_0')).
% 0.21/0.45 tff(16,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.45 tff(17,plain,(
% 0.21/0.45 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[16])).
% 0.21/0.45 tff(18,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.45 tff(20,plain,
% 0.21/0.45 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(21,plain,
% 0.21/0.45 ((~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))) <=> (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(22,plain,
% 0.21/0.45 (((((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) | $false) <=> (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(23,plain,
% 0.21/0.45 ((~$true) <=> $false),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(24,plain,
% 0.21/0.45 (($true | (((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)) <=> in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)))) <=> $true),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(25,plain,
% 0.21/0.45 ((set_difference(B!5, C!4) = set_difference(B!5, C!4)) <=> $true),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(26,plain,
% 0.21/0.45 (((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)) <=> in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)))) <=> ($true | (((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)) <=> in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[25])).
% 0.21/0.45 tff(27,plain,
% 0.21/0.45 (((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)) <=> in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)))) <=> $true),
% 0.21/0.45 inference(transitivity,[status(thm)],[26, 24])).
% 0.21/0.45 tff(28,plain,
% 0.21/0.45 ((~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)) <=> in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4))))) <=> (~$true)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[27])).
% 0.21/0.45 tff(29,plain,
% 0.21/0.45 ((~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)) <=> in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4))))) <=> $false),
% 0.21/0.45 inference(transitivity,[status(thm)],[28, 23])).
% 0.21/0.45 tff(30,plain,
% 0.21/0.45 ((~(~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))) <=> (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(31,plain,
% 0.21/0.45 (($false | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))) <=> (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(32,plain,
% 0.21/0.45 ((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) <=> (~$true)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[25])).
% 0.21/0.45 tff(33,plain,
% 0.21/0.45 ((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) <=> $false),
% 0.21/0.45 inference(transitivity,[status(thm)],[32, 23])).
% 0.21/0.45 tff(34,plain,
% 0.21/0.45 (((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))) <=> ($false | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[33, 21])).
% 0.21/0.45 tff(35,plain,
% 0.21/0.45 (((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))) <=> (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[34, 31])).
% 0.21/0.45 tff(36,plain,
% 0.21/0.45 ((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))) <=> (~(~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[35])).
% 0.21/0.45 tff(37,plain,
% 0.21/0.45 ((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))) <=> (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[36, 30])).
% 0.21/0.45 tff(38,plain,
% 0.21/0.45 (((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))) | (~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)) <=> in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)))))) <=> ((((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) | $false)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[37, 29])).
% 0.21/0.45 tff(39,plain,
% 0.21/0.45 (((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))) | (~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)) <=> in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)))))) <=> (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[38, 22])).
% 0.21/0.45 tff(40,plain,
% 0.21/0.45 ((~((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))) | (~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)) <=> in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4))))))) <=> (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[39])).
% 0.21/0.46 tff(41,plain,
% 0.21/0.46 ((~((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))) | (~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)) <=> in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4))))))) <=> (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[40, 21])).
% 0.21/0.46 tff(42,plain,
% 0.21/0.46 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))) | (~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)) <=> in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[41])).
% 0.21/0.46 tff(43,plain,
% 0.21/0.46 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))) | (~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)) <=> in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[42, 20])).
% 0.21/0.46 tff(44,plain,
% 0.21/0.46 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))) | (~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)) <=> in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(45,plain,
% 0.21/0.46 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.46 tff(46,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[45, 19, 1])).
% 0.21/0.46 tff(47,plain,(~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(48,plain,
% 0.21/0.46 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(49,plain,
% 0.21/0.46 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.46 tff(50,plain,
% 0.21/0.46 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(51,plain,
% 0.21/0.46 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.46 tff(52,plain,
% 0.21/0.46 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[51, 49])).
% 0.21/0.46 tff(53,plain,
% 0.21/0.46 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(54,plain,
% 0.21/0.46 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.46 tff(55,plain,
% 0.21/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(56,plain,
% 0.21/0.46 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(57,plain,
% 0.21/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.46 tff(58,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.21/0.46 tff(59,plain,
% 0.21/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.46 tff(60,plain,
% 0.21/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.46 tff(61,plain,(
% 0.21/0.46 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[60])).
% 0.21/0.46 tff(62,plain,
% 0.21/0.46 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.21/0.46 tff(63,plain,
% 0.21/0.46 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.21/0.46 tff(64,plain,
% 0.21/0.46 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(set_difference(A!6, C!4), set_difference(B!5, C!4))) | ![C: $i] : ((~in(C, set_difference(A!6, C!4))) | in(C, set_difference(B!5, C!4))))) | (~(subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(65,plain,
% 0.21/0.46 (~((~((~subset(set_difference(A!6, C!4), set_difference(B!5, C!4))) | ![C: $i] : ((~in(C, set_difference(A!6, C!4))) | in(C, set_difference(B!5, C!4))))) | (~(subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.21/0.46 tff(66,plain,
% 0.21/0.46 (((~((~subset(set_difference(A!6, C!4), set_difference(B!5, C!4))) | ![C: $i] : ((~in(C, set_difference(A!6, C!4))) | in(C, set_difference(B!5, C!4))))) | (~(subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))))) | (subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(67,plain,
% 0.21/0.46 (subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.21/0.46 tff(68,plain,
% 0.21/0.46 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(69,plain,
% 0.21/0.46 ((~![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_difference(A, C), set_difference(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(70,axiom,(~![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_difference(A, C), set_difference(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t33_xboole_1')).
% 0.21/0.46 tff(71,plain,
% 0.21/0.46 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.46 tff(72,plain,
% 0.21/0.46 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[71, 68])).
% 0.21/0.46 tff(73,plain,
% 0.21/0.46 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.21/0.46 tff(74,plain,
% 0.21/0.46 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[73, 68])).
% 0.21/0.46 tff(75,plain,(
% 0.21/0.46 ~((~subset(A!6, B!5)) | subset(set_difference(A!6, C!4), set_difference(B!5, C!4)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[74])).
% 0.21/0.46 tff(76,plain,
% 0.21/0.46 (~subset(set_difference(A!6, C!4), set_difference(B!5, C!4))),
% 0.21/0.46 inference(or_elim,[status(thm)],[75])).
% 0.21/0.46 tff(77,plain,
% 0.21/0.46 ((~(subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))) | subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(78,plain,
% 0.21/0.47 ((~(subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.21/0.47 tff(79,plain,
% 0.21/0.47 (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[78, 67])).
% 0.21/0.47 tff(80,plain,
% 0.21/0.47 (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) | (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(81,plain,
% 0.21/0.47 (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.21/0.47 tff(82,plain,
% 0.21/0.47 ((((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(83,plain,
% 0.21/0.47 ((((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.47 tff(84,plain,
% 0.21/0.47 ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[83, 47])).
% 0.21/0.47 tff(85,assumption,(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))), introduced(assumption)).
% 0.21/0.47 tff(86,plain,
% 0.21/0.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(87,plain,
% 0.21/0.47 ((~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))) <=> (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(88,plain,
% 0.21/0.47 (((((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | $false) <=> (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(89,plain,
% 0.21/0.47 (($true | (((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)) <=> in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)))) <=> $true),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(90,plain,
% 0.21/0.47 ((set_difference(A!6, C!4) = set_difference(A!6, C!4)) <=> $true),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(91,plain,
% 0.21/0.47 (((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)) <=> in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)))) <=> ($true | (((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)) <=> in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.47 tff(92,plain,
% 0.21/0.47 (((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)) <=> in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)))) <=> $true),
% 0.21/0.47 inference(transitivity,[status(thm)],[91, 89])).
% 0.21/0.47 tff(93,plain,
% 0.21/0.47 ((~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)) <=> in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4))))) <=> (~$true)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.47 tff(94,plain,
% 0.21/0.47 ((~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)) <=> in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4))))) <=> $false),
% 0.21/0.47 inference(transitivity,[status(thm)],[93, 23])).
% 0.21/0.47 tff(95,plain,
% 0.21/0.47 ((~(~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))))) <=> (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(96,plain,
% 0.21/0.47 (($false | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))))) <=> (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(97,plain,
% 0.21/0.47 ((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) <=> (~$true)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.47 tff(98,plain,
% 0.21/0.47 ((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) <=> $false),
% 0.21/0.47 inference(transitivity,[status(thm)],[97, 23])).
% 0.21/0.47 tff(99,plain,
% 0.21/0.47 (((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))))) <=> ($false | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[98, 87])).
% 0.21/0.47 tff(100,plain,
% 0.21/0.47 (((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))))) <=> (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[99, 96])).
% 0.21/0.47 tff(101,plain,
% 0.21/0.47 ((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))))) <=> (~(~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[100])).
% 0.21/0.47 tff(102,plain,
% 0.21/0.47 ((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))))) <=> (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[101, 95])).
% 0.21/0.47 tff(103,plain,
% 0.21/0.47 (((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))))) | (~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)) <=> in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)))))) <=> ((((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | $false)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[102, 94])).
% 0.21/0.47 tff(104,plain,
% 0.21/0.47 (((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))))) | (~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)) <=> in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)))))) <=> (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[103, 88])).
% 0.21/0.47 tff(105,plain,
% 0.21/0.47 ((~((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))))) | (~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)) <=> in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4))))))) <=> (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[104])).
% 0.21/0.47 tff(106,plain,
% 0.21/0.47 ((~((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))))) | (~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)) <=> in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4))))))) <=> (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[105, 87])).
% 0.21/0.47 tff(107,plain,
% 0.21/0.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))))) | (~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)) <=> in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[106])).
% 0.21/0.47 tff(108,plain,
% 0.21/0.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))))) | (~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)) <=> in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[107, 86])).
% 0.21/0.47 tff(109,plain,
% 0.21/0.47 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))))) | (~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)) <=> in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(110,plain,
% 0.21/0.47 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.47 tff(111,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[110, 19, 85])).
% 0.21/0.47 tff(112,plain,(~(((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(114,plain,
% 0.21/0.47 (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[113, 79])).
% 0.21/0.47 tff(115,plain,
% 0.21/0.48 ((((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))) | (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(116,plain,
% 0.21/0.48 ((((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) <=> in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.21/0.48 tff(117,plain,
% 0.21/0.48 (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[116, 112])).
% 0.21/0.48 tff(118,plain,
% 0.21/0.48 (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) | (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(119,plain,
% 0.21/0.48 (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.21/0.48 tff(120,plain,
% 0.21/0.48 ((~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))) | (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(121,plain,
% 0.21/0.48 ((~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))) | (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.21/0.48 tff(122,plain,
% 0.21/0.48 (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[121, 84])).
% 0.21/0.48 tff(123,plain,
% 0.21/0.48 (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(124,plain,
% 0.21/0.48 (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[123, 117])).
% 0.21/0.48 tff(125,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_0(B!5, A!6), A!6)) | in(tptp_fun_C_0(B!5, A!6), B!5)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(126,plain,
% 0.21/0.48 (~((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_0(B!5, A!6), A!6)) | in(tptp_fun_C_0(B!5, A!6), B!5))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[125, 63])).
% 0.21/0.48 tff(127,plain,
% 0.21/0.48 (((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_0(B!5, A!6), A!6)) | in(tptp_fun_C_0(B!5, A!6), B!5)))))) | ((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(128,plain,
% 0.21/0.48 ((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.21/0.48 tff(129,plain,
% 0.21/0.48 (subset(A!6, B!5)),
% 0.21/0.48 inference(or_elim,[status(thm)],[75])).
% 0.21/0.48 tff(130,plain,
% 0.21/0.48 ((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(131,plain,
% 0.21/0.48 ((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.21/0.48 tff(132,plain,
% 0.21/0.48 (![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[131, 128])).
% 0.21/0.48 tff(133,plain,
% 0.21/0.48 (((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5))) <=> ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(134,plain,
% 0.21/0.48 ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(135,plain,
% 0.21/0.48 ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.48 tff(136,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[135, 132, 124, 122])).
% 0.21/0.48 % SZS output end Proof
% 0.21/0.48 % E exiting
%------------------------------------------------------------------------------