TSTP Solution File: SEU159+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU159+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 : Tue Sep 20 07:27:52 EDT 2022
% Result : Theorem 47.68s 30.47s
% Output : Proof 47.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU159+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 09:43:02 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 47.68/30.47 % SZS status Theorem
% 47.68/30.47 % SZS output start Proof
% 47.68/30.47 tff(in_type, type, (
% 47.68/30.47 in: ( $i * $i ) > $o)).
% 47.68/30.47 tff(set_union2_type, type, (
% 47.68/30.47 set_union2: ( $i * $i ) > $i)).
% 47.68/30.47 tff(unordered_pair_type, type, (
% 47.68/30.47 unordered_pair: ( $i * $i ) > $i)).
% 47.68/30.47 tff(tptp_fun_A_21_type, type, (
% 47.68/30.47 tptp_fun_A_21: $i)).
% 47.68/30.47 tff(tptp_fun_B_20_type, type, (
% 47.68/30.47 tptp_fun_B_20: $i)).
% 47.68/30.47 tff(tptp_fun_C_19_type, type, (
% 47.68/30.47 tptp_fun_C_19: $i)).
% 47.68/30.47 tff(set_difference_type, type, (
% 47.68/30.47 set_difference: ( $i * $i ) > $i)).
% 47.68/30.47 tff(subset_type, type, (
% 47.68/30.47 subset: ( $i * $i ) > $o)).
% 47.68/30.47 tff(tptp_fun_C_10_type, type, (
% 47.68/30.47 tptp_fun_C_10: ( $i * $i ) > $i)).
% 47.68/30.47 tff(tptp_fun_D_3_type, type, (
% 47.68/30.47 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 47.68/30.47 tff(singleton_type, type, (
% 47.68/30.47 singleton: $i > $i)).
% 47.68/30.47 tff(tptp_fun_C_0_type, type, (
% 47.68/30.47 tptp_fun_C_0: ( $i * $i ) > $i)).
% 47.68/30.47 tff(tptp_fun_D_4_type, type, (
% 47.68/30.47 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 47.68/30.47 tff(1,plain,
% 47.68/30.47 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 47.68/30.47 inference(bind,[status(th)],[])).
% 47.68/30.47 tff(2,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 47.68/30.47 inference(quant_intro,[status(thm)],[1])).
% 47.68/30.47 tff(3,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 47.68/30.47 inference(pull_quant,[status(thm)],[])).
% 47.68/30.47 tff(4,plain,
% 47.68/30.47 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> (~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), pull_quant((~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A)))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))) <=> (?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))), pull_quant((?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> (~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))), pull_quant((~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))))),
% 47.68/30.47 inference(bind,[status(th)],[])).
% 47.68/30.47 tff(5,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 47.68/30.47 inference(quant_intro,[status(thm)],[4])).
% 47.68/30.47 tff(6,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 47.68/30.47 inference(transitivity,[status(thm)],[5, 3])).
% 47.68/30.47 tff(7,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 47.68/30.47 inference(transitivity,[status(thm)],[6, 2])).
% 47.68/30.47 tff(8,plain,
% 47.68/30.47 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 47.68/30.47 inference(bind,[status(th)],[])).
% 47.68/30.47 tff(9,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 47.68/30.47 inference(quant_intro,[status(thm)],[8])).
% 47.68/30.47 tff(10,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 47.68/30.47 inference(transitivity,[status(thm)],[9, 7])).
% 47.68/30.47 tff(11,plain,
% 47.68/30.47 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))), rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))))),
% 47.68/30.47 inference(bind,[status(th)],[])).
% 47.68/30.47 tff(12,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 47.68/30.47 inference(quant_intro,[status(thm)],[11])).
% 47.68/30.47 tff(13,plain,
% 47.68/30.47 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))),
% 47.68/30.47 inference(bind,[status(th)],[])).
% 47.68/30.47 tff(14,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))),
% 47.68/30.47 inference(quant_intro,[status(thm)],[13])).
% 47.68/30.47 tff(15,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 47.68/30.47 inference(rewrite,[status(thm)],[])).
% 47.68/30.47 tff(16,plain,
% 47.68/30.47 (^[A: $i, B: $i, C: $i] : rewrite(((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))))),
% 47.68/30.47 inference(bind,[status(th)],[])).
% 47.68/30.47 tff(17,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 47.68/30.47 inference(quant_intro,[status(thm)],[16])).
% 47.68/30.47 tff(18,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_tarski')).
% 47.68/30.47 tff(19,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 47.68/30.47 inference(modus_ponens,[status(thm)],[18, 17])).
% 47.68/30.47 tff(20,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 47.68/30.47 inference(modus_ponens,[status(thm)],[19, 15])).
% 47.68/30.47 tff(21,plain,(
% 47.68/30.47 ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))),
% 47.68/30.47 inference(skolemize,[status(sab)],[20])).
% 47.68/30.47 tff(22,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))),
% 47.68/30.47 inference(modus_ponens,[status(thm)],[21, 14])).
% 47.68/30.47 tff(23,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 47.68/30.47 inference(modus_ponens,[status(thm)],[22, 12])).
% 47.68/30.47 tff(24,plain,
% 47.68/30.47 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 47.68/30.47 inference(modus_ponens,[status(thm)],[23, 10])).
% 47.68/30.47 tff(25,plain,
% 47.68/30.47 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))),
% 47.68/30.47 inference(quant_inst,[status(thm)],[])).
% 47.68/30.47 tff(26,plain,
% 47.68/30.47 (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))),
% 47.68/30.47 inference(unit_resolution,[status(thm)],[25, 24])).
% 47.68/30.47 tff(27,plain,
% 47.68/30.47 (((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))) | ((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))))),
% 47.68/30.47 inference(tautology,[status(thm)],[])).
% 47.68/30.47 tff(28,plain,
% 47.68/30.47 ((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 47.68/30.47 inference(unit_resolution,[status(thm)],[27, 26])).
% 47.68/30.47 tff(29,plain,
% 47.68/30.47 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 47.68/30.47 inference(bind,[status(th)],[])).
% 47.68/30.47 tff(30,plain,
% 47.68/30.47 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 47.68/30.47 inference(quant_intro,[status(thm)],[29])).
% 47.68/30.47 tff(31,plain,
% 47.68/30.47 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 47.68/30.47 inference(rewrite,[status(thm)],[])).
% 47.68/30.47 tff(32,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 47.68/30.47 tff(33,plain,
% 47.68/30.47 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 47.68/30.47 inference(modus_ponens,[status(thm)],[32, 31])).
% 47.68/30.47 tff(34,plain,(
% 47.68/30.47 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 47.68/30.47 inference(skolemize,[status(sab)],[33])).
% 47.68/30.47 tff(35,plain,
% 47.68/30.47 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 47.68/30.47 inference(modus_ponens,[status(thm)],[34, 30])).
% 47.68/30.47 tff(36,plain,
% 47.68/30.47 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))),
% 47.68/30.47 inference(quant_inst,[status(thm)],[])).
% 47.68/30.47 tff(37,plain,
% 47.68/30.47 (unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)),
% 47.68/30.47 inference(unit_resolution,[status(thm)],[36, 35])).
% 47.68/30.47 tff(38,plain,
% 47.68/30.47 ((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))))) | (~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 47.68/30.47 inference(tautology,[status(thm)],[])).
% 47.68/30.47 tff(39,plain,
% 47.68/30.47 ((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 47.68/30.48 inference(unit_resolution,[status(thm)],[38, 37])).
% 47.68/30.48 tff(40,plain,
% 47.68/30.48 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 47.68/30.48 inference(unit_resolution,[status(thm)],[39, 28])).
% 47.68/30.48 tff(41,plain,
% 47.68/30.48 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!21, B!20) = unordered_pair(B!20, A!21))),
% 47.68/30.48 inference(quant_inst,[status(thm)],[])).
% 47.68/30.48 tff(42,plain,
% 47.68/30.48 (unordered_pair(A!21, B!20) = unordered_pair(B!20, A!21)),
% 47.68/30.48 inference(unit_resolution,[status(thm)],[41, 35])).
% 47.68/30.48 tff(43,plain,
% 47.68/30.48 (unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)),
% 47.68/30.48 inference(symmetry,[status(thm)],[42])).
% 47.68/30.48 tff(44,plain,
% 47.68/30.48 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))),
% 47.68/30.48 inference(monotonicity,[status(thm)],[43])).
% 47.68/30.48 tff(45,plain,
% 47.68/30.48 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20)) <=> in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21))),
% 47.68/30.48 inference(symmetry,[status(thm)],[44])).
% 47.68/30.48 tff(46,assumption,(~((~in(A!21, C!19)) | (~in(B!20, C!19)))), introduced(assumption)).
% 47.68/30.48 tff(47,plain,
% 47.68/30.48 (((~subset(unordered_pair(A!21, B!20), C!19)) <=> (~((~in(A!21, C!19)) | (~in(B!20, C!19))))) <=> (subset(unordered_pair(A!21, B!20), C!19) <=> ((~in(A!21, C!19)) | (~in(B!20, C!19))))),
% 47.68/30.48 inference(rewrite,[status(thm)],[])).
% 47.68/30.48 tff(48,plain,
% 47.68/30.48 ((in(A!21, C!19) & in(B!20, C!19)) <=> (~((~in(A!21, C!19)) | (~in(B!20, C!19))))),
% 47.68/30.48 inference(rewrite,[status(thm)],[])).
% 47.68/30.48 tff(49,plain,
% 47.68/30.48 (((~subset(unordered_pair(A!21, B!20), C!19)) <=> (in(A!21, C!19) & in(B!20, C!19))) <=> ((~subset(unordered_pair(A!21, B!20), C!19)) <=> (~((~in(A!21, C!19)) | (~in(B!20, C!19)))))),
% 47.68/30.48 inference(monotonicity,[status(thm)],[48])).
% 47.68/30.48 tff(50,plain,
% 47.68/30.48 (((~subset(unordered_pair(A!21, B!20), C!19)) <=> (in(A!21, C!19) & in(B!20, C!19))) <=> (subset(unordered_pair(A!21, B!20), C!19) <=> ((~in(A!21, C!19)) | (~in(B!20, C!19))))),
% 47.68/30.48 inference(transitivity,[status(thm)],[49, 47])).
% 47.68/30.48 tff(51,plain,
% 47.68/30.48 ((~(subset(unordered_pair(A!21, B!20), C!19) <=> (in(A!21, C!19) & in(B!20, C!19)))) <=> ((~subset(unordered_pair(A!21, B!20), C!19)) <=> (in(A!21, C!19) & in(B!20, C!19)))),
% 47.68/30.48 inference(rewrite,[status(thm)],[])).
% 47.68/30.48 tff(52,plain,
% 47.68/30.48 ((~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))) <=> (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C))))),
% 47.68/30.48 inference(rewrite,[status(thm)],[])).
% 47.68/30.48 tff(53,axiom,(~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t38_zfmisc_1')).
% 47.68/30.48 tff(54,plain,
% 47.68/30.48 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[53, 52])).
% 47.68/30.48 tff(55,plain,
% 47.68/30.48 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[54, 52])).
% 47.68/30.48 tff(56,plain,
% 47.68/30.48 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[55, 52])).
% 47.68/30.48 tff(57,plain,
% 47.68/30.48 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[56, 52])).
% 47.68/30.48 tff(58,plain,
% 47.68/30.48 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[57, 52])).
% 47.68/30.48 tff(59,plain,
% 47.68/30.48 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[58, 52])).
% 47.68/30.48 tff(60,plain,
% 47.68/30.48 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[59, 52])).
% 47.68/30.48 tff(61,plain,(
% 47.68/30.48 ~(subset(unordered_pair(A!21, B!20), C!19) <=> (in(A!21, C!19) & in(B!20, C!19)))),
% 47.68/30.48 inference(skolemize,[status(sab)],[60])).
% 47.68/30.48 tff(62,plain,
% 47.68/30.48 ((~subset(unordered_pair(A!21, B!20), C!19)) <=> (in(A!21, C!19) & in(B!20, C!19))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[61, 51])).
% 47.68/30.48 tff(63,plain,
% 47.68/30.48 (subset(unordered_pair(A!21, B!20), C!19) <=> ((~in(A!21, C!19)) | (~in(B!20, C!19)))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[62, 50])).
% 47.68/30.48 tff(64,plain,
% 47.68/30.48 ((~subset(unordered_pair(A!21, B!20), C!19)) | ((~in(A!21, C!19)) | (~in(B!20, C!19))) | (~(subset(unordered_pair(A!21, B!20), C!19) <=> ((~in(A!21, C!19)) | (~in(B!20, C!19)))))),
% 47.68/30.48 inference(tautology,[status(thm)],[])).
% 47.68/30.48 tff(65,plain,
% 47.68/30.48 ((~subset(unordered_pair(A!21, B!20), C!19)) | ((~in(A!21, C!19)) | (~in(B!20, C!19)))),
% 47.68/30.48 inference(unit_resolution,[status(thm)],[64, 63])).
% 47.68/30.48 tff(66,plain,
% 47.68/30.48 (~subset(unordered_pair(A!21, B!20), C!19)),
% 47.68/30.48 inference(unit_resolution,[status(thm)],[65, 46])).
% 47.68/30.48 tff(67,plain,
% 47.68/30.48 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))))),
% 47.68/30.48 inference(bind,[status(th)],[])).
% 47.68/30.48 tff(68,plain,
% 47.68/30.48 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(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_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 47.68/30.48 inference(quant_intro,[status(thm)],[67])).
% 47.68/30.48 tff(69,plain,
% 47.68/30.48 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))))),
% 47.68/30.48 inference(bind,[status(th)],[])).
% 47.68/30.48 tff(70,plain,
% 47.68/30.48 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(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_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 47.68/30.48 inference(quant_intro,[status(thm)],[69])).
% 47.68/30.48 tff(71,plain,
% 47.68/30.48 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(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_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 47.68/30.48 inference(transitivity,[status(thm)],[70, 68])).
% 47.68/30.48 tff(72,plain,
% 47.68/30.48 (^[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_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))))),
% 47.68/30.48 inference(bind,[status(th)],[])).
% 47.68/30.48 tff(73,plain,
% 47.68/30.48 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(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_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 47.68/30.48 inference(quant_intro,[status(thm)],[72])).
% 47.68/30.48 tff(74,plain,
% 47.68/30.48 (![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)))),
% 47.68/30.48 inference(rewrite,[status(thm)],[])).
% 47.68/30.48 tff(75,plain,
% 47.68/30.48 (^[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))))),
% 47.68/30.48 inference(bind,[status(th)],[])).
% 47.68/30.48 tff(76,plain,
% 47.68/30.48 (![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)))),
% 47.68/30.48 inference(quant_intro,[status(thm)],[75])).
% 47.68/30.48 tff(77,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')).
% 47.68/30.48 tff(78,plain,
% 47.68/30.48 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[77, 76])).
% 47.68/30.48 tff(79,plain,
% 47.68/30.48 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[78, 74])).
% 47.68/30.48 tff(80,plain,(
% 47.68/30.48 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))),
% 47.68/30.48 inference(skolemize,[status(sab)],[79])).
% 47.68/30.48 tff(81,plain,
% 47.68/30.48 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[80, 73])).
% 47.68/30.48 tff(82,plain,
% 47.68/30.48 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[81, 71])).
% 47.68/30.48 tff(83,plain,
% 47.68/30.48 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))) | (~((~((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19)))) | (~(subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)))))))),
% 47.68/30.48 inference(quant_inst,[status(thm)],[])).
% 47.68/30.48 tff(84,plain,
% 47.68/30.48 (~((~((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19)))) | (~(subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))))),
% 47.68/30.48 inference(unit_resolution,[status(thm)],[83, 82])).
% 47.68/30.48 tff(85,plain,
% 47.68/30.48 (((~((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19)))) | (~(subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)))))) | (subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))),
% 47.68/30.48 inference(tautology,[status(thm)],[])).
% 47.68/30.48 tff(86,plain,
% 47.68/30.48 (subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)))),
% 47.68/30.48 inference(unit_resolution,[status(thm)],[85, 84])).
% 47.68/30.48 tff(87,plain,
% 47.68/30.48 ((~(subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)))),
% 47.68/30.48 inference(tautology,[status(thm)],[])).
% 47.68/30.48 tff(88,plain,
% 47.68/30.48 (subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)))),
% 47.68/30.48 inference(unit_resolution,[status(thm)],[87, 86])).
% 47.68/30.48 tff(89,plain,
% 47.68/30.48 (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))),
% 47.68/30.48 inference(unit_resolution,[status(thm)],[88, 66])).
% 47.68/30.48 tff(90,plain,
% 47.68/30.48 (((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))),
% 47.68/30.48 inference(tautology,[status(thm)],[])).
% 47.68/30.48 tff(91,plain,
% 47.68/30.48 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))),
% 47.68/30.48 inference(unit_resolution,[status(thm)],[90, 89])).
% 47.68/30.48 tff(92,plain,
% 47.68/30.48 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[91, 45])).
% 47.68/30.48 tff(93,plain,
% 47.68/30.48 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21))) | ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 47.68/30.48 inference(tautology,[status(thm)],[])).
% 47.68/30.48 tff(94,plain,
% 47.68/30.48 ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)),
% 47.68/30.48 inference(unit_resolution,[status(thm)],[93, 92, 40])).
% 47.68/30.48 tff(95,plain,
% 47.68/30.48 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 47.68/30.48 inference(bind,[status(th)],[])).
% 47.68/30.48 tff(96,plain,
% 47.68/30.48 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 47.68/30.48 inference(quant_intro,[status(thm)],[95])).
% 47.68/30.48 tff(97,plain,
% 47.68/30.48 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 47.68/30.48 inference(pull_quant,[status(thm)],[])).
% 47.68/30.48 tff(98,plain,
% 47.68/30.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 47.68/30.48 inference(bind,[status(th)],[])).
% 47.68/30.48 tff(99,plain,
% 47.68/30.48 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 47.68/30.48 inference(quant_intro,[status(thm)],[98])).
% 47.68/30.48 tff(100,plain,
% 47.68/30.48 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 47.68/30.48 inference(transitivity,[status(thm)],[99, 97])).
% 47.68/30.48 tff(101,plain,
% 47.68/30.48 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 47.68/30.48 inference(transitivity,[status(thm)],[100, 96])).
% 47.68/30.48 tff(102,plain,
% 47.68/30.48 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 47.68/30.48 inference(bind,[status(th)],[])).
% 47.68/30.48 tff(103,plain,
% 47.68/30.48 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 47.68/30.48 inference(quant_intro,[status(thm)],[102])).
% 47.68/30.48 tff(104,plain,
% 47.68/30.48 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 47.68/30.48 inference(transitivity,[status(thm)],[103, 101])).
% 47.68/30.48 tff(105,plain,
% 47.68/30.48 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 47.68/30.48 inference(bind,[status(th)],[])).
% 47.68/30.48 tff(106,plain,
% 47.68/30.48 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 47.68/30.48 inference(quant_intro,[status(thm)],[105])).
% 47.68/30.48 tff(107,plain,
% 47.68/30.48 (^[A: $i, B: $i] : rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))),
% 47.68/30.48 inference(bind,[status(th)],[])).
% 47.68/30.48 tff(108,plain,
% 47.68/30.48 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 47.68/30.48 inference(quant_intro,[status(thm)],[107])).
% 47.68/30.48 tff(109,plain,
% 47.68/30.48 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 47.68/30.48 inference(rewrite,[status(thm)],[])).
% 47.68/30.48 tff(110,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 47.68/30.48 tff(111,plain,
% 47.68/30.48 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[110, 109])).
% 47.68/30.48 tff(112,plain,(
% 47.68/30.48 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 47.68/30.48 inference(skolemize,[status(sab)],[111])).
% 47.68/30.48 tff(113,plain,
% 47.68/30.48 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[112, 108])).
% 47.68/30.48 tff(114,plain,
% 47.68/30.48 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[113, 106])).
% 47.68/30.48 tff(115,plain,
% 47.68/30.48 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 47.68/30.48 inference(modus_ponens,[status(thm)],[114, 104])).
% 47.68/30.48 tff(116,plain,
% 47.68/30.48 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 47.68/30.48 inference(rewrite,[status(thm)],[])).
% 47.68/30.48 tff(117,plain,
% 47.68/30.48 ((~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 47.68/30.48 inference(rewrite,[status(thm)],[])).
% 47.68/30.48 tff(118,plain,
% 47.68/30.48 ((((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)) | $false) <=> ((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 47.68/30.48 inference(rewrite,[status(thm)],[])).
% 47.68/30.48 tff(119,plain,
% 47.68/30.48 ((~$true) <=> $false),
% 47.68/30.48 inference(rewrite,[status(thm)],[])).
% 47.68/30.48 tff(120,plain,
% 47.68/30.48 (($true | ((~in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20))) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20))) <=> $true),
% 47.68/30.48 inference(rewrite,[status(thm)],[])).
% 47.68/30.48 tff(121,plain,
% 47.68/30.48 ((singleton(B!20) = singleton(B!20)) <=> $true),
% 47.68/30.48 inference(rewrite,[status(thm)],[])).
% 47.68/30.48 tff(122,plain,
% 47.68/30.48 (((singleton(B!20) = singleton(B!20)) | ((~in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20))) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20))) <=> ($true | ((~in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20))) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20)))),
% 47.68/30.48 inference(monotonicity,[status(thm)],[121])).
% 47.68/30.48 tff(123,plain,
% 47.68/30.48 (((singleton(B!20) = singleton(B!20)) | ((~in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20))) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20))) <=> $true),
% 47.68/30.48 inference(transitivity,[status(thm)],[122, 120])).
% 47.68/30.48 tff(124,plain,
% 47.68/30.48 ((~((singleton(B!20) = singleton(B!20)) | ((~in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20))) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20)))) <=> (~$true)),
% 47.68/30.48 inference(monotonicity,[status(thm)],[123])).
% 47.68/30.48 tff(125,plain,
% 47.68/30.48 ((~((singleton(B!20) = singleton(B!20)) | ((~in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20))) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20)))) <=> $false),
% 47.68/30.48 inference(transitivity,[status(thm)],[124, 119])).
% 47.68/30.48 tff(126,plain,
% 47.68/30.48 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) <=> ((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 47.68/30.48 inference(rewrite,[status(thm)],[])).
% 47.68/30.48 tff(127,plain,
% 47.68/30.48 (($false | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 47.68/30.48 inference(rewrite,[status(thm)],[])).
% 47.68/30.48 tff(128,plain,
% 47.68/30.48 ((~(singleton(B!20) = singleton(B!20))) <=> (~$true)),
% 47.68/30.48 inference(monotonicity,[status(thm)],[121])).
% 47.68/30.48 tff(129,plain,
% 47.68/30.48 ((~(singleton(B!20) = singleton(B!20))) <=> $false),
% 47.68/30.48 inference(transitivity,[status(thm)],[128, 119])).
% 47.68/30.48 tff(130,plain,
% 47.68/30.48 (((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) <=> ($false | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 47.68/30.49 inference(monotonicity,[status(thm)],[129])).
% 47.68/30.49 tff(131,plain,
% 47.68/30.49 (((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 47.68/30.49 inference(transitivity,[status(thm)],[130, 127])).
% 47.68/30.49 tff(132,plain,
% 47.68/30.49 ((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) <=> (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 47.68/30.49 inference(monotonicity,[status(thm)],[131])).
% 47.68/30.49 tff(133,plain,
% 47.68/30.49 ((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) <=> ((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 47.68/30.49 inference(transitivity,[status(thm)],[132, 126])).
% 47.68/30.49 tff(134,plain,
% 47.68/30.49 (((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) | (~((singleton(B!20) = singleton(B!20)) | ((~in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20))) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20))))) <=> (((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)) | $false)),
% 47.68/30.49 inference(monotonicity,[status(thm)],[133, 125])).
% 47.68/30.49 tff(135,plain,
% 47.68/30.49 (((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) | (~((singleton(B!20) = singleton(B!20)) | ((~in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20))) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20))))) <=> ((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 47.68/30.49 inference(transitivity,[status(thm)],[134, 118])).
% 47.68/30.49 tff(136,plain,
% 47.68/30.49 ((~((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) | (~((singleton(B!20) = singleton(B!20)) | ((~in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20))) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20)))))) <=> (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 47.68/30.49 inference(monotonicity,[status(thm)],[135])).
% 47.68/30.49 tff(137,plain,
% 47.68/30.49 ((~((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) | (~((singleton(B!20) = singleton(B!20)) | ((~in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20))) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20)))))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 47.68/30.49 inference(transitivity,[status(thm)],[136, 117])).
% 47.68/30.49 tff(138,plain,
% 47.68/30.49 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) | (~((singleton(B!20) = singleton(B!20)) | ((~in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20))) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 47.68/30.49 inference(monotonicity,[status(thm)],[137])).
% 47.68/30.49 tff(139,plain,
% 47.68/30.49 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) | (~((singleton(B!20) = singleton(B!20)) | ((~in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20))) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 47.68/30.49 inference(transitivity,[status(thm)],[138, 116])).
% 47.68/30.49 tff(140,plain,
% 47.68/30.49 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) | (~((singleton(B!20) = singleton(B!20)) | ((~in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20))) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20))))))),
% 47.68/30.49 inference(quant_inst,[status(thm)],[])).
% 47.68/30.49 tff(141,plain,
% 47.68/30.49 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 47.68/30.49 inference(modus_ponens,[status(thm)],[140, 139])).
% 47.68/30.49 tff(142,plain,
% 47.68/30.49 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)),
% 47.68/30.49 inference(unit_resolution,[status(thm)],[141, 115])).
% 47.68/30.49 tff(143,plain,
% 47.68/30.49 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))),
% 47.68/30.49 inference(bind,[status(th)],[])).
% 47.68/30.49 tff(144,plain,
% 47.68/30.49 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 47.68/30.49 inference(quant_intro,[status(thm)],[143])).
% 47.68/30.49 tff(145,plain,
% 47.68/30.49 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 47.68/30.49 inference(pull_quant,[status(thm)],[])).
% 47.68/30.49 tff(146,plain,
% 47.68/30.49 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))))),
% 47.68/30.49 inference(bind,[status(th)],[])).
% 47.68/30.49 tff(147,plain,
% 47.68/30.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 47.68/30.49 inference(quant_intro,[status(thm)],[146])).
% 47.68/30.49 tff(148,plain,
% 47.68/30.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 47.68/30.49 inference(transitivity,[status(thm)],[147, 145])).
% 47.68/30.49 tff(149,plain,
% 47.68/30.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 47.68/30.49 inference(transitivity,[status(thm)],[148, 144])).
% 47.68/30.49 tff(150,plain,
% 47.68/30.49 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))),
% 47.68/30.49 inference(bind,[status(th)],[])).
% 47.68/30.49 tff(151,plain,
% 47.68/30.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 47.68/30.49 inference(quant_intro,[status(thm)],[150])).
% 47.68/30.49 tff(152,plain,
% 47.68/30.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 47.68/30.49 inference(transitivity,[status(thm)],[151, 149])).
% 47.68/30.49 tff(153,plain,
% 47.68/30.49 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), monotonicity(rewrite(((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))) <=> ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))), (((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))) <=> ((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))))),
% 47.68/30.49 inference(bind,[status(th)],[])).
% 47.68/30.49 tff(154,plain,
% 47.68/30.49 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 47.68/30.49 inference(quant_intro,[status(thm)],[153])).
% 47.68/30.49 tff(155,plain,
% 47.68/30.49 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))),
% 47.68/30.49 inference(bind,[status(th)],[])).
% 47.68/30.49 tff(156,plain,
% 47.68/30.49 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))),
% 47.68/30.49 inference(quant_intro,[status(thm)],[155])).
% 47.68/30.49 tff(157,plain,
% 47.68/30.49 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 47.68/30.49 inference(rewrite,[status(thm)],[])).
% 47.68/30.49 tff(158,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_xboole_0')).
% 47.68/30.49 tff(159,plain,
% 47.68/30.49 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 47.68/30.49 inference(modus_ponens,[status(thm)],[158, 157])).
% 47.68/30.49 tff(160,plain,(
% 47.68/30.49 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))),
% 47.68/30.49 inference(skolemize,[status(sab)],[159])).
% 47.68/30.49 tff(161,plain,
% 47.68/30.49 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))),
% 47.68/30.49 inference(modus_ponens,[status(thm)],[160, 156])).
% 47.68/30.49 tff(162,plain,
% 47.68/30.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 47.68/30.49 inference(modus_ponens,[status(thm)],[161, 154])).
% 47.68/30.49 tff(163,plain,
% 47.68/30.49 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 47.68/30.49 inference(modus_ponens,[status(thm)],[162, 152])).
% 47.68/30.49 tff(164,plain,
% 47.68/30.49 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)))))))))),
% 47.68/30.49 inference(rewrite,[status(thm)],[])).
% 47.68/30.49 tff(165,plain,
% 47.68/30.49 ((~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19))))))) <=> (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20))))))))),
% 47.68/30.49 inference(rewrite,[status(thm)],[])).
% 47.68/30.49 tff(166,plain,
% 47.68/30.49 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)))))))))),
% 47.68/30.49 inference(monotonicity,[status(thm)],[165])).
% 47.68/30.49 tff(167,plain,
% 47.68/30.49 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)))))))))),
% 47.68/30.49 inference(transitivity,[status(thm)],[166, 164])).
% 47.68/30.49 tff(168,plain,
% 47.68/30.49 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)))))))),
% 47.68/30.49 inference(quant_inst,[status(thm)],[])).
% 47.68/30.49 tff(169,plain,
% 47.68/30.49 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20))))))))),
% 47.68/30.49 inference(modus_ponens,[status(thm)],[168, 167])).
% 47.68/30.49 tff(170,plain,
% 47.68/30.49 (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)))))))),
% 47.68/30.49 inference(unit_resolution,[status(thm)],[169, 163])).
% 47.68/30.49 tff(171,plain,
% 47.68/30.49 (((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20))))))) | ((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))),
% 47.68/30.49 inference(tautology,[status(thm)],[])).
% 47.68/30.49 tff(172,plain,
% 47.68/30.49 ((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))))),
% 47.68/30.49 inference(unit_resolution,[status(thm)],[171, 170])).
% 47.68/30.49 tff(173,plain,
% 47.68/30.49 (((~in(A!21, C!19)) | (~in(B!20, C!19))) | in(B!20, C!19)),
% 47.68/30.49 inference(tautology,[status(thm)],[])).
% 47.68/30.49 tff(174,plain,
% 47.68/30.49 (in(B!20, C!19)),
% 47.68/30.49 inference(unit_resolution,[status(thm)],[173, 46])).
% 47.68/30.49 tff(175,plain,
% 47.68/30.49 (^[A: $i, B: $i] : refl(((~in(A, B)) | (set_union2(singleton(A), B) = B)) <=> ((~in(A, B)) | (set_union2(singleton(A), B) = B)))),
% 47.68/30.49 inference(bind,[status(th)],[])).
% 47.68/30.49 tff(176,plain,
% 47.68/30.49 (![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 47.68/30.49 inference(quant_intro,[status(thm)],[175])).
% 47.68/30.49 tff(177,plain,
% 47.68/30.49 (![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 47.68/30.49 inference(rewrite,[status(thm)],[])).
% 47.68/30.49 tff(178,plain,
% 47.68/30.49 (^[A: $i, B: $i] : rewrite((in(A, B) => (set_union2(singleton(A), B) = B)) <=> ((~in(A, B)) | (set_union2(singleton(A), B) = B)))),
% 47.68/30.49 inference(bind,[status(th)],[])).
% 47.68/30.49 tff(179,plain,
% 47.68/30.49 (![A: $i, B: $i] : (in(A, B) => (set_union2(singleton(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 47.68/30.49 inference(quant_intro,[status(thm)],[178])).
% 47.68/30.49 tff(180,axiom,(![A: $i, B: $i] : (in(A, B) => (set_union2(singleton(A), B) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l23_zfmisc_1')).
% 47.68/30.49 tff(181,plain,
% 47.68/30.49 (![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 47.68/30.49 inference(modus_ponens,[status(thm)],[180, 179])).
% 47.68/30.49 tff(182,plain,
% 47.68/30.49 (![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 47.68/30.49 inference(modus_ponens,[status(thm)],[181, 177])).
% 47.68/30.49 tff(183,plain,(
% 47.68/30.49 ![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 47.68/30.49 inference(skolemize,[status(sab)],[182])).
% 47.68/30.49 tff(184,plain,
% 47.68/30.49 (![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 47.68/30.49 inference(modus_ponens,[status(thm)],[183, 176])).
% 47.68/30.49 tff(185,plain,
% 47.68/30.49 (((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | ((~in(B!20, C!19)) | (set_union2(singleton(B!20), C!19) = C!19))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | (~in(B!20, C!19)) | (set_union2(singleton(B!20), C!19) = C!19))),
% 47.68/30.49 inference(rewrite,[status(thm)],[])).
% 47.68/30.49 tff(186,plain,
% 47.68/30.49 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | ((~in(B!20, C!19)) | (set_union2(singleton(B!20), C!19) = C!19))),
% 47.68/30.49 inference(quant_inst,[status(thm)],[])).
% 47.68/30.49 tff(187,plain,
% 47.68/30.49 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | (~in(B!20, C!19)) | (set_union2(singleton(B!20), C!19) = C!19)),
% 47.68/30.49 inference(modus_ponens,[status(thm)],[186, 185])).
% 47.68/30.49 tff(188,plain,
% 47.68/30.49 (set_union2(singleton(B!20), C!19) = C!19),
% 47.68/30.49 inference(unit_resolution,[status(thm)],[187, 184, 174])).
% 47.68/30.49 tff(189,plain,
% 47.68/30.49 (C!19 = set_union2(singleton(B!20), C!19)),
% 47.68/30.49 inference(symmetry,[status(thm)],[188])).
% 47.68/30.49 tff(190,plain,
% 47.68/30.49 ((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))))),
% 47.68/30.50 inference(tautology,[status(thm)],[])).
% 47.68/30.50 tff(191,plain,
% 47.68/30.50 ((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))))),
% 47.68/30.50 inference(unit_resolution,[status(thm)],[190, 189])).
% 47.68/30.50 tff(192,plain,
% 47.68/30.50 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))),
% 47.68/30.50 inference(unit_resolution,[status(thm)],[191, 172])).
% 47.68/30.50 tff(193,plain,
% 47.68/30.50 (((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)) | (~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))),
% 47.68/30.50 inference(tautology,[status(thm)],[])).
% 47.68/30.50 tff(194,plain,
% 47.68/30.50 (~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)),
% 47.68/30.50 inference(unit_resolution,[status(thm)],[193, 89])).
% 47.68/30.50 tff(195,plain,
% 47.68/30.50 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))))),
% 47.68/30.50 inference(tautology,[status(thm)],[])).
% 47.68/30.50 tff(196,plain,
% 47.68/30.50 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))))) | (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))))),
% 47.68/30.50 inference(unit_resolution,[status(thm)],[195, 194])).
% 47.68/30.50 tff(197,plain,
% 47.68/30.50 (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))),
% 47.68/30.50 inference(unit_resolution,[status(thm)],[196, 192])).
% 47.68/30.50 tff(198,plain,
% 47.68/30.50 ((in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))) | (~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))),
% 47.68/30.50 inference(tautology,[status(thm)],[])).
% 47.68/30.50 tff(199,plain,
% 47.68/30.50 (~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))),
% 47.68/30.50 inference(unit_resolution,[status(thm)],[198, 197])).
% 47.68/30.50 tff(200,plain,
% 47.68/30.50 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) | (~(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 47.68/30.50 inference(tautology,[status(thm)],[])).
% 47.68/30.50 tff(201,plain,
% 47.68/30.50 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) | (~(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 47.68/30.50 inference(unit_resolution,[status(thm)],[200, 199])).
% 47.68/30.50 tff(202,plain,
% 47.68/30.50 (~(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)),
% 47.68/30.50 inference(unit_resolution,[status(thm)],[201, 142])).
% 47.68/30.50 tff(203,plain,
% 47.68/30.50 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 47.68/30.50 inference(rewrite,[status(thm)],[])).
% 47.68/30.50 tff(204,plain,
% 47.68/30.50 ((~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 47.68/30.50 inference(rewrite,[status(thm)],[])).
% 47.68/30.50 tff(205,plain,
% 47.68/30.50 ((((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)) | $false) <=> ((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 47.68/30.50 inference(rewrite,[status(thm)],[])).
% 47.68/30.50 tff(206,plain,
% 47.68/30.50 (($true | ((~in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21))) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21))) <=> $true),
% 47.68/30.50 inference(rewrite,[status(thm)],[])).
% 47.68/30.50 tff(207,plain,
% 47.68/30.50 ((singleton(A!21) = singleton(A!21)) <=> $true),
% 47.68/30.50 inference(rewrite,[status(thm)],[])).
% 47.68/30.50 tff(208,plain,
% 47.68/30.50 (((singleton(A!21) = singleton(A!21)) | ((~in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21))) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21))) <=> ($true | ((~in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21))) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21)))),
% 47.68/30.50 inference(monotonicity,[status(thm)],[207])).
% 47.68/30.50 tff(209,plain,
% 47.68/30.50 (((singleton(A!21) = singleton(A!21)) | ((~in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21))) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21))) <=> $true),
% 47.68/30.50 inference(transitivity,[status(thm)],[208, 206])).
% 47.68/30.50 tff(210,plain,
% 47.68/30.50 ((~((singleton(A!21) = singleton(A!21)) | ((~in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21))) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21)))) <=> (~$true)),
% 47.68/30.50 inference(monotonicity,[status(thm)],[209])).
% 47.68/30.50 tff(211,plain,
% 47.68/30.50 ((~((singleton(A!21) = singleton(A!21)) | ((~in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21))) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21)))) <=> $false),
% 47.68/30.50 inference(transitivity,[status(thm)],[210, 119])).
% 47.68/30.50 tff(212,plain,
% 47.68/30.50 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) <=> ((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 47.68/30.50 inference(rewrite,[status(thm)],[])).
% 47.68/30.50 tff(213,plain,
% 47.68/30.50 (($false | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 47.68/30.50 inference(rewrite,[status(thm)],[])).
% 47.68/30.50 tff(214,plain,
% 47.68/30.50 ((~(singleton(A!21) = singleton(A!21))) <=> (~$true)),
% 47.68/30.50 inference(monotonicity,[status(thm)],[207])).
% 47.68/30.50 tff(215,plain,
% 47.68/30.50 ((~(singleton(A!21) = singleton(A!21))) <=> $false),
% 47.68/30.50 inference(transitivity,[status(thm)],[214, 119])).
% 47.68/30.50 tff(216,plain,
% 47.68/30.50 (((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) <=> ($false | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 47.68/30.50 inference(monotonicity,[status(thm)],[215])).
% 47.68/30.50 tff(217,plain,
% 47.68/30.50 (((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 47.68/30.50 inference(transitivity,[status(thm)],[216, 213])).
% 47.68/30.50 tff(218,plain,
% 47.68/30.50 ((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) <=> (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 47.68/30.50 inference(monotonicity,[status(thm)],[217])).
% 47.68/30.50 tff(219,plain,
% 47.68/30.50 ((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) <=> ((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 47.68/30.50 inference(transitivity,[status(thm)],[218, 212])).
% 47.68/30.50 tff(220,plain,
% 47.68/30.50 (((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~((singleton(A!21) = singleton(A!21)) | ((~in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21))) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21))))) <=> (((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)) | $false)),
% 47.68/30.50 inference(monotonicity,[status(thm)],[219, 211])).
% 47.68/30.50 tff(221,plain,
% 47.68/30.50 (((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~((singleton(A!21) = singleton(A!21)) | ((~in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21))) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21))))) <=> ((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 47.68/30.50 inference(transitivity,[status(thm)],[220, 205])).
% 47.68/30.50 tff(222,plain,
% 47.68/30.50 ((~((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~((singleton(A!21) = singleton(A!21)) | ((~in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21))) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21)))))) <=> (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 47.68/30.50 inference(monotonicity,[status(thm)],[221])).
% 47.68/30.50 tff(223,plain,
% 47.68/30.50 ((~((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~((singleton(A!21) = singleton(A!21)) | ((~in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21))) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21)))))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 47.68/30.50 inference(transitivity,[status(thm)],[222, 204])).
% 47.68/30.50 tff(224,plain,
% 47.68/30.50 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~((singleton(A!21) = singleton(A!21)) | ((~in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21))) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 47.68/30.50 inference(monotonicity,[status(thm)],[223])).
% 47.68/30.50 tff(225,plain,
% 47.68/30.50 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~((singleton(A!21) = singleton(A!21)) | ((~in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21))) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 47.68/30.50 inference(transitivity,[status(thm)],[224, 203])).
% 47.68/30.50 tff(226,plain,
% 47.68/30.50 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~((singleton(A!21) = singleton(A!21)) | ((~in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21))) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21))))))),
% 47.68/30.50 inference(quant_inst,[status(thm)],[])).
% 47.68/30.50 tff(227,plain,
% 47.68/30.50 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 47.68/30.50 inference(modus_ponens,[status(thm)],[226, 225])).
% 47.68/30.50 tff(228,plain,
% 47.68/30.50 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)),
% 47.68/30.50 inference(unit_resolution,[status(thm)],[227, 115])).
% 47.68/30.50 tff(229,plain,
% 47.68/30.50 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21)))))))))),
% 47.68/30.50 inference(rewrite,[status(thm)],[])).
% 47.68/30.50 tff(230,plain,
% 47.68/30.50 ((~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21)) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19))))))) <=> (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21))))))))),
% 47.68/30.50 inference(rewrite,[status(thm)],[])).
% 47.68/30.50 tff(231,plain,
% 47.68/30.50 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21)) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21)))))))))),
% 47.68/30.50 inference(monotonicity,[status(thm)],[230])).
% 47.68/30.50 tff(232,plain,
% 47.68/30.50 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21)) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21)))))))))),
% 47.68/30.50 inference(transitivity,[status(thm)],[231, 229])).
% 47.68/30.50 tff(233,plain,
% 47.68/30.50 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21)) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)))))))),
% 47.68/30.50 inference(quant_inst,[status(thm)],[])).
% 47.68/30.50 tff(234,plain,
% 47.68/30.50 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21))))))))),
% 47.68/30.50 inference(modus_ponens,[status(thm)],[233, 232])).
% 47.68/30.50 tff(235,plain,
% 47.68/30.50 (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21)))))))),
% 47.68/30.50 inference(unit_resolution,[status(thm)],[234, 163])).
% 47.68/30.50 tff(236,plain,
% 47.68/30.50 (((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | ((~in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21))))))) | ((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))),
% 47.68/30.50 inference(tautology,[status(thm)],[])).
% 47.68/30.50 tff(237,plain,
% 47.68/30.50 ((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))))),
% 47.68/30.50 inference(unit_resolution,[status(thm)],[236, 235])).
% 47.68/30.50 tff(238,plain,
% 47.68/30.50 (((~in(A!21, C!19)) | (~in(B!20, C!19))) | in(A!21, C!19)),
% 47.68/30.50 inference(tautology,[status(thm)],[])).
% 47.68/30.50 tff(239,plain,
% 47.68/30.50 (in(A!21, C!19)),
% 47.68/30.50 inference(unit_resolution,[status(thm)],[238, 46])).
% 47.68/30.50 tff(240,plain,
% 47.68/30.50 (((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | ((~in(A!21, C!19)) | (set_union2(singleton(A!21), C!19) = C!19))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | (~in(A!21, C!19)) | (set_union2(singleton(A!21), C!19) = C!19))),
% 47.68/30.50 inference(rewrite,[status(thm)],[])).
% 47.68/30.50 tff(241,plain,
% 47.68/30.50 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | ((~in(A!21, C!19)) | (set_union2(singleton(A!21), C!19) = C!19))),
% 47.68/30.50 inference(quant_inst,[status(thm)],[])).
% 47.68/30.50 tff(242,plain,
% 47.68/30.50 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | (~in(A!21, C!19)) | (set_union2(singleton(A!21), C!19) = C!19)),
% 47.68/30.50 inference(modus_ponens,[status(thm)],[241, 240])).
% 47.68/30.50 tff(243,plain,
% 47.68/30.50 (set_union2(singleton(A!21), C!19) = C!19),
% 47.68/30.50 inference(unit_resolution,[status(thm)],[242, 184, 239])).
% 47.68/30.50 tff(244,plain,
% 47.68/30.50 (C!19 = set_union2(singleton(A!21), C!19)),
% 47.68/30.50 inference(symmetry,[status(thm)],[243])).
% 47.68/30.50 tff(245,plain,
% 47.68/30.50 ((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))))),
% 47.68/30.51 inference(tautology,[status(thm)],[])).
% 47.68/30.51 tff(246,plain,
% 47.68/30.51 ((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[245, 244])).
% 47.68/30.51 tff(247,plain,
% 47.68/30.51 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[246, 237])).
% 47.68/30.51 tff(248,plain,
% 47.68/30.51 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))))),
% 47.68/30.51 inference(tautology,[status(thm)],[])).
% 47.68/30.51 tff(249,plain,
% 47.68/30.51 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))))) | (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[248, 194])).
% 47.68/30.51 tff(250,plain,
% 47.68/30.51 (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[249, 247])).
% 47.68/30.51 tff(251,plain,
% 47.68/30.51 ((in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))) | (~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))),
% 47.68/30.51 inference(tautology,[status(thm)],[])).
% 47.68/30.51 tff(252,plain,
% 47.68/30.51 (~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[251, 250])).
% 47.68/30.51 tff(253,plain,
% 47.68/30.51 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) | (~(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 47.68/30.51 inference(tautology,[status(thm)],[])).
% 47.68/30.51 tff(254,plain,
% 47.68/30.51 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) | (~(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[253, 252])).
% 47.68/30.51 tff(255,plain,
% 47.68/30.51 (~(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[254, 228])).
% 47.68/30.51 tff(256,plain,
% 47.68/30.51 ((~((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)),
% 47.68/30.51 inference(tautology,[status(thm)],[])).
% 47.68/30.51 tff(257,plain,
% 47.68/30.51 ($false),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[256, 255, 202, 94])).
% 47.68/30.51 tff(258,plain,((~in(A!21, C!19)) | (~in(B!20, C!19))), inference(lemma,lemma(discharge,[]))).
% 47.68/30.51 tff(259,plain,
% 47.68/30.51 (subset(unordered_pair(A!21, B!20), C!19) | (~((~in(A!21, C!19)) | (~in(B!20, C!19)))) | (~(subset(unordered_pair(A!21, B!20), C!19) <=> ((~in(A!21, C!19)) | (~in(B!20, C!19)))))),
% 47.68/30.51 inference(tautology,[status(thm)],[])).
% 47.68/30.51 tff(260,plain,
% 47.68/30.51 (subset(unordered_pair(A!21, B!20), C!19) | (~((~in(A!21, C!19)) | (~in(B!20, C!19))))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[259, 63])).
% 47.68/30.51 tff(261,plain,
% 47.68/30.51 (subset(unordered_pair(A!21, B!20), C!19)),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[260, 258])).
% 47.68/30.51 tff(262,plain,
% 47.68/30.51 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 47.68/30.51 inference(bind,[status(th)],[])).
% 47.68/30.51 tff(263,plain,
% 47.68/30.51 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 47.68/30.51 inference(quant_intro,[status(thm)],[262])).
% 47.68/30.51 tff(264,plain,
% 47.68/30.51 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 47.68/30.51 inference(rewrite,[status(thm)],[])).
% 47.68/30.51 tff(265,plain,
% 47.68/30.51 (^[A: $i, B: $i] : rewrite((subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 47.68/30.51 inference(bind,[status(th)],[])).
% 47.68/30.51 tff(266,plain,
% 47.68/30.51 (![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 47.68/30.51 inference(quant_intro,[status(thm)],[265])).
% 47.68/30.51 tff(267,axiom,(![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t45_xboole_1')).
% 47.68/30.51 tff(268,plain,
% 47.68/30.51 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 47.68/30.51 inference(modus_ponens,[status(thm)],[267, 266])).
% 47.68/30.51 tff(269,plain,
% 47.68/30.51 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 47.68/30.51 inference(modus_ponens,[status(thm)],[268, 264])).
% 47.68/30.51 tff(270,plain,(
% 47.68/30.51 ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 47.68/30.51 inference(skolemize,[status(sab)],[269])).
% 47.68/30.51 tff(271,plain,
% 47.68/30.51 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 47.68/30.51 inference(modus_ponens,[status(thm)],[270, 263])).
% 47.68/30.51 tff(272,plain,
% 47.68/30.51 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(unordered_pair(A!21, B!20), C!19)) | (C!19 = set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20)))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(unordered_pair(A!21, B!20), C!19)) | (C!19 = set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20)))))),
% 47.68/30.51 inference(rewrite,[status(thm)],[])).
% 47.68/30.51 tff(273,plain,
% 47.68/30.51 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(unordered_pair(A!21, B!20), C!19)) | (C!19 = set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20)))))),
% 47.68/30.51 inference(quant_inst,[status(thm)],[])).
% 47.68/30.51 tff(274,plain,
% 47.68/30.51 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(unordered_pair(A!21, B!20), C!19)) | (C!19 = set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20))))),
% 47.68/30.51 inference(modus_ponens,[status(thm)],[273, 272])).
% 47.68/30.51 tff(275,plain,
% 47.68/30.51 ((~subset(unordered_pair(A!21, B!20), C!19)) | (C!19 = set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20))))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[274, 271])).
% 47.68/30.51 tff(276,plain,
% 47.68/30.51 (C!19 = set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20)))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[275, 261])).
% 47.68/30.51 tff(277,plain,
% 47.68/30.51 (set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20))) = C!19),
% 47.68/30.51 inference(symmetry,[status(thm)],[276])).
% 47.68/30.51 tff(278,plain,
% 47.68/30.51 (set_difference(C!19, unordered_pair(A!21, B!20)) = set_difference(C!19, unordered_pair(B!20, A!21))),
% 47.68/30.51 inference(monotonicity,[status(thm)],[42])).
% 47.68/30.51 tff(279,plain,
% 47.68/30.51 (set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20))) = set_union2(unordered_pair(B!20, A!21), set_difference(C!19, unordered_pair(B!20, A!21)))),
% 47.68/30.51 inference(monotonicity,[status(thm)],[42, 278])).
% 47.68/30.51 tff(280,plain,
% 47.68/30.51 (set_union2(unordered_pair(B!20, A!21), set_difference(C!19, unordered_pair(B!20, A!21))) = set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20)))),
% 47.68/30.51 inference(symmetry,[status(thm)],[279])).
% 47.68/30.51 tff(281,plain,
% 47.68/30.51 (^[A: $i, B: $i] : refl((set_union2(A, set_difference(B, A)) = set_union2(A, B)) <=> (set_union2(A, set_difference(B, A)) = set_union2(A, B)))),
% 47.68/30.51 inference(bind,[status(th)],[])).
% 47.68/30.51 tff(282,plain,
% 47.68/30.51 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B)) <=> ![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 47.68/30.51 inference(quant_intro,[status(thm)],[281])).
% 47.68/30.51 tff(283,plain,
% 47.68/30.51 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B)) <=> ![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 47.68/30.51 inference(rewrite,[status(thm)],[])).
% 47.68/30.51 tff(284,axiom,(![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t39_xboole_1')).
% 47.68/30.51 tff(285,plain,
% 47.68/30.51 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 47.68/30.51 inference(modus_ponens,[status(thm)],[284, 283])).
% 47.68/30.51 tff(286,plain,(
% 47.68/30.51 ![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 47.68/30.51 inference(skolemize,[status(sab)],[285])).
% 47.68/30.51 tff(287,plain,
% 47.68/30.51 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 47.68/30.51 inference(modus_ponens,[status(thm)],[286, 282])).
% 47.68/30.51 tff(288,plain,
% 47.68/30.51 ((~![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))) | (set_union2(unordered_pair(B!20, A!21), set_difference(C!19, unordered_pair(B!20, A!21))) = set_union2(unordered_pair(B!20, A!21), C!19))),
% 47.68/30.51 inference(quant_inst,[status(thm)],[])).
% 47.68/30.51 tff(289,plain,
% 47.68/30.51 (set_union2(unordered_pair(B!20, A!21), set_difference(C!19, unordered_pair(B!20, A!21))) = set_union2(unordered_pair(B!20, A!21), C!19)),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[288, 287])).
% 47.68/30.51 tff(290,plain,
% 47.68/30.51 (set_union2(unordered_pair(B!20, A!21), C!19) = set_union2(unordered_pair(B!20, A!21), set_difference(C!19, unordered_pair(B!20, A!21)))),
% 47.68/30.51 inference(symmetry,[status(thm)],[289])).
% 47.68/30.51 tff(291,plain,
% 47.68/30.51 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 47.68/30.51 inference(bind,[status(th)],[])).
% 47.68/30.51 tff(292,plain,
% 47.68/30.51 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 47.68/30.51 inference(quant_intro,[status(thm)],[291])).
% 47.68/30.51 tff(293,plain,
% 47.68/30.51 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 47.68/30.51 inference(rewrite,[status(thm)],[])).
% 47.68/30.51 tff(294,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 47.68/30.51 tff(295,plain,
% 47.68/30.51 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 47.68/30.51 inference(modus_ponens,[status(thm)],[294, 293])).
% 47.68/30.51 tff(296,plain,(
% 47.68/30.51 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 47.68/30.51 inference(skolemize,[status(sab)],[295])).
% 47.68/30.51 tff(297,plain,
% 47.68/30.51 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 47.68/30.51 inference(modus_ponens,[status(thm)],[296, 292])).
% 47.68/30.51 tff(298,plain,
% 47.68/30.51 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(C!19, unordered_pair(B!20, A!21)) = set_union2(unordered_pair(B!20, A!21), C!19))),
% 47.68/30.51 inference(quant_inst,[status(thm)],[])).
% 47.68/30.51 tff(299,plain,
% 47.68/30.51 (set_union2(C!19, unordered_pair(B!20, A!21)) = set_union2(unordered_pair(B!20, A!21), C!19)),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[298, 297])).
% 47.68/30.51 tff(300,plain,
% 47.68/30.51 (set_union2(C!19, unordered_pair(B!20, A!21)) = C!19),
% 47.68/30.51 inference(transitivity,[status(thm)],[299, 290, 280, 277])).
% 47.68/30.51 tff(301,plain,
% 47.68/30.51 (in(B!20, set_union2(C!19, unordered_pair(B!20, A!21))) <=> in(B!20, C!19)),
% 47.68/30.51 inference(monotonicity,[status(thm)],[300])).
% 47.68/30.51 tff(302,plain,
% 47.68/30.51 (in(B!20, C!19) <=> in(B!20, set_union2(C!19, unordered_pair(B!20, A!21)))),
% 47.68/30.51 inference(symmetry,[status(thm)],[301])).
% 47.68/30.51 tff(303,plain,
% 47.68/30.51 ((~in(B!20, C!19)) <=> (~in(B!20, set_union2(C!19, unordered_pair(B!20, A!21))))),
% 47.68/30.51 inference(monotonicity,[status(thm)],[302])).
% 47.68/30.51 tff(304,plain,
% 47.68/30.51 (in(A!21, unordered_pair(A!21, B!20)) <=> in(A!21, unordered_pair(B!20, A!21))),
% 47.68/30.51 inference(monotonicity,[status(thm)],[42])).
% 47.68/30.51 tff(305,plain,
% 47.68/30.51 (in(A!21, unordered_pair(B!20, A!21)) <=> in(A!21, unordered_pair(A!21, B!20))),
% 47.68/30.51 inference(symmetry,[status(thm)],[304])).
% 47.68/30.51 tff(306,assumption,((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))), introduced(assumption)).
% 47.68/30.51 tff(307,plain,
% 47.68/30.51 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))),
% 47.68/30.51 inference(rewrite,[status(thm)],[])).
% 47.68/30.51 tff(308,plain,
% 47.68/30.51 ((~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(A!21, unordered_pair(B!20, A!21)) <=> ((A!21 = B!20) | (A!21 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))) <=> (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))),
% 47.68/30.51 inference(rewrite,[status(thm)],[])).
% 47.68/30.51 tff(309,plain,
% 47.68/30.51 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(A!21, unordered_pair(B!20, A!21)) <=> ((A!21 = B!20) | (A!21 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))),
% 47.68/30.51 inference(monotonicity,[status(thm)],[308])).
% 47.68/30.51 tff(310,plain,
% 47.68/30.51 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(A!21, unordered_pair(B!20, A!21)) <=> ((A!21 = B!20) | (A!21 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))),
% 47.68/30.51 inference(transitivity,[status(thm)],[309, 307])).
% 47.68/30.51 tff(311,plain,
% 47.68/30.51 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(A!21, unordered_pair(B!20, A!21)) <=> ((A!21 = B!20) | (A!21 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))),
% 47.68/30.51 inference(quant_inst,[status(thm)],[])).
% 47.68/30.51 tff(312,plain,
% 47.68/30.51 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))),
% 47.68/30.51 inference(modus_ponens,[status(thm)],[311, 310])).
% 47.68/30.51 tff(313,plain,
% 47.68/30.51 ($false),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[312, 24, 306])).
% 47.68/30.51 tff(314,plain,(~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))), inference(lemma,lemma(discharge,[]))).
% 47.68/30.51 tff(315,plain,
% 47.68/30.51 (((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))) | ((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))),
% 47.68/30.51 inference(tautology,[status(thm)],[])).
% 47.68/30.51 tff(316,plain,
% 47.68/30.51 ((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[315, 314])).
% 47.68/30.51 tff(317,plain,
% 47.68/30.51 ((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21))),
% 47.68/30.51 inference(tautology,[status(thm)],[])).
% 47.68/30.51 tff(318,plain,
% 47.68/30.51 ((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | in(A!21, unordered_pair(B!20, A!21))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[317, 37])).
% 47.68/30.51 tff(319,plain,
% 47.68/30.51 (in(A!21, unordered_pair(B!20, A!21))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[318, 316])).
% 47.68/30.51 tff(320,plain,
% 47.68/30.51 (in(A!21, unordered_pair(A!21, B!20))),
% 47.68/30.51 inference(modus_ponens,[status(thm)],[319, 305])).
% 47.68/30.51 tff(321,assumption,(~in(A!21, unordered_pair(A!21, B!20))), introduced(assumption)).
% 47.68/30.51 tff(322,plain,
% 47.68/30.51 ($false),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[321, 320])).
% 47.68/30.51 tff(323,plain,(in(A!21, unordered_pair(A!21, B!20))), inference(lemma,lemma(discharge,[]))).
% 47.68/30.51 tff(324,plain,
% 47.68/30.51 (((~((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19)))) | (~(subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)))))) | ((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19)))),
% 47.68/30.51 inference(tautology,[status(thm)],[])).
% 47.68/30.51 tff(325,plain,
% 47.68/30.51 ((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[324, 84])).
% 47.68/30.51 tff(326,plain,
% 47.68/30.51 ((~((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19)))) | (~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))),
% 47.68/30.51 inference(tautology,[status(thm)],[])).
% 47.68/30.51 tff(327,plain,
% 47.68/30.51 ((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[326, 325])).
% 47.68/30.51 tff(328,plain,
% 47.68/30.51 (![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[327, 261])).
% 47.68/30.51 tff(329,plain,
% 47.68/30.51 (((~![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))) | ((~in(A!21, unordered_pair(A!21, B!20))) | in(A!21, C!19))) <=> ((~![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))) | (~in(A!21, unordered_pair(A!21, B!20))) | in(A!21, C!19))),
% 47.68/30.51 inference(rewrite,[status(thm)],[])).
% 47.68/30.51 tff(330,plain,
% 47.68/30.51 ((~![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))) | ((~in(A!21, unordered_pair(A!21, B!20))) | in(A!21, C!19))),
% 47.68/30.51 inference(quant_inst,[status(thm)],[])).
% 47.68/30.51 tff(331,plain,
% 47.68/30.51 ((~![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))) | (~in(A!21, unordered_pair(A!21, B!20))) | in(A!21, C!19)),
% 47.68/30.51 inference(modus_ponens,[status(thm)],[330, 329])).
% 47.68/30.51 tff(332,plain,
% 47.68/30.51 (in(A!21, C!19)),
% 47.68/30.51 inference(unit_resolution,[status(thm)],[331, 328, 323])).
% 47.68/30.51 tff(333,plain,
% 47.68/30.51 ((~((~in(A!21, C!19)) | (~in(B!20, C!19)))) | (~in(A!21, C!19)) | (~in(B!20, C!19))),
% 47.68/30.52 inference(tautology,[status(thm)],[])).
% 47.68/30.52 tff(334,plain,
% 47.68/30.52 ((~in(A!21, C!19)) | (~in(B!20, C!19))),
% 47.68/30.52 inference(unit_resolution,[status(thm)],[333, 258])).
% 47.68/30.52 tff(335,plain,
% 47.68/30.52 (~in(B!20, C!19)),
% 47.68/30.52 inference(unit_resolution,[status(thm)],[334, 332])).
% 47.68/30.52 tff(336,plain,
% 47.68/30.52 (~in(B!20, set_union2(C!19, unordered_pair(B!20, A!21)))),
% 47.68/30.52 inference(modus_ponens,[status(thm)],[335, 303])).
% 47.68/30.52 tff(337,assumption,((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))), introduced(assumption)).
% 47.68/30.52 tff(338,plain,
% 47.68/30.52 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))),
% 47.68/30.52 inference(rewrite,[status(thm)],[])).
% 47.68/30.52 tff(339,plain,
% 47.68/30.52 ((~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(B!20, unordered_pair(B!20, A!21)) <=> ((B!20 = B!20) | (B!20 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))) <=> (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))),
% 47.68/30.52 inference(rewrite,[status(thm)],[])).
% 47.68/30.52 tff(340,plain,
% 47.68/30.52 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(B!20, unordered_pair(B!20, A!21)) <=> ((B!20 = B!20) | (B!20 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))),
% 47.68/30.52 inference(monotonicity,[status(thm)],[339])).
% 47.68/30.52 tff(341,plain,
% 47.68/30.52 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(B!20, unordered_pair(B!20, A!21)) <=> ((B!20 = B!20) | (B!20 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))),
% 47.68/30.52 inference(transitivity,[status(thm)],[340, 338])).
% 47.68/30.52 tff(342,plain,
% 47.68/30.52 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(B!20, unordered_pair(B!20, A!21)) <=> ((B!20 = B!20) | (B!20 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))),
% 47.68/30.52 inference(quant_inst,[status(thm)],[])).
% 47.68/30.52 tff(343,plain,
% 47.68/30.52 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))),
% 47.68/30.52 inference(modus_ponens,[status(thm)],[342, 341])).
% 47.68/30.52 tff(344,plain,
% 47.68/30.52 ($false),
% 47.68/30.52 inference(unit_resolution,[status(thm)],[343, 24, 337])).
% 47.68/30.52 tff(345,plain,(~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))), inference(lemma,lemma(discharge,[]))).
% 47.68/30.52 tff(346,plain,
% 47.68/30.52 (((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | ((~in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21))) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))) | ((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))),
% 47.68/30.52 inference(tautology,[status(thm)],[])).
% 47.68/30.52 tff(347,plain,
% 47.68/30.52 ((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21))),
% 47.68/30.52 inference(unit_resolution,[status(thm)],[346, 345])).
% 47.68/30.52 tff(348,plain,
% 47.68/30.52 ((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21))),
% 47.68/30.52 inference(tautology,[status(thm)],[])).
% 47.68/30.52 tff(349,plain,
% 47.68/30.52 ((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | in(B!20, unordered_pair(B!20, A!21))),
% 47.68/30.52 inference(unit_resolution,[status(thm)],[348, 37])).
% 47.68/30.52 tff(350,plain,
% 47.68/30.52 (in(B!20, unordered_pair(B!20, A!21))),
% 47.68/30.52 inference(unit_resolution,[status(thm)],[349, 347])).
% 47.68/30.52 tff(351,plain,
% 47.68/30.52 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))) | (~((~((~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21)))))) | (~(subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21))) | (~((~in(tptp_fun_C_10(set_union2(C!19, unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21))) | in(tptp_fun_C_10(set_union2(C!19, unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21)), set_union2(C!19, unordered_pair(B!20, A!21)))))))))),
% 47.68/30.52 inference(quant_inst,[status(thm)],[])).
% 47.68/30.52 tff(352,plain,
% 47.68/30.52 (~((~((~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21)))))) | (~(subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21))) | (~((~in(tptp_fun_C_10(set_union2(C!19, unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21))) | in(tptp_fun_C_10(set_union2(C!19, unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21)), set_union2(C!19, unordered_pair(B!20, A!21))))))))),
% 47.68/30.52 inference(unit_resolution,[status(thm)],[351, 82])).
% 47.68/30.52 tff(353,plain,
% 47.68/30.52 (((~((~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21)))))) | (~(subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21))) | (~((~in(tptp_fun_C_10(set_union2(C!19, unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21))) | in(tptp_fun_C_10(set_union2(C!19, unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21)), set_union2(C!19, unordered_pair(B!20, A!21)))))))) | ((~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21)))))),
% 47.68/30.52 inference(tautology,[status(thm)],[])).
% 47.68/30.52 tff(354,plain,
% 47.68/30.52 ((~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))),
% 47.68/30.52 inference(unit_resolution,[status(thm)],[353, 352])).
% 47.68/30.52 tff(355,plain,
% 47.68/30.52 (set_union2(unordered_pair(B!20, A!21), C!19) = set_union2(C!19, unordered_pair(B!20, A!21))),
% 47.68/30.52 inference(symmetry,[status(thm)],[299])).
% 47.68/30.52 tff(356,plain,
% 47.68/30.52 (subset(unordered_pair(B!20, A!21), set_union2(unordered_pair(B!20, A!21), C!19)) <=> subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))),
% 47.68/30.52 inference(monotonicity,[status(thm)],[355])).
% 47.68/30.56 tff(357,plain,
% 47.68/30.56 (^[A: $i, B: $i] : refl(subset(A, set_union2(A, B)) <=> subset(A, set_union2(A, B)))),
% 47.68/30.56 inference(bind,[status(th)],[])).
% 47.68/30.56 tff(358,plain,
% 47.68/30.56 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 47.68/30.56 inference(quant_intro,[status(thm)],[357])).
% 47.68/30.56 tff(359,plain,
% 47.68/30.56 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 47.68/30.56 inference(rewrite,[status(thm)],[])).
% 47.68/30.56 tff(360,axiom,(![A: $i, B: $i] : subset(A, set_union2(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_xboole_1')).
% 47.68/30.56 tff(361,plain,
% 47.68/30.56 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 47.68/30.56 inference(modus_ponens,[status(thm)],[360, 359])).
% 47.68/30.56 tff(362,plain,(
% 47.68/30.56 ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 47.68/30.56 inference(skolemize,[status(sab)],[361])).
% 47.68/30.56 tff(363,plain,
% 47.68/30.56 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 47.68/30.56 inference(modus_ponens,[status(thm)],[362, 358])).
% 47.68/30.56 tff(364,plain,
% 47.68/30.56 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(unordered_pair(B!20, A!21), set_union2(unordered_pair(B!20, A!21), C!19))),
% 47.68/30.56 inference(quant_inst,[status(thm)],[])).
% 47.68/30.56 tff(365,plain,
% 47.68/30.56 (subset(unordered_pair(B!20, A!21), set_union2(unordered_pair(B!20, A!21), C!19))),
% 47.68/30.56 inference(unit_resolution,[status(thm)],[364, 363])).
% 47.68/30.56 tff(366,plain,
% 47.68/30.56 (subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))),
% 47.68/30.56 inference(modus_ponens,[status(thm)],[365, 356])).
% 47.68/30.56 tff(367,plain,
% 47.68/30.56 ((~((~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21)))))) | (~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))),
% 47.68/30.56 inference(tautology,[status(thm)],[])).
% 47.68/30.56 tff(368,plain,
% 47.68/30.56 ((~((~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21)))))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))),
% 47.68/30.56 inference(unit_resolution,[status(thm)],[367, 366])).
% 47.68/30.56 tff(369,plain,
% 47.68/30.56 (![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))),
% 47.68/30.56 inference(unit_resolution,[status(thm)],[368, 354])).
% 47.68/30.56 tff(370,plain,
% 47.68/30.56 (((~![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))) | ((~in(B!20, unordered_pair(B!20, A!21))) | in(B!20, set_union2(C!19, unordered_pair(B!20, A!21))))) <=> ((~![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))) | (~in(B!20, unordered_pair(B!20, A!21))) | in(B!20, set_union2(C!19, unordered_pair(B!20, A!21))))),
% 47.68/30.56 inference(rewrite,[status(thm)],[])).
% 47.68/30.56 tff(371,plain,
% 47.68/30.56 ((~![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))) | ((~in(B!20, unordered_pair(B!20, A!21))) | in(B!20, set_union2(C!19, unordered_pair(B!20, A!21))))),
% 47.68/30.56 inference(quant_inst,[status(thm)],[])).
% 47.68/30.56 tff(372,plain,
% 47.68/30.56 ((~![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))) | (~in(B!20, unordered_pair(B!20, A!21))) | in(B!20, set_union2(C!19, unordered_pair(B!20, A!21)))),
% 47.68/30.56 inference(modus_ponens,[status(thm)],[371, 370])).
% 47.68/30.56 tff(373,plain,
% 47.68/30.56 (in(B!20, set_union2(C!19, unordered_pair(B!20, A!21)))),
% 47.68/30.56 inference(unit_resolution,[status(thm)],[372, 369, 350])).
% 47.68/30.56 tff(374,plain,
% 47.68/30.56 ($false),
% 47.68/30.56 inference(unit_resolution,[status(thm)],[373, 336])).
% 47.68/30.56 % SZS output end Proof
%------------------------------------------------------------------------------