TSTP Solution File: SEU149+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU149+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 07:27:47 EDT 2022
% Result : Theorem 6.62s 4.51s
% Output : Proof 6.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU149+3 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n022.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Sep 3 09:43:09 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.34 Usage: tptp [options] [-file:]file
% 0.11/0.34 -h, -? prints this message.
% 0.11/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.34 -m, -model generate model.
% 0.11/0.34 -p, -proof generate proof.
% 0.11/0.34 -c, -core generate unsat core of named formulas.
% 0.11/0.34 -st, -statistics display statistics.
% 0.11/0.34 -t:timeout set timeout (in second).
% 0.11/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.34 -<param>:<value> configuration parameter and value.
% 0.11/0.34 -o:<output-file> file to place output in.
% 6.62/4.51 % SZS status Theorem
% 6.62/4.51 % SZS output start Proof
% 6.62/4.51 tff(tptp_fun_A_6_type, type, (
% 6.62/4.51 tptp_fun_A_6: $i)).
% 6.62/4.51 tff(tptp_fun_C_0_type, type, (
% 6.62/4.51 tptp_fun_C_0: ( $i * $i ) > $i)).
% 6.62/4.51 tff(unordered_pair_type, type, (
% 6.62/4.51 unordered_pair: ( $i * $i ) > $i)).
% 6.62/4.51 tff(tptp_fun_C_4_type, type, (
% 6.62/4.51 tptp_fun_C_4: $i)).
% 6.62/4.51 tff(tptp_fun_B_5_type, type, (
% 6.62/4.51 tptp_fun_B_5: $i)).
% 6.62/4.51 tff(in_type, type, (
% 6.62/4.51 in: ( $i * $i ) > $o)).
% 6.62/4.51 tff(singleton_type, type, (
% 6.62/4.51 singleton: $i > $i)).
% 6.62/4.51 tff(tptp_fun_D_1_type, type, (
% 6.62/4.51 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 6.62/4.51 tff(1,assumption,(~in(B!5, unordered_pair(B!5, C!4))), introduced(assumption)).
% 6.62/4.51 tff(2,plain,
% 6.62/4.51 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 6.62/4.51 inference(bind,[status(th)],[])).
% 6.62/4.51 tff(3,plain,
% 6.62/4.51 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 6.62/4.51 inference(quant_intro,[status(thm)],[2])).
% 6.62/4.51 tff(4,plain,
% 6.62/4.51 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 6.62/4.51 inference(pull_quant,[status(thm)],[])).
% 6.62/4.51 tff(5,plain,
% 6.62/4.51 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 6.62/4.51 inference(bind,[status(th)],[])).
% 6.62/4.51 tff(6,plain,
% 6.62/4.51 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 6.62/4.51 inference(quant_intro,[status(thm)],[5])).
% 6.62/4.51 tff(7,plain,
% 6.62/4.51 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 6.62/4.51 inference(transitivity,[status(thm)],[6, 4])).
% 6.62/4.51 tff(8,plain,
% 6.62/4.51 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 6.62/4.51 inference(transitivity,[status(thm)],[7, 3])).
% 6.62/4.51 tff(9,plain,
% 6.62/4.51 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 6.62/4.51 inference(bind,[status(th)],[])).
% 6.62/4.51 tff(10,plain,
% 6.62/4.51 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 6.62/4.51 inference(quant_intro,[status(thm)],[9])).
% 6.62/4.51 tff(11,plain,
% 6.62/4.51 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 6.62/4.51 inference(transitivity,[status(thm)],[10, 8])).
% 6.62/4.51 tff(12,plain,
% 6.62/4.51 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 6.62/4.51 inference(bind,[status(th)],[])).
% 6.62/4.51 tff(13,plain,
% 6.62/4.51 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 6.62/4.51 inference(quant_intro,[status(thm)],[12])).
% 6.62/4.51 tff(14,plain,
% 6.62/4.51 (^[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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 6.62/4.51 inference(bind,[status(th)],[])).
% 6.62/4.51 tff(15,plain,
% 6.62/4.51 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))),
% 6.62/4.52 inference(quant_intro,[status(thm)],[14])).
% 6.62/4.52 tff(16,plain,
% 6.62/4.52 (![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))))),
% 6.62/4.52 inference(rewrite,[status(thm)],[])).
% 6.62/4.52 tff(17,plain,
% 6.62/4.52 (^[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)))))),
% 6.62/4.52 inference(bind,[status(th)],[])).
% 6.62/4.52 tff(18,plain,
% 6.62/4.52 (![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))))),
% 6.62/4.52 inference(quant_intro,[status(thm)],[17])).
% 6.62/4.52 tff(19,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')).
% 6.62/4.52 tff(20,plain,
% 6.62/4.52 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[19, 18])).
% 6.62/4.52 tff(21,plain,
% 6.62/4.52 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[20, 16])).
% 6.62/4.52 tff(22,plain,(
% 6.62/4.52 ![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 6.62/4.52 inference(skolemize,[status(sab)],[21])).
% 6.62/4.52 tff(23,plain,
% 6.62/4.52 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[22, 15])).
% 6.62/4.52 tff(24,plain,
% 6.62/4.52 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[23, 13])).
% 6.62/4.52 tff(25,plain,
% 6.62/4.52 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[24, 11])).
% 6.62/4.52 tff(26,plain,
% 6.62/4.52 (((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | in(B!5, unordered_pair(B!5, C!4))) <=> ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | in(B!5, unordered_pair(B!5, C!4)))),
% 6.62/4.52 inference(rewrite,[status(thm)],[])).
% 6.62/4.52 tff(27,plain,
% 6.62/4.52 ((~(~in(B!5, unordered_pair(B!5, C!4)))) <=> in(B!5, unordered_pair(B!5, C!4))),
% 6.62/4.52 inference(rewrite,[status(thm)],[])).
% 6.62/4.52 tff(28,plain,
% 6.62/4.52 (((~in(B!5, unordered_pair(B!5, C!4))) | $false) <=> (~in(B!5, unordered_pair(B!5, C!4)))),
% 6.62/4.52 inference(rewrite,[status(thm)],[])).
% 6.62/4.52 tff(29,plain,
% 6.62/4.52 ((~$true) <=> $false),
% 6.62/4.52 inference(rewrite,[status(thm)],[])).
% 6.62/4.52 tff(30,plain,
% 6.62/4.52 (($true | ((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))) <=> $true),
% 6.62/4.52 inference(rewrite,[status(thm)],[])).
% 6.62/4.52 tff(31,plain,
% 6.62/4.52 (((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))) <=> ((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))),
% 6.62/4.52 inference(rewrite,[status(thm)],[])).
% 6.62/4.52 tff(32,plain,
% 6.62/4.52 ((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) <=> $true),
% 6.62/4.52 inference(rewrite,[status(thm)],[])).
% 6.62/4.52 tff(33,plain,
% 6.62/4.52 (((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))) <=> ($true | ((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))))),
% 6.62/4.52 inference(monotonicity,[status(thm)],[32, 31])).
% 6.62/4.52 tff(34,plain,
% 6.62/4.52 (((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))) <=> $true),
% 6.62/4.52 inference(transitivity,[status(thm)],[33, 30])).
% 6.62/4.52 tff(35,plain,
% 6.62/4.52 ((~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))))) <=> (~$true)),
% 6.62/4.52 inference(monotonicity,[status(thm)],[34])).
% 6.62/4.52 tff(36,plain,
% 6.62/4.52 ((~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))))) <=> $false),
% 6.62/4.52 inference(transitivity,[status(thm)],[35, 29])).
% 6.62/4.52 tff(37,plain,
% 6.62/4.52 ((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) <=> (~in(B!5, unordered_pair(B!5, C!4)))),
% 6.62/4.52 inference(rewrite,[status(thm)],[])).
% 6.62/4.52 tff(38,plain,
% 6.62/4.52 (((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) | (~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))))) <=> ((~in(B!5, unordered_pair(B!5, C!4))) | $false)),
% 6.62/4.52 inference(monotonicity,[status(thm)],[37, 36])).
% 6.62/4.52 tff(39,plain,
% 6.62/4.52 (((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) | (~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))))) <=> (~in(B!5, unordered_pair(B!5, C!4)))),
% 6.62/4.52 inference(transitivity,[status(thm)],[38, 28])).
% 6.62/4.52 tff(40,plain,
% 6.62/4.52 ((~((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) | (~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))))))) <=> (~(~in(B!5, unordered_pair(B!5, C!4))))),
% 6.62/4.52 inference(monotonicity,[status(thm)],[39])).
% 6.62/4.52 tff(41,plain,
% 6.62/4.52 ((~((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) | (~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))))))) <=> in(B!5, unordered_pair(B!5, C!4))),
% 6.62/4.52 inference(transitivity,[status(thm)],[40, 27])).
% 6.62/4.52 tff(42,plain,
% 6.62/4.52 (((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) | (~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))))))) <=> ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | in(B!5, unordered_pair(B!5, C!4)))),
% 6.62/4.52 inference(monotonicity,[status(thm)],[41])).
% 6.62/4.52 tff(43,plain,
% 6.62/4.52 (((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) | (~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))))))) <=> ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | in(B!5, unordered_pair(B!5, C!4)))),
% 6.62/4.52 inference(transitivity,[status(thm)],[42, 26])).
% 6.62/4.52 tff(44,plain,
% 6.62/4.52 ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) | (~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4))) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))))))),
% 6.62/4.52 inference(quant_inst,[status(thm)],[])).
% 6.62/4.52 tff(45,plain,
% 6.62/4.52 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | in(B!5, unordered_pair(B!5, C!4))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[44, 43])).
% 6.62/4.52 tff(46,plain,
% 6.62/4.52 ($false),
% 6.62/4.52 inference(unit_resolution,[status(thm)],[45, 25, 1])).
% 6.62/4.52 tff(47,plain,(in(B!5, unordered_pair(B!5, C!4))), inference(lemma,lemma(discharge,[]))).
% 6.62/4.52 tff(48,plain,
% 6.62/4.52 ((B!5 = A!6) <=> (A!6 = B!5)),
% 6.62/4.52 inference(commutativity,[status(thm)],[])).
% 6.62/4.52 tff(49,plain,
% 6.62/4.52 ((A!6 = B!5) <=> (B!5 = A!6)),
% 6.62/4.52 inference(symmetry,[status(thm)],[48])).
% 6.62/4.52 tff(50,plain,
% 6.62/4.52 ((~(A!6 = B!5)) <=> (~(B!5 = A!6))),
% 6.62/4.52 inference(monotonicity,[status(thm)],[49])).
% 6.62/4.52 tff(51,plain,
% 6.62/4.52 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) <=> (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B)))),
% 6.62/4.52 inference(rewrite,[status(thm)],[])).
% 6.62/4.52 tff(52,plain,
% 6.62/4.52 ((~![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (A = B))) <=> (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B)))),
% 6.62/4.52 inference(rewrite,[status(thm)],[])).
% 6.62/4.52 tff(53,axiom,(~![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (A = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_zfmisc_1')).
% 6.62/4.52 tff(54,plain,
% 6.62/4.52 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[53, 52])).
% 6.62/4.52 tff(55,plain,
% 6.62/4.52 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[54, 51])).
% 6.62/4.52 tff(56,plain,
% 6.62/4.52 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[55, 51])).
% 6.62/4.52 tff(57,plain,
% 6.62/4.52 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[56, 51])).
% 6.62/4.52 tff(58,plain,
% 6.62/4.52 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[57, 51])).
% 6.62/4.52 tff(59,plain,
% 6.62/4.52 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[58, 51])).
% 6.62/4.52 tff(60,plain,
% 6.62/4.52 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[59, 51])).
% 6.62/4.52 tff(61,plain,(
% 6.62/4.52 ~((~(singleton(A!6) = unordered_pair(B!5, C!4))) | (A!6 = B!5))),
% 6.62/4.52 inference(skolemize,[status(sab)],[60])).
% 6.62/4.52 tff(62,plain,
% 6.62/4.52 (~(A!6 = B!5)),
% 6.62/4.52 inference(or_elim,[status(thm)],[61])).
% 6.62/4.52 tff(63,plain,
% 6.62/4.52 (~(B!5 = A!6)),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[62, 50])).
% 6.62/4.52 tff(64,plain,
% 6.62/4.52 ((~(in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6))) | (~in(B!5, unordered_pair(B!5, C!4))) | (B!5 = A!6)),
% 6.62/4.52 inference(tautology,[status(thm)],[])).
% 6.62/4.52 tff(65,plain,
% 6.62/4.52 (~(in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6))),
% 6.62/4.52 inference(unit_resolution,[status(thm)],[64, 63, 47])).
% 6.62/4.52 tff(66,plain,
% 6.62/4.52 (singleton(A!6) = unordered_pair(B!5, C!4)),
% 6.62/4.52 inference(or_elim,[status(thm)],[61])).
% 6.62/4.52 tff(67,plain,
% 6.62/4.52 (unordered_pair(B!5, C!4) = singleton(A!6)),
% 6.62/4.52 inference(symmetry,[status(thm)],[66])).
% 6.62/4.52 tff(68,plain,
% 6.62/4.52 ((~((~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6)))) | (~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6))),
% 6.62/4.52 inference(tautology,[status(thm)],[])).
% 6.62/4.52 tff(69,plain,
% 6.62/4.52 (~((~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6)))),
% 6.62/4.52 inference(unit_resolution,[status(thm)],[68, 67, 65])).
% 6.62/4.52 tff(70,plain,
% 6.62/4.52 (((~((~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6)))) | (~((unordered_pair(B!5, C!4) = singleton(A!6)) | ((~in(tptp_fun_C_0(unordered_pair(B!5, C!4), A!6), unordered_pair(B!5, C!4))) <=> (tptp_fun_C_0(unordered_pair(B!5, C!4), A!6) = A!6))))) | ((~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6)))),
% 6.62/4.52 inference(tautology,[status(thm)],[])).
% 6.62/4.52 tff(71,plain,
% 6.62/4.52 ((~((~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6)))) | (~((unordered_pair(B!5, C!4) = singleton(A!6)) | ((~in(tptp_fun_C_0(unordered_pair(B!5, C!4), A!6), unordered_pair(B!5, C!4))) <=> (tptp_fun_C_0(unordered_pair(B!5, C!4), A!6) = A!6))))),
% 6.62/4.52 inference(unit_resolution,[status(thm)],[70, 69])).
% 6.62/4.52 tff(72,plain,
% 6.62/4.52 (^[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)))))))),
% 6.62/4.52 inference(bind,[status(th)],[])).
% 6.62/4.52 tff(73,plain,
% 6.62/4.52 (![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))))))),
% 6.62/4.52 inference(quant_intro,[status(thm)],[72])).
% 6.62/4.52 tff(74,plain,
% 6.62/4.52 (![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))))))),
% 6.62/4.52 inference(pull_quant,[status(thm)],[])).
% 6.62/4.52 tff(75,plain,
% 6.62/4.52 (^[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))))))))),
% 6.62/4.52 inference(bind,[status(th)],[])).
% 6.62/4.52 tff(76,plain,
% 6.62/4.52 (![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))))))),
% 6.62/4.52 inference(quant_intro,[status(thm)],[75])).
% 6.62/4.52 tff(77,plain,
% 6.62/4.52 (![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))))))),
% 6.62/4.52 inference(transitivity,[status(thm)],[76, 74])).
% 6.62/4.52 tff(78,plain,
% 6.62/4.52 (![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))))))),
% 6.62/4.52 inference(transitivity,[status(thm)],[77, 73])).
% 6.62/4.52 tff(79,plain,
% 6.62/4.52 (^[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)))))))),
% 6.62/4.52 inference(bind,[status(th)],[])).
% 6.62/4.52 tff(80,plain,
% 6.62/4.52 (![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))))))),
% 6.62/4.52 inference(quant_intro,[status(thm)],[79])).
% 6.62/4.52 tff(81,plain,
% 6.62/4.52 (![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))))))),
% 6.62/4.52 inference(transitivity,[status(thm)],[80, 78])).
% 6.62/4.52 tff(82,plain,
% 6.62/4.52 (^[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))))))))),
% 6.62/4.52 inference(bind,[status(th)],[])).
% 6.62/4.52 tff(83,plain,
% 6.62/4.52 (![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))))))),
% 6.62/4.52 inference(quant_intro,[status(thm)],[82])).
% 6.62/4.52 tff(84,plain,
% 6.62/4.52 (^[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)))))),
% 6.62/4.52 inference(bind,[status(th)],[])).
% 6.62/4.52 tff(85,plain,
% 6.62/4.52 (![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))))),
% 6.62/4.52 inference(quant_intro,[status(thm)],[84])).
% 6.62/4.52 tff(86,plain,
% 6.62/4.52 (![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)))),
% 6.62/4.52 inference(rewrite,[status(thm)],[])).
% 6.62/4.52 tff(87,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 6.62/4.52 tff(88,plain,
% 6.62/4.52 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[87, 86])).
% 6.62/4.52 tff(89,plain,(
% 6.62/4.52 ![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)))))),
% 6.62/4.52 inference(skolemize,[status(sab)],[88])).
% 6.62/4.52 tff(90,plain,
% 6.62/4.52 (![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))))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[89, 85])).
% 6.62/4.52 tff(91,plain,
% 6.62/4.52 (![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))))))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[90, 83])).
% 6.62/4.52 tff(92,plain,
% 6.62/4.52 (![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))))))),
% 6.62/4.52 inference(modus_ponens,[status(thm)],[91, 81])).
% 6.62/4.52 tff(93,plain,
% 6.62/4.52 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6)))) | (~((unordered_pair(B!5, C!4) = singleton(A!6)) | ((~in(tptp_fun_C_0(unordered_pair(B!5, C!4), A!6), unordered_pair(B!5, C!4))) <=> (tptp_fun_C_0(unordered_pair(B!5, C!4), A!6) = A!6))))))),
% 6.62/4.52 inference(quant_inst,[status(thm)],[])).
% 6.62/4.52 tff(94,plain,
% 6.62/4.52 ($false),
% 6.62/4.52 inference(unit_resolution,[status(thm)],[93, 92, 71])).
% 6.62/4.52 % SZS output end Proof
%------------------------------------------------------------------------------