TSTP Solution File: SET988+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET988+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 05:08:49 EDT 2022
% Result : Theorem 0.78s 0.76s
% Output : Proof 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET988+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 08:55:40 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.78/0.76 % SZS status Theorem
% 0.78/0.76 % SZS output start Proof
% 0.78/0.76 tff(ordered_pair_type, type, (
% 0.78/0.76 ordered_pair: ( $i * $i ) > $i)).
% 0.78/0.76 tff(tptp_fun_D_10_type, type, (
% 0.78/0.76 tptp_fun_D_10: $i > $i)).
% 0.78/0.76 tff(tptp_fun_B_17_type, type, (
% 0.78/0.76 tptp_fun_B_17: $i > $i)).
% 0.78/0.76 tff(tptp_fun_A_9_type, type, (
% 0.78/0.76 tptp_fun_A_9: $i)).
% 0.78/0.76 tff(tptp_fun_C_11_type, type, (
% 0.78/0.76 tptp_fun_C_11: $i > $i)).
% 0.78/0.76 tff(in_type, type, (
% 0.78/0.76 in: ( $i * $i ) > $o)).
% 0.78/0.76 tff(relation_type, type, (
% 0.78/0.76 relation: $i > $o)).
% 0.78/0.76 tff(tptp_fun_D_15_type, type, (
% 0.78/0.76 tptp_fun_D_15: $i > $i)).
% 0.78/0.76 tff(tptp_fun_C_16_type, type, (
% 0.78/0.76 tptp_fun_C_16: $i > $i)).
% 0.78/0.76 tff(function_type, type, (
% 0.78/0.76 function: $i > $o)).
% 0.78/0.76 tff(tptp_fun_D_12_type, type, (
% 0.78/0.76 tptp_fun_D_12: $i > $i)).
% 0.78/0.76 tff(tptp_fun_B_14_type, type, (
% 0.78/0.76 tptp_fun_B_14: $i > $i)).
% 0.78/0.76 tff(tptp_fun_C_13_type, type, (
% 0.78/0.76 tptp_fun_C_13: $i > $i)).
% 0.78/0.76 tff(1,plain,
% 0.78/0.76 (^[A: $i] : refl((~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))))),
% 0.78/0.76 inference(bind,[status(th)],[])).
% 0.78/0.76 tff(2,plain,
% 0.78/0.76 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))),
% 0.78/0.76 inference(quant_intro,[status(thm)],[1])).
% 0.78/0.76 tff(3,plain,
% 0.78/0.76 (^[A: $i] : rewrite((~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))))),
% 0.78/0.76 inference(bind,[status(th)],[])).
% 0.78/0.76 tff(4,plain,
% 0.78/0.76 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))),
% 0.78/0.76 inference(quant_intro,[status(thm)],[3])).
% 0.78/0.76 tff(5,plain,
% 0.78/0.76 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))),
% 0.78/0.76 inference(transitivity,[status(thm)],[4, 2])).
% 0.78/0.76 tff(6,plain,
% 0.78/0.76 (^[A: $i] : trans(monotonicity(rewrite(((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) <=> ((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))), rewrite((relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))) <=> (relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))), ((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) & (relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))) <=> (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) & (relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))), rewrite((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) & (relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))), ((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) & (relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))))),
% 0.78/0.76 inference(bind,[status(th)],[])).
% 0.78/0.76 tff(7,plain,
% 0.78/0.76 (![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) & (relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))),
% 0.78/0.76 inference(quant_intro,[status(thm)],[6])).
% 0.78/0.76 tff(8,plain,
% 0.78/0.76 (^[A: $i] : rewrite((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (~(~(B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))))) & (relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))) <=> (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) & (relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))),
% 0.78/0.76 inference(bind,[status(th)],[])).
% 0.78/0.76 tff(9,plain,
% 0.78/0.76 (![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (~(~(B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))))) & (relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))) <=> ![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) & (relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))),
% 0.78/0.76 inference(quant_intro,[status(thm)],[8])).
% 0.78/0.76 tff(10,plain,
% 0.78/0.76 (![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D)))))) <=> ![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))),
% 0.78/0.76 inference(rewrite,[status(thm)],[])).
% 0.78/0.76 tff(11,axiom,(![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_relat_1')).
% 0.78/0.76 tff(12,plain,
% 0.78/0.76 (![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))),
% 0.78/0.76 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.78/0.76 tff(13,plain,(
% 0.78/0.76 ![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (~(~(B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))))) & (relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))),
% 0.78/0.76 inference(skolemize,[status(sab)],[12])).
% 0.78/0.76 tff(14,plain,
% 0.78/0.76 (![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) & (relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))),
% 0.78/0.76 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.78/0.76 tff(15,plain,
% 0.78/0.76 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))),
% 0.78/0.76 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.78/0.76 tff(16,plain,
% 0.78/0.76 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))),
% 0.78/0.76 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.78/0.76 tff(17,plain,
% 0.78/0.76 ((~![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))) | (~((~((~relation(A!9)) | ![B: $i] : ((~in(B, A!9)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D))))))))))),
% 0.78/0.76 inference(quant_inst,[status(thm)],[])).
% 0.78/0.76 tff(18,plain,
% 0.78/0.76 (~((~((~relation(A!9)) | ![B: $i] : ((~in(B, A!9)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))))))))),
% 0.78/0.76 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.78/0.76 tff(19,plain,
% 0.78/0.76 (((~((~relation(A!9)) | ![B: $i] : ((~in(B, A!9)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D))))))))) | (relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))))))),
% 0.78/0.76 inference(tautology,[status(thm)],[])).
% 0.78/0.76 tff(20,plain,
% 0.78/0.76 (relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D))))))),
% 0.78/0.76 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.78/0.76 tff(21,assumption,((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9))))))), introduced(assumption)).
% 0.78/0.76 tff(22,plain,
% 0.78/0.76 (^[A: $i] : refl((~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))) <=> (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))))),
% 0.78/0.76 inference(bind,[status(th)],[])).
% 0.78/0.76 tff(23,plain,
% 0.78/0.76 (![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))) <=> ![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))),
% 0.78/0.76 inference(quant_intro,[status(thm)],[22])).
% 0.78/0.76 tff(24,plain,
% 0.78/0.76 (^[A: $i] : rewrite((~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))) <=> (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))))),
% 0.78/0.77 inference(bind,[status(th)],[])).
% 0.78/0.77 tff(25,plain,
% 0.78/0.77 (![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))) <=> ![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))),
% 0.78/0.77 inference(quant_intro,[status(thm)],[24])).
% 0.78/0.77 tff(26,plain,
% 0.78/0.77 (![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))) <=> ![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))),
% 0.78/0.77 inference(transitivity,[status(thm)],[25, 23])).
% 0.78/0.77 tff(27,plain,
% 0.78/0.77 (^[A: $i] : trans(monotonicity(rewrite(((~function(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D))) <=> ((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))), rewrite((function(A) | (~((~(in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A) & in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))) | (tptp_fun_C_13(A) = tptp_fun_D_12(A))))) <=> (function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))), ((((~function(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D))) & (function(A) | (~((~(in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A) & in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))) | (tptp_fun_C_13(A) = tptp_fun_D_12(A)))))) <=> (((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A)))) & (function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))), rewrite((((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A)))) & (function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))) <=> (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))), ((((~function(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D))) & (function(A) | (~((~(in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A) & in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))) | (tptp_fun_C_13(A) = tptp_fun_D_12(A)))))) <=> (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))))),
% 0.78/0.77 inference(bind,[status(th)],[])).
% 0.78/0.77 tff(28,plain,
% 0.78/0.77 (![A: $i] : (((~function(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D))) & (function(A) | (~((~(in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A) & in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))) | (tptp_fun_C_13(A) = tptp_fun_D_12(A)))))) <=> ![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))),
% 0.78/0.77 inference(quant_intro,[status(thm)],[27])).
% 0.78/0.77 tff(29,plain,
% 0.78/0.77 (![A: $i] : (function(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D))) <=> ![A: $i] : (function(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))),
% 0.78/0.77 inference(rewrite,[status(thm)],[])).
% 0.78/0.77 tff(30,plain,
% 0.78/0.77 (^[A: $i] : rewrite((function(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A)) => (C = D))) <=> (function(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D))))),
% 0.78/0.77 inference(bind,[status(th)],[])).
% 0.78/0.77 tff(31,plain,
% 0.78/0.77 (![A: $i] : (function(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A)) => (C = D))) <=> ![A: $i] : (function(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))),
% 0.78/0.77 inference(quant_intro,[status(thm)],[30])).
% 0.78/0.77 tff(32,axiom,(![A: $i] : (function(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A)) => (C = D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_funct_1')).
% 0.78/0.77 tff(33,plain,
% 0.78/0.77 (![A: $i] : (function(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.78/0.77 tff(34,plain,
% 0.78/0.77 (![A: $i] : (function(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.78/0.77 tff(35,plain,(
% 0.78/0.77 ![A: $i] : (((~function(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D))) & (function(A) | (~((~(in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A) & in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))) | (tptp_fun_C_13(A) = tptp_fun_D_12(A))))))),
% 0.78/0.77 inference(skolemize,[status(sab)],[34])).
% 0.78/0.77 tff(36,plain,
% 0.78/0.77 (![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.78/0.77 tff(37,plain,
% 0.78/0.77 (![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.78/0.77 tff(38,plain,
% 0.78/0.77 ((~![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))) | (~((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9))))))))),
% 0.78/0.77 inference(quant_inst,[status(thm)],[])).
% 0.78/0.77 tff(39,plain,
% 0.78/0.77 ($false),
% 0.78/0.77 inference(unit_resolution,[status(thm)],[38, 37, 21])).
% 0.78/0.77 tff(40,plain,(~((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)))))))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.77 tff(41,plain,
% 0.78/0.77 (((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9))))))) | (function(A!9) | (~((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)))))),
% 0.78/0.77 inference(tautology,[status(thm)],[])).
% 0.78/0.77 tff(42,plain,
% 0.78/0.77 (function(A!9) | (~((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9))))),
% 0.78/0.77 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.78/0.77 tff(43,assumption,(~((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)))), introduced(assumption)).
% 0.78/0.77 tff(44,plain,
% 0.78/0.77 (((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9))) | in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)),
% 0.78/0.77 inference(tautology,[status(thm)],[])).
% 0.78/0.77 tff(45,plain,
% 0.78/0.77 (in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)),
% 0.78/0.77 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.78/0.77 tff(46,plain,
% 0.78/0.77 (((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9))) | in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)),
% 0.78/0.77 inference(tautology,[status(thm)],[])).
% 0.78/0.77 tff(47,plain,
% 0.78/0.77 (in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)),
% 0.78/0.77 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.78/0.77 tff(48,plain,
% 0.78/0.77 (((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9))) | (~(tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)))),
% 0.78/0.77 inference(tautology,[status(thm)],[])).
% 0.78/0.77 tff(49,plain,
% 0.78/0.77 (~(tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))),
% 0.78/0.77 inference(unit_resolution,[status(thm)],[48, 43])).
% 0.78/0.77 tff(50,plain,
% 0.78/0.77 (^[B: $i, C: $i, D: $i] : refl(((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))) <=> ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))),
% 0.78/0.77 inference(bind,[status(th)],[])).
% 0.78/0.77 tff(51,plain,
% 0.78/0.77 (![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))) <=> ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))),
% 0.78/0.77 inference(quant_intro,[status(thm)],[50])).
% 0.78/0.77 tff(52,plain,
% 0.78/0.77 (^[B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9)) <=> (~((~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))), ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) <=> (~(~((~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))))), rewrite((~(~((~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) <=> ((~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))), ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) <=> ((~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))), (((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D)) <=> (((~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))) | (C = D)))), rewrite((((~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))) | (C = D)) <=> ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))), (((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D)) <=> ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))))),
% 0.78/0.77 inference(bind,[status(th)],[])).
% 0.78/0.77 tff(53,plain,
% 0.78/0.77 (![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D)) <=> ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))),
% 0.78/0.77 inference(quant_intro,[status(thm)],[52])).
% 0.78/0.77 tff(54,plain,
% 0.78/0.77 (((![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D))) & (~(relation(A!9) & function(A!9)))) <=> (![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D)) & (~(relation(A!9) & function(A!9))))),
% 0.78/0.77 inference(rewrite,[status(thm)],[])).
% 0.78/0.77 tff(55,plain,
% 0.78/0.77 ((![B: $i] : ((~in(B, A!9)) | (~(~(ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D))) <=> (![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D)))),
% 0.78/0.77 inference(rewrite,[status(thm)],[])).
% 0.78/0.77 tff(56,plain,
% 0.78/0.77 (((![B: $i] : ((~in(B, A!9)) | (~(~(ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D))) & (~(relation(A!9) & function(A!9)))) <=> ((![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D))) & (~(relation(A!9) & function(A!9))))),
% 0.78/0.77 inference(monotonicity,[status(thm)],[55])).
% 0.78/0.77 tff(57,plain,
% 0.78/0.77 (((![B: $i] : ((~in(B, A!9)) | (~(~(ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D))) & (~(relation(A!9) & function(A!9)))) <=> (![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D)) & (~(relation(A!9) & function(A!9))))),
% 0.78/0.77 inference(transitivity,[status(thm)],[56, 54])).
% 0.78/0.77 tff(58,plain,
% 0.78/0.77 ((~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A)))) <=> (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A))))),
% 0.78/0.77 inference(rewrite,[status(thm)],[])).
% 0.78/0.77 tff(59,plain,
% 0.78/0.77 ((~![A: $i] : ((![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A)) => (C = D))) => (relation(A) & function(A)))) <=> (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A))))),
% 0.78/0.77 inference(rewrite,[status(thm)],[])).
% 0.78/0.77 tff(60,axiom,(~![A: $i] : ((![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A)) => (C = D))) => (relation(A) & function(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_funct_1')).
% 0.78/0.77 tff(61,plain,
% 0.78/0.77 (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A)))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.78/0.77 tff(62,plain,
% 0.78/0.77 (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A)))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.78/0.77 tff(63,plain,
% 0.78/0.77 (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A)))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.78/0.77 tff(64,plain,
% 0.78/0.77 (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A)))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[63, 58])).
% 0.78/0.77 tff(65,plain,
% 0.78/0.77 (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A)))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[64, 58])).
% 0.78/0.77 tff(66,plain,
% 0.78/0.77 (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A)))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.78/0.77 tff(67,plain,
% 0.78/0.77 (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A)))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[66, 58])).
% 0.78/0.77 tff(68,plain,
% 0.78/0.77 (![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D)) & (~(relation(A!9) & function(A!9)))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.78/0.77 tff(69,plain,
% 0.78/0.77 (![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D))),
% 0.78/0.77 inference(and_elim,[status(thm)],[68])).
% 0.78/0.77 tff(70,plain,
% 0.78/0.77 (![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[69, 53])).
% 0.78/0.77 tff(71,plain,
% 0.78/0.77 (![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[70, 51])).
% 0.78/0.77 tff(72,plain,
% 0.78/0.77 (((~![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))) | ((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)))) <=> ((~![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)))),
% 0.78/0.77 inference(rewrite,[status(thm)],[])).
% 0.78/0.77 tff(73,plain,
% 0.78/0.77 ((~![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))) | ((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)))),
% 0.78/0.77 inference(quant_inst,[status(thm)],[])).
% 0.78/0.77 tff(74,plain,
% 0.78/0.77 ((~![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.78/0.77 tff(75,plain,
% 0.78/0.77 ($false),
% 0.78/0.77 inference(unit_resolution,[status(thm)],[74, 71, 49, 47, 45])).
% 0.78/0.77 tff(76,plain,((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.77 tff(77,plain,
% 0.78/0.77 ((~(function(A!9) | (~((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)))))) | function(A!9) | (~((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9))))),
% 0.78/0.77 inference(tautology,[status(thm)],[])).
% 0.78/0.77 tff(78,plain,
% 0.78/0.77 ((~(function(A!9) | (~((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)))))) | function(A!9)),
% 0.78/0.77 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.78/0.77 tff(79,plain,
% 0.78/0.77 (function(A!9)),
% 0.78/0.77 inference(unit_resolution,[status(thm)],[78, 42])).
% 0.78/0.77 tff(80,plain,
% 0.78/0.77 ((~(~((~relation(A!9)) | (~function(A!9))))) <=> ((~relation(A!9)) | (~function(A!9)))),
% 0.78/0.77 inference(rewrite,[status(thm)],[])).
% 0.78/0.77 tff(81,plain,
% 0.78/0.77 ((relation(A!9) & function(A!9)) <=> (~((~relation(A!9)) | (~function(A!9))))),
% 0.78/0.77 inference(rewrite,[status(thm)],[])).
% 0.78/0.77 tff(82,plain,
% 0.78/0.77 ((~(relation(A!9) & function(A!9))) <=> (~(~((~relation(A!9)) | (~function(A!9)))))),
% 0.78/0.77 inference(monotonicity,[status(thm)],[81])).
% 0.78/0.77 tff(83,plain,
% 0.78/0.77 ((~(relation(A!9) & function(A!9))) <=> ((~relation(A!9)) | (~function(A!9)))),
% 0.78/0.77 inference(transitivity,[status(thm)],[82, 80])).
% 0.78/0.77 tff(84,plain,
% 0.78/0.77 (~(relation(A!9) & function(A!9))),
% 0.78/0.77 inference(and_elim,[status(thm)],[68])).
% 0.78/0.77 tff(85,plain,
% 0.78/0.77 ((~relation(A!9)) | (~function(A!9))),
% 0.78/0.77 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.78/0.77 tff(86,plain,
% 0.78/0.77 (~relation(A!9)),
% 0.78/0.77 inference(unit_resolution,[status(thm)],[85, 79])).
% 0.78/0.77 tff(87,plain,
% 0.78/0.77 ((~(relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))))))) | relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D))))))),
% 0.78/0.77 inference(tautology,[status(thm)],[])).
% 0.78/0.77 tff(88,plain,
% 0.78/0.77 ((~(relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))))))) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D))))))),
% 0.78/0.77 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.78/0.77 tff(89,plain,
% 0.78/0.77 (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))))),
% 0.78/0.77 inference(unit_resolution,[status(thm)],[88, 20])).
% 0.78/0.77 tff(90,plain,
% 0.78/0.77 (((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D))))) | in(tptp_fun_B_17(A!9), A!9)),
% 0.78/0.77 inference(tautology,[status(thm)],[])).
% 0.78/0.77 tff(91,plain,
% 0.78/0.77 (in(tptp_fun_B_17(A!9), A!9)),
% 0.78/0.77 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.78/0.77 tff(92,plain,
% 0.78/0.77 (^[B: $i] : refl(((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) <=> ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)))),
% 0.78/0.77 inference(bind,[status(th)],[])).
% 0.78/0.77 tff(93,plain,
% 0.78/0.77 (![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) <=> ![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B))),
% 0.78/0.78 inference(quant_intro,[status(thm)],[92])).
% 0.78/0.78 tff(94,plain,
% 0.78/0.78 (![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B))),
% 0.78/0.78 inference(and_elim,[status(thm)],[68])).
% 0.78/0.78 tff(95,plain,
% 0.78/0.78 (![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B))),
% 0.78/0.78 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.78/0.78 tff(96,plain,
% 0.78/0.78 (((~![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B))) | ((~in(tptp_fun_B_17(A!9), A!9)) | (ordered_pair(tptp_fun_C_11(tptp_fun_B_17(A!9)), tptp_fun_D_10(tptp_fun_B_17(A!9))) = tptp_fun_B_17(A!9)))) <=> ((~![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B))) | (~in(tptp_fun_B_17(A!9), A!9)) | (ordered_pair(tptp_fun_C_11(tptp_fun_B_17(A!9)), tptp_fun_D_10(tptp_fun_B_17(A!9))) = tptp_fun_B_17(A!9)))),
% 0.78/0.78 inference(rewrite,[status(thm)],[])).
% 0.78/0.78 tff(97,plain,
% 0.78/0.78 ((~![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B))) | ((~in(tptp_fun_B_17(A!9), A!9)) | (ordered_pair(tptp_fun_C_11(tptp_fun_B_17(A!9)), tptp_fun_D_10(tptp_fun_B_17(A!9))) = tptp_fun_B_17(A!9)))),
% 0.78/0.78 inference(quant_inst,[status(thm)],[])).
% 0.78/0.78 tff(98,plain,
% 0.78/0.78 ((~![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B))) | (~in(tptp_fun_B_17(A!9), A!9)) | (ordered_pair(tptp_fun_C_11(tptp_fun_B_17(A!9)), tptp_fun_D_10(tptp_fun_B_17(A!9))) = tptp_fun_B_17(A!9))),
% 0.78/0.78 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.78/0.78 tff(99,plain,
% 0.78/0.78 (ordered_pair(tptp_fun_C_11(tptp_fun_B_17(A!9)), tptp_fun_D_10(tptp_fun_B_17(A!9))) = tptp_fun_B_17(A!9)),
% 0.78/0.78 inference(unit_resolution,[status(thm)],[98, 95, 91])).
% 0.78/0.78 tff(100,plain,
% 0.78/0.78 (tptp_fun_B_17(A!9) = ordered_pair(tptp_fun_C_11(tptp_fun_B_17(A!9)), tptp_fun_D_10(tptp_fun_B_17(A!9)))),
% 0.78/0.78 inference(symmetry,[status(thm)],[99])).
% 0.78/0.78 tff(101,plain,
% 0.78/0.78 (((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D))))) | ![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))),
% 0.78/0.78 inference(tautology,[status(thm)],[])).
% 0.78/0.78 tff(102,plain,
% 0.78/0.78 (![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))),
% 0.78/0.78 inference(unit_resolution,[status(thm)],[101, 89])).
% 0.78/0.78 tff(103,plain,
% 0.78/0.78 ((~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))) | (~(tptp_fun_B_17(A!9) = ordered_pair(tptp_fun_C_11(tptp_fun_B_17(A!9)), tptp_fun_D_10(tptp_fun_B_17(A!9)))))),
% 0.78/0.78 inference(quant_inst,[status(thm)],[])).
% 0.78/0.78 tff(104,plain,
% 0.78/0.78 ($false),
% 0.78/0.78 inference(unit_resolution,[status(thm)],[103, 102, 100])).
% 0.78/0.78 % SZS output end Proof
%------------------------------------------------------------------------------