TSTP Solution File: SEU217+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU217+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 07:28:14 EDT 2022
% Result : Theorem 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU217+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Sep 3 10:43:25 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.22/0.41 % SZS status Theorem
% 0.22/0.41 % SZS output start Proof
% 0.22/0.41 tff(apply_type, type, (
% 0.22/0.41 apply: ( $i * $i ) > $i)).
% 0.22/0.41 tff(identity_relation_type, type, (
% 0.22/0.41 identity_relation: $i > $i)).
% 0.22/0.41 tff(tptp_fun_A_8_type, type, (
% 0.22/0.41 tptp_fun_A_8: $i)).
% 0.22/0.41 tff(in_type, type, (
% 0.22/0.41 in: ( $i * $i ) > $o)).
% 0.22/0.41 tff(relation_dom_type, type, (
% 0.22/0.41 relation_dom: $i > $i)).
% 0.22/0.41 tff(function_type, type, (
% 0.22/0.41 function: $i > $o)).
% 0.22/0.41 tff(relation_type, type, (
% 0.22/0.41 relation: $i > $o)).
% 0.22/0.41 tff(tptp_fun_C_9_type, type, (
% 0.22/0.41 tptp_fun_C_9: ( $i * $i ) > $i)).
% 0.22/0.41 tff(tptp_fun_B_7_type, type, (
% 0.22/0.41 tptp_fun_B_7: $i)).
% 0.22/0.41 tff(1,plain,
% 0.22/0.41 (^[A: $i] : refl((~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(2,plain,
% 0.22/0.41 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.41 tff(3,plain,
% 0.22/0.41 (^[A: $i] : rewrite((relation(identity_relation(A)) & function(identity_relation(A))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(4,plain,
% 0.22/0.41 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.41 tff(5,plain,
% 0.22/0.41 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(6,axiom,(![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_funct_1')).
% 0.22/0.41 tff(7,plain,
% 0.22/0.41 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.22/0.41 tff(8,plain,(
% 0.22/0.41 ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.22/0.41 inference(skolemize,[status(sab)],[7])).
% 0.22/0.41 tff(9,plain,
% 0.22/0.41 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.22/0.41 tff(10,plain,
% 0.22/0.41 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.22/0.41 tff(11,plain,
% 0.22/0.41 ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(A!8))) | (~function(identity_relation(A!8)))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(12,plain,
% 0.22/0.41 (~((~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.22/0.41 tff(13,plain,
% 0.22/0.41 (((~relation(identity_relation(A!8))) | (~function(identity_relation(A!8)))) | function(identity_relation(A!8))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(14,plain,
% 0.22/0.41 (function(identity_relation(A!8))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.22/0.41 tff(15,plain,
% 0.22/0.41 (^[A: $i] : refl(relation(identity_relation(A)) <=> relation(identity_relation(A)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(16,plain,
% 0.22/0.41 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.22/0.41 tff(17,plain,
% 0.22/0.41 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(18,axiom,(![A: $i] : relation(identity_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_relat_1')).
% 0.22/0.41 tff(19,plain,
% 0.22/0.41 (![A: $i] : relation(identity_relation(A))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.22/0.41 tff(20,plain,(
% 0.22/0.41 ![A: $i] : relation(identity_relation(A))),
% 0.22/0.41 inference(skolemize,[status(sab)],[19])).
% 0.22/0.41 tff(21,plain,
% 0.22/0.41 (![A: $i] : relation(identity_relation(A))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.22/0.41 tff(22,plain,
% 0.22/0.41 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(A!8))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(23,plain,
% 0.22/0.41 (relation(identity_relation(A!8))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.22/0.41 tff(24,plain,
% 0.22/0.41 (^[A: $i, B: $i] : trans(monotonicity(rewrite((~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))) <=> (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))))), rewrite(((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(25,plain,
% 0.22/0.41 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.22/0.41 tff(26,plain,
% 0.22/0.41 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(27,plain,
% 0.22/0.41 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.22/0.41 tff(28,plain,
% 0.22/0.41 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(29,plain,
% 0.22/0.41 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.22/0.41 tff(30,plain,
% 0.22/0.41 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[29, 27])).
% 0.22/0.41 tff(31,plain,
% 0.22/0.41 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), trans(monotonicity(rewrite(((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) <=> ((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))), rewrite(((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))) <=> ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))), ((((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) <=> (((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))), rewrite((((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) <=> (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))), ((((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) <=> (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))))), (((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))) <=> (((~relation(B)) | (~function(B))) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))))), rewrite((((~relation(B)) | (~function(B))) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))))), (((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(32,plain,
% 0.22/0.42 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[31])).
% 0.22/0.42 tff(33,plain,
% 0.22/0.42 (^[A: $i, B: $i] : rewrite(((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))) <=> ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(34,plain,
% 0.22/0.42 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[33])).
% 0.22/0.42 tff(35,plain,
% 0.22/0.42 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(36,plain,
% 0.22/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C)))) <=> ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))), (((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))), rewrite(((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))) <=> ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))), (((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 (![A: $i, B: $i] : ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.22/0.42 tff(38,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t34_funct_1')).
% 0.22/0.42 tff(39,plain,
% 0.22/0.42 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.22/0.42 tff(40,plain,
% 0.22/0.42 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.22/0.42 tff(41,plain,(
% 0.22/0.42 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A))))))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[40])).
% 0.22/0.42 tff(42,plain,
% 0.22/0.42 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.22/0.42 tff(43,plain,
% 0.22/0.42 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.22/0.42 tff(44,plain,
% 0.22/0.42 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[43, 30])).
% 0.22/0.42 tff(45,plain,
% 0.22/0.42 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[44, 25])).
% 0.22/0.42 tff(46,plain,
% 0.22/0.42 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(47,plain,
% 0.22/0.42 (((~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C)))))) <=> ((~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(48,plain,
% 0.22/0.42 ((~((~((identity_relation(A!8) = identity_relation(A!8)) | (~(relation_dom(identity_relation(A!8)) = A!8)) | (~((~in(tptp_fun_C_9(identity_relation(A!8), A!8), A!8)) | (apply(identity_relation(A!8), tptp_fun_C_9(identity_relation(A!8), A!8)) = tptp_fun_C_9(identity_relation(A!8), A!8)))))) | (~((~(identity_relation(A!8) = identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))))))))) <=> (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C)))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(49,plain,
% 0.22/0.42 (((~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))) | (~((~((identity_relation(A!8) = identity_relation(A!8)) | (~(relation_dom(identity_relation(A!8)) = A!8)) | (~((~in(tptp_fun_C_9(identity_relation(A!8), A!8), A!8)) | (apply(identity_relation(A!8), tptp_fun_C_9(identity_relation(A!8), A!8)) = tptp_fun_C_9(identity_relation(A!8), A!8)))))) | (~((~(identity_relation(A!8) = identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C)))))))))) <=> ((~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[48])).
% 0.22/0.42 tff(50,plain,
% 0.22/0.42 (((~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))) | (~((~((identity_relation(A!8) = identity_relation(A!8)) | (~(relation_dom(identity_relation(A!8)) = A!8)) | (~((~in(tptp_fun_C_9(identity_relation(A!8), A!8), A!8)) | (apply(identity_relation(A!8), tptp_fun_C_9(identity_relation(A!8), A!8)) = tptp_fun_C_9(identity_relation(A!8), A!8)))))) | (~((~(identity_relation(A!8) = identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C)))))))))) <=> ((~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[49, 47])).
% 0.22/0.42 tff(51,plain,
% 0.22/0.42 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))) | (~((~((identity_relation(A!8) = identity_relation(A!8)) | (~(relation_dom(identity_relation(A!8)) = A!8)) | (~((~in(tptp_fun_C_9(identity_relation(A!8), A!8), A!8)) | (apply(identity_relation(A!8), tptp_fun_C_9(identity_relation(A!8), A!8)) = tptp_fun_C_9(identity_relation(A!8), A!8)))))) | (~((~(identity_relation(A!8) = identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C)))))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[50])).
% 0.22/0.42 tff(52,plain,
% 0.22/0.42 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))) | (~((~((identity_relation(A!8) = identity_relation(A!8)) | (~(relation_dom(identity_relation(A!8)) = A!8)) | (~((~in(tptp_fun_C_9(identity_relation(A!8), A!8), A!8)) | (apply(identity_relation(A!8), tptp_fun_C_9(identity_relation(A!8), A!8)) = tptp_fun_C_9(identity_relation(A!8), A!8)))))) | (~((~(identity_relation(A!8) = identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[51, 46])).
% 0.22/0.42 tff(53,plain,
% 0.22/0.42 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))) | (~((~((identity_relation(A!8) = identity_relation(A!8)) | (~(relation_dom(identity_relation(A!8)) = A!8)) | (~((~in(tptp_fun_C_9(identity_relation(A!8), A!8), A!8)) | (apply(identity_relation(A!8), tptp_fun_C_9(identity_relation(A!8), A!8)) = tptp_fun_C_9(identity_relation(A!8), A!8)))))) | (~((~(identity_relation(A!8) = identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))))))))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(54,plain,
% 0.22/0.42 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_9(B, A), A)) | (apply(B, tptp_fun_C_9(B, A)) = tptp_fun_C_9(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(A!8))) | (~function(identity_relation(A!8))) | (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.22/0.42 tff(55,plain,
% 0.22/0.42 (~((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[54, 45, 23, 14])).
% 0.22/0.42 tff(56,plain,
% 0.22/0.42 (((~(relation_dom(identity_relation(A!8)) = A!8)) | (~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C)))) | ![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(57,plain,
% 0.22/0.42 (![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.22/0.42 tff(58,plain,
% 0.22/0.42 ((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) <=> (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(59,plain,
% 0.22/0.42 ((~![A: $i, B: $i] : (in(B, A) => (apply(identity_relation(A), B) = B))) <=> (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(60,axiom,(~![A: $i, B: $i] : (in(B, A) => (apply(identity_relation(A), B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t35_funct_1')).
% 0.22/0.42 tff(61,plain,
% 0.22/0.42 (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.22/0.42 tff(62,plain,
% 0.22/0.42 (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.22/0.42 tff(63,plain,
% 0.22/0.42 (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.22/0.42 tff(64,plain,
% 0.22/0.42 (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[63, 58])).
% 0.22/0.42 tff(65,plain,
% 0.22/0.42 (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[64, 58])).
% 0.22/0.43 tff(66,plain,
% 0.22/0.43 (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.22/0.43 tff(67,plain,
% 0.22/0.43 (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[66, 58])).
% 0.22/0.43 tff(68,plain,(
% 0.22/0.43 ~((~in(B!7, A!8)) | (apply(identity_relation(A!8), B!7) = B!7))),
% 0.22/0.43 inference(skolemize,[status(sab)],[67])).
% 0.22/0.43 tff(69,plain,
% 0.22/0.43 (~(apply(identity_relation(A!8), B!7) = B!7)),
% 0.22/0.43 inference(or_elim,[status(thm)],[68])).
% 0.22/0.43 tff(70,plain,
% 0.22/0.43 (in(B!7, A!8)),
% 0.22/0.43 inference(or_elim,[status(thm)],[68])).
% 0.22/0.43 tff(71,plain,
% 0.22/0.43 (((~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))) | ((~in(B!7, A!8)) | (apply(identity_relation(A!8), B!7) = B!7))) <=> ((~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))) | (~in(B!7, A!8)) | (apply(identity_relation(A!8), B!7) = B!7))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(72,plain,
% 0.22/0.43 ((~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))) | ((~in(B!7, A!8)) | (apply(identity_relation(A!8), B!7) = B!7))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(73,plain,
% 0.22/0.43 ((~![C: $i] : ((~in(C, A!8)) | (apply(identity_relation(A!8), C) = C))) | (~in(B!7, A!8)) | (apply(identity_relation(A!8), B!7) = B!7)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.22/0.43 tff(74,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[73, 70, 69, 57])).
% 0.22/0.43 % SZS output end Proof
%------------------------------------------------------------------------------