TSTP Solution File: SEU008+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU008+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:16 EDT 2022
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : SEU008+1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 08:53:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(in_type, type, (
% 0.20/0.44 in: ( $i * $i ) > $o)).
% 0.20/0.44 tff(relation_dom_type, type, (
% 0.20/0.44 relation_dom: $i > $i)).
% 0.20/0.44 tff(identity_relation_type, type, (
% 0.20/0.44 identity_relation: $i > $i)).
% 0.20/0.44 tff(tptp_fun_A_13_type, type, (
% 0.20/0.44 tptp_fun_A_13: $i)).
% 0.20/0.44 tff(tptp_fun_B_12_type, type, (
% 0.20/0.44 tptp_fun_B_12: $i)).
% 0.20/0.44 tff(apply_type, type, (
% 0.20/0.44 apply: ( $i * $i ) > $i)).
% 0.20/0.44 tff(function_type, type, (
% 0.20/0.44 function: $i > $o)).
% 0.20/0.44 tff(relation_type, type, (
% 0.20/0.44 relation: $i > $o)).
% 0.20/0.44 tff(tptp_fun_C_10_type, type, (
% 0.20/0.44 tptp_fun_C_10: ( $i * $i ) > $i)).
% 0.20/0.44 tff(tptp_fun_C_11_type, type, (
% 0.20/0.44 tptp_fun_C_11: $i)).
% 0.20/0.44 tff(set_intersection2_type, type, (
% 0.20/0.44 set_intersection2: ( $i * $i ) > $i)).
% 0.20/0.44 tff(tptp_fun_D_0_type, type, (
% 0.20/0.44 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(relation_composition_type, type, (
% 0.20/0.44 relation_composition: ( $i * $i ) > $i)).
% 0.20/0.44 tff(1,plain,
% 0.20/0.44 (^[A: $i] : refl((~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(2,plain,
% 0.20/0.44 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 (^[A: $i] : rewrite((relation(identity_relation(A)) & function(identity_relation(A))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.44 tff(5,plain,
% 0.20/0.44 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(6,axiom,(![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_funct_1')).
% 0.20/0.44 tff(7,plain,
% 0.20/0.44 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.44 tff(8,plain,(
% 0.20/0.44 ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[7])).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.44 tff(11,plain,
% 0.20/0.44 ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 (~((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13)))) | function(identity_relation(A!13))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 (function(identity_relation(A!13))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (^[A: $i] : refl(relation(identity_relation(A)) <=> relation(identity_relation(A)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(16,plain,
% 0.20/0.44 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(18,axiom,(![A: $i] : relation(identity_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_relat_1')).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 (![A: $i] : relation(identity_relation(A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.44 tff(20,plain,(
% 0.20/0.44 ![A: $i] : relation(identity_relation(A))),
% 0.20/0.44 inference(skolemize,[status(sab)],[19])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (![A: $i] : relation(identity_relation(A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.44 tff(22,plain,
% 0.20/0.44 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(A!13))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(23,plain,
% 0.20/0.44 (relation(identity_relation(A!13))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 (^[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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))) <=> (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 (^[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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (^[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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[29, 27])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (^[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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))) <=> ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 (^[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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (^[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)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.44 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')).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (![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)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.20/0.45 tff(41,plain,(
% 0.20/0.45 ![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[40])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[43, 30])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[44, 25])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C)))))) <=> ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 ((~((~((identity_relation(A!13) = identity_relation(A!13)) | (~(relation_dom(identity_relation(A!13)) = A!13)) | (~((~in(tptp_fun_C_10(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_10(identity_relation(A!13), A!13)) = tptp_fun_C_10(identity_relation(A!13), A!13)))))) | (~((~(identity_relation(A!13) = identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))))))))) <=> (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~((identity_relation(A!13) = identity_relation(A!13)) | (~(relation_dom(identity_relation(A!13)) = A!13)) | (~((~in(tptp_fun_C_10(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_10(identity_relation(A!13), A!13)) = tptp_fun_C_10(identity_relation(A!13), A!13)))))) | (~((~(identity_relation(A!13) = identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C)))))))))) <=> ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[48])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~((identity_relation(A!13) = identity_relation(A!13)) | (~(relation_dom(identity_relation(A!13)) = A!13)) | (~((~in(tptp_fun_C_10(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_10(identity_relation(A!13), A!13)) = tptp_fun_C_10(identity_relation(A!13), A!13)))))) | (~((~(identity_relation(A!13) = identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C)))))))))) <=> ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[49, 47])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~((identity_relation(A!13) = identity_relation(A!13)) | (~(relation_dom(identity_relation(A!13)) = A!13)) | (~((~in(tptp_fun_C_10(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_10(identity_relation(A!13), A!13)) = tptp_fun_C_10(identity_relation(A!13), A!13)))))) | (~((~(identity_relation(A!13) = identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C)))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~((identity_relation(A!13) = identity_relation(A!13)) | (~(relation_dom(identity_relation(A!13)) = A!13)) | (~((~in(tptp_fun_C_10(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_10(identity_relation(A!13), A!13)) = tptp_fun_C_10(identity_relation(A!13), A!13)))))) | (~((~(identity_relation(A!13) = identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[51, 46])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~((identity_relation(A!13) = identity_relation(A!13)) | (~(relation_dom(identity_relation(A!13)) = A!13)) | (~((~in(tptp_fun_C_10(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_10(identity_relation(A!13), A!13)) = tptp_fun_C_10(identity_relation(A!13), A!13)))))) | (~((~(identity_relation(A!13) = identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[54, 45, 23, 14])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 (((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C)))) | (relation_dom(identity_relation(A!13)) = A!13)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (relation_dom(identity_relation(A!13)) = A!13),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (in(B!12, relation_dom(identity_relation(A!13))) <=> in(B!12, A!13)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[57])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (in(B!12, A!13) <=> in(B!12, relation_dom(identity_relation(A!13)))),
% 0.20/0.45 inference(symmetry,[status(thm)],[58])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.20/0.45 inference(pull_quant,[status(thm)],[])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[64, 62])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[65, 61])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.46 tff(69,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[68, 66])).
% 0.20/0.46 tff(70,plain,
% 0.20/0.46 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))), rewrite(((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))) <=> ((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))) & ((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))) & ((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(71,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(73,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(75,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_xboole_0')).
% 0.20/0.46 tff(76,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.46 tff(77,plain,(
% 0.20/0.46 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[76])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.20/0.46 tff(79,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[79, 69])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | ((~in(B!12, set_intersection2(relation_dom(C!11), A!13))) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | ((~in(B!12, set_intersection2(relation_dom(C!11), A!13))) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 ((~(in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))) <=> ((~in(B!12, set_intersection2(relation_dom(C!11), A!13))) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 (((in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11))))) | $false) <=> (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 ((~$true) <=> $false),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 (($true | (in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13))))) <=> $true),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 ((in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13)))) <=> (in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 ((set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13)) <=> $true),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (((set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13))))) <=> ($true | (in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[87, 86])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (((set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13))))) <=> $true),
% 0.20/0.46 inference(transitivity,[status(thm)],[88, 85])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 ((~((set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13)))))) <=> (~$true)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[89])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 ((~((set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13)))))) <=> $false),
% 0.20/0.46 inference(transitivity,[status(thm)],[90, 84])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 ((~(in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11))))))) <=> (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (($false | (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11))))))) <=> (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 ((~(set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13))) <=> (~$true)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[87])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 ((~(set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13))) <=> $false),
% 0.20/0.47 inference(transitivity,[status(thm)],[94, 84])).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 (((~(set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13))) | (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11))))))) <=> ($false | (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[95])).
% 0.20/0.47 tff(97,plain,
% 0.20/0.47 (((~(set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13))) | (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11))))))) <=> (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[96, 93])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 ((~((~(set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13))) | (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))))) <=> (~(in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[97])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 ((~((~(set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13))) | (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))))) <=> (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[98, 92])).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 (((~((~(set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13))) | (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))))) | (~((set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13))))))) <=> ((in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11))))) | $false)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[99, 91])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (((~((~(set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13))) | (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))))) | (~((set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13))))))) <=> (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[100, 83])).
% 0.20/0.47 tff(102,plain,
% 0.20/0.47 ((~((~((~(set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13))) | (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))))) | (~((set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13)))))))) <=> (~(in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[101])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 ((~((~((~(set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13))) | (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))))) | (~((set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13)))))))) <=> ((~in(B!12, set_intersection2(relation_dom(C!11), A!13))) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[102, 82])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | (~((~((~(set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13))) | (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))))) | (~((set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | ((~in(B!12, set_intersection2(relation_dom(C!11), A!13))) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | (~((~((~(set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13))) | (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))))) | (~((set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | ((~in(B!12, set_intersection2(relation_dom(C!11), A!13))) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[104, 81])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | (~((~((~(set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13))) | (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))))) | (~((set_intersection2(relation_dom(C!11), A!13) = set_intersection2(relation_dom(C!11), A!13)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), set_intersection2(relation_dom(C!11), A!13)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), relation_dom(C!11))) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(C!11), A!13), A!13, relation_dom(C!11)), A!13))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | ((~in(B!12, set_intersection2(relation_dom(C!11), A!13))) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 ((~in(B!12, set_intersection2(relation_dom(C!11), A!13))) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[107, 80])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 ((~((apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12)) | (~(relation(C!11) & function(C!11))) | (~in(B!12, set_intersection2(relation_dom(C!11), A!13))))) <=> (~((apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12)) | (~(relation(C!11) & function(C!11))) | (~in(B!12, set_intersection2(relation_dom(C!11), A!13)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 ((~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A))))) <=> (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 ((~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (in(B, set_intersection2(relation_dom(C), A)) => (apply(C, B) = apply(relation_composition(identity_relation(A), C), B))))) <=> (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(112,axiom,(~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (in(B, set_intersection2(relation_dom(C), A)) => (apply(C, B) = apply(relation_composition(identity_relation(A), C), B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t38_funct_1')).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[115, 110])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[116, 110])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[118, 110])).
% 0.20/0.47 tff(120,plain,(
% 0.20/0.47 ~((apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12)) | (~(relation(C!11) & function(C!11))) | (~in(B!12, set_intersection2(relation_dom(C!11), A!13))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[119])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 (~((apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12)) | (~(relation(C!11) & function(C!11))) | (~in(B!12, set_intersection2(relation_dom(C!11), A!13))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[120, 109])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (in(B!12, set_intersection2(relation_dom(C!11), A!13))),
% 0.20/0.47 inference(or_elim,[status(thm)],[121])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 ((~((~in(B!12, set_intersection2(relation_dom(C!11), A!13))) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))) | (~in(B!12, set_intersection2(relation_dom(C!11), A!13))) | (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 ((~((~in(B!12, set_intersection2(relation_dom(C!11), A!13))) <=> ((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))) | (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (~((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[124, 108])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (((~in(B!12, A!13)) | (~in(B!12, relation_dom(C!11)))) | in(B!12, A!13)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 (in(B!12, A!13)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (in(B!12, relation_dom(identity_relation(A!13)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[127, 59])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 ((apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, B!12)) <=> (apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12))),
% 0.20/0.47 inference(commutativity,[status(thm)],[])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 (((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C)))) | ![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 (![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[130, 55])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 (((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | ((~in(B!12, A!13)) | (apply(identity_relation(A!13), B!12) = B!12))) <=> ((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~in(B!12, A!13)) | (apply(identity_relation(A!13), B!12) = B!12))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(133,plain,
% 0.20/0.47 ((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | ((~in(B!12, A!13)) | (apply(identity_relation(A!13), B!12) = B!12))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 ((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~in(B!12, A!13)) | (apply(identity_relation(A!13), B!12) = B!12)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (apply(identity_relation(A!13), B!12) = B!12),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[134, 127, 131])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (apply(C!11, apply(identity_relation(A!13), B!12)) = apply(C!11, B!12)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[135])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 ((apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))) <=> (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, B!12))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[136])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 ((apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))) <=> (apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12))),
% 0.20/0.48 inference(transitivity,[status(thm)],[137, 129])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 ((apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12)) <=> (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12)))),
% 0.20/0.48 inference(symmetry,[status(thm)],[138])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 ((~(apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12))) <=> (~(apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.48 tff(141,plain,
% 0.20/0.48 (~(apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12))),
% 0.20/0.48 inference(or_elim,[status(thm)],[121])).
% 0.20/0.48 tff(142,plain,
% 0.20/0.48 (~(apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.48 tff(143,plain,
% 0.20/0.48 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(144,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[143])).
% 0.20/0.48 tff(145,plain,
% 0.20/0.48 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(146,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[145])).
% 0.20/0.48 tff(147,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[146, 144])).
% 0.20/0.48 tff(148,plain,
% 0.20/0.48 (^[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))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | ((~relation(C)) | (~function(C)))))), rewrite(((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | ((~relation(C)) | (~function(C)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))), (![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(149,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[148])).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(151,plain,
% 0.20/0.48 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))) <=> ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), rewrite(((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[151])).
% 0.20/0.48 tff(153,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_funct_1')).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.20/0.48 tff(156,plain,(
% 0.20/0.48 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[155])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[157, 147])).
% 0.20/0.48 tff(159,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(160,plain,
% 0.20/0.48 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) <=> ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 (^[C: $i] : rewrite(((apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 (![C: $i] : ((apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[161])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[162])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[163, 160])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[164])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[165, 159])).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (~relation(C)) | (~function(C))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(168,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 (![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[168, 158, 23, 14])).
% 0.20/0.48 tff(170,plain,
% 0.20/0.48 (relation(C!11) & function(C!11)),
% 0.20/0.48 inference(or_elim,[status(thm)],[121])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 (function(C!11)),
% 0.20/0.48 inference(and_elim,[status(thm)],[170])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 (relation(C!11)),
% 0.20/0.48 inference(and_elim,[status(thm)],[170])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | ((~relation(C!11)) | (~function(C!11)) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | (~relation(C!11)) | (~function(C!11)) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 (((~relation(C!11)) | (~function(C!11)) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))) <=> ((~relation(C!11)) | (~function(C!11)) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | ((~relation(C!11)) | (~function(C!11)) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | ((~relation(C!11)) | (~function(C!11)) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[174])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | ((~relation(C!11)) | (~function(C!11)) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | (~relation(C!11)) | (~function(C!11)) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[175, 173])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | ((~relation(C!11)) | (~function(C!11)) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(178,plain,
% 0.20/0.48 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | (~relation(C!11)) | (~function(C!11)) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.49 tff(179,plain,
% 0.20/0.49 ((~in(B!12, relation_dom(identity_relation(A!13)))) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[178, 172, 171, 169])).
% 0.20/0.49 tff(180,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[179, 142, 128])).
% 0.20/0.49 % SZS output end Proof
%------------------------------------------------------------------------------