%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU221+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 : Sat Jun 21 05:27:17 AM UTC 2025
% Result : Theorem 0.93s 1.09s
% Output : Proof 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU221+2 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:21:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.93/1.09 % SZS status Theorem
% 0.93/1.09 % SZS output start Proof
% 0.93/1.09 tff(tptp_fun_C_46_type, type, (
% 0.93/1.09 tptp_fun_C_46: $i > $i)).
% 0.93/1.09 tff(function_inverse_type, type, (
% 0.93/1.09 function_inverse: $i > $i)).
% 0.93/1.09 tff(tptp_fun_A_75_type, type, (
% 0.93/1.09 tptp_fun_A_75: $i)).
% 0.93/1.09 tff(tptp_fun_B_47_type, type, (
% 0.93/1.09 tptp_fun_B_47: $i > $i)).
% 0.93/1.09 tff(apply_type, type, (
% 0.93/1.09 apply: ( $i * $i ) > $i)).
% 0.93/1.09 tff(relation_composition_type, type, (
% 0.93/1.09 relation_composition: ( $i * $i ) > $i)).
% 0.93/1.09 tff(in_type, type, (
% 0.93/1.09 in: ( $i * $i ) > $o)).
% 0.93/1.09 tff(relation_rng_type, type, (
% 0.93/1.09 relation_rng: $i > $i)).
% 0.93/1.09 tff(relation_dom_type, type, (
% 0.93/1.09 relation_dom: $i > $i)).
% 0.93/1.09 tff(one_to_one_type, type, (
% 0.93/1.09 one_to_one: $i > $o)).
% 0.93/1.09 tff(function_type, type, (
% 0.93/1.09 function: $i > $o)).
% 0.93/1.09 tff(relation_type, type, (
% 0.93/1.09 relation: $i > $o)).
% 0.93/1.09 tff(1,plain,
% 0.93/1.09 ((~(one_to_one(function_inverse(A!75)) | (~(relation(A!75) & function(A!75))) | (~one_to_one(A!75)))) <=> (~(one_to_one(function_inverse(A!75)) | (~(relation(A!75) & function(A!75))) | (~one_to_one(A!75))))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(2,plain,
% 0.93/1.09 ((~![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))) <=> (~![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A))))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(3,plain,
% 0.93/1.09 ((~![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => one_to_one(function_inverse(A))))) <=> (~![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A))))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(4,axiom,(~![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => one_to_one(function_inverse(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t62_funct_1')).
% 0.93/1.09 tff(5,plain,
% 0.93/1.09 (~![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.93/1.09 tff(6,plain,
% 0.93/1.09 (~![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.93/1.09 tff(7,plain,
% 0.93/1.09 (~![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.93/1.09 tff(8,plain,
% 0.93/1.09 (~![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.93/1.09 tff(9,plain,(
% 0.93/1.09 ~(one_to_one(function_inverse(A!75)) | (~(relation(A!75) & function(A!75))) | (~one_to_one(A!75)))),
% 0.93/1.09 inference(skolemize,[status(sab)],[8])).
% 0.93/1.09 tff(10,plain,
% 0.93/1.09 (~(one_to_one(function_inverse(A!75)) | (~(relation(A!75) & function(A!75))) | (~one_to_one(A!75)))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.93/1.09 tff(11,plain,
% 0.93/1.09 (one_to_one(A!75)),
% 0.93/1.09 inference(or_elim,[status(thm)],[10])).
% 0.93/1.09 tff(12,plain,
% 0.93/1.09 (relation(A!75) & function(A!75)),
% 0.93/1.09 inference(or_elim,[status(thm)],[10])).
% 0.93/1.09 tff(13,plain,
% 0.93/1.09 (function(A!75)),
% 0.93/1.09 inference(and_elim,[status(thm)],[12])).
% 0.93/1.09 tff(14,plain,
% 0.93/1.09 (relation(A!75)),
% 0.93/1.09 inference(and_elim,[status(thm)],[12])).
% 0.93/1.09 tff(15,plain,
% 0.93/1.09 (^[A: $i] : refl(((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))) <=> ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))))),
% 0.93/1.09 inference(bind,[status(th)],[])).
% 0.93/1.09 tff(16,plain,
% 0.93/1.09 (![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))) <=> ![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.93/1.09 inference(quant_intro,[status(thm)],[15])).
% 0.93/1.09 tff(17,plain,
% 0.93/1.09 (^[A: $i] : trans(monotonicity(rewrite(((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) <=> (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))), trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), ((((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))))), rewrite(((~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))) <=> ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))), ((((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))))),
% 0.93/1.09 inference(bind,[status(th)],[])).
% 0.93/1.09 tff(18,plain,
% 0.93/1.09 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.93/1.09 inference(quant_intro,[status(thm)],[17])).
% 0.93/1.09 tff(19,plain,
% 0.93/1.09 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(20,plain,
% 0.93/1.09 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A))))) <=> ((~one_to_one(A)) | ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))))),
% 0.93/1.09 inference(bind,[status(th)],[])).
% 0.93/1.09 tff(21,plain,
% 0.93/1.09 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> ![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.93/1.10 inference(quant_intro,[status(thm)],[20])).
% 0.93/1.10 tff(22,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t55_funct_1')).
% 0.93/1.10 tff(23,plain,
% 0.93/1.10 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.93/1.10 tff(24,plain,
% 0.93/1.10 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.93/1.10 tff(25,plain,(
% 0.93/1.10 ![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.93/1.10 inference(skolemize,[status(sab)],[24])).
% 0.93/1.10 tff(26,plain,
% 0.93/1.10 (![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.93/1.10 tff(27,plain,
% 0.93/1.10 (![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.93/1.10 tff(28,plain,
% 0.93/1.10 (((~![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | (~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75)))))))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(29,plain,
% 0.93/1.10 (((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75))))))) <=> ((~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75)))))))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(30,plain,
% 0.93/1.10 ((~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75)))))) <=> (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75))))))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(31,plain,
% 0.93/1.10 (((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75))))))) <=> ((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75)))))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[30])).
% 0.93/1.10 tff(32,plain,
% 0.93/1.10 (((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75))))))) <=> ((~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75)))))))),
% 0.93/1.10 inference(transitivity,[status(thm)],[31, 29])).
% 0.93/1.10 tff(33,plain,
% 0.93/1.10 (((~![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75))))))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[32])).
% 0.93/1.10 tff(34,plain,
% 0.93/1.10 (((~![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | (~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75)))))))),
% 0.93/1.10 inference(transitivity,[status(thm)],[33, 28])).
% 0.93/1.10 tff(35,plain,
% 0.93/1.10 ((~![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75)))))))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(36,plain,
% 0.93/1.10 ((~![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | (~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75))))))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.93/1.10 tff(37,plain,
% 0.93/1.10 (~((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75)))))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[36, 27, 14, 13, 11])).
% 0.93/1.10 tff(38,plain,
% 0.93/1.10 (((~(relation_rng(A!75) = relation_dom(function_inverse(A!75)))) | (~(relation_dom(A!75) = relation_rng(function_inverse(A!75))))) | (relation_rng(A!75) = relation_dom(function_inverse(A!75)))),
% 0.93/1.10 inference(tautology,[status(thm)],[])).
% 0.93/1.10 tff(39,plain,
% 0.93/1.10 (relation_rng(A!75) = relation_dom(function_inverse(A!75))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.93/1.10 tff(40,plain,
% 0.93/1.10 (in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75)) <=> in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[39])).
% 0.93/1.10 tff(41,plain,
% 0.93/1.10 (in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75))) <=> in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))),
% 0.93/1.10 inference(symmetry,[status(thm)],[40])).
% 0.93/1.10 tff(42,plain,
% 0.93/1.10 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))))),
% 0.93/1.10 inference(bind,[status(th)],[])).
% 0.93/1.10 tff(43,plain,
% 0.93/1.10 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.93/1.10 inference(quant_intro,[status(thm)],[42])).
% 0.93/1.10 tff(44,plain,
% 0.93/1.10 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), rewrite((relation(function_inverse(A)) & function(function_inverse(A))) <=> (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))), (((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> (((~relation(A)) | (~function(A))) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))), (((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))))),
% 0.93/1.10 inference(bind,[status(th)],[])).
% 0.93/1.10 tff(45,plain,
% 0.93/1.10 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.93/1.10 inference(quant_intro,[status(thm)],[44])).
% 0.93/1.10 tff(46,plain,
% 0.93/1.10 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(47,plain,
% 0.93/1.10 (^[A: $i] : rewrite(((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))))),
% 0.93/1.10 inference(bind,[status(th)],[])).
% 0.93/1.10 tff(48,plain,
% 0.93/1.10 (![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.93/1.10 inference(quant_intro,[status(thm)],[47])).
% 0.93/1.10 tff(49,axiom,(![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_funct_1')).
% 0.93/1.10 tff(50,plain,
% 0.93/1.10 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.93/1.10 tff(51,plain,
% 0.93/1.10 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.93/1.10 tff(52,plain,(
% 0.93/1.10 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.93/1.10 inference(skolemize,[status(sab)],[51])).
% 0.93/1.10 tff(53,plain,
% 0.93/1.10 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.93/1.10 tff(54,plain,
% 0.93/1.10 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.93/1.10 tff(55,plain,
% 0.93/1.10 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!75)) | (~function(A!75)) | (~((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(A!75)) | (~function(A!75)) | (~((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))))))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(56,plain,
% 0.93/1.10 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!75)) | (~function(A!75)) | (~((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))))))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(57,plain,
% 0.93/1.10 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(A!75)) | (~function(A!75)) | (~((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75)))))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.93/1.10 tff(58,plain,
% 0.93/1.10 (~((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[57, 54, 14, 13])).
% 0.93/1.10 tff(59,plain,
% 0.93/1.10 (((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75)))) | relation(function_inverse(A!75))),
% 0.93/1.10 inference(tautology,[status(thm)],[])).
% 0.93/1.10 tff(60,plain,
% 0.93/1.10 (relation(function_inverse(A!75))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.93/1.10 tff(61,plain,
% 0.93/1.10 (((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75)))) | function(function_inverse(A!75))),
% 0.93/1.10 inference(tautology,[status(thm)],[])).
% 0.93/1.10 tff(62,plain,
% 0.93/1.10 (function(function_inverse(A!75))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.93/1.10 tff(63,plain,
% 0.93/1.10 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))))))))))),
% 0.93/1.10 inference(bind,[status(th)],[])).
% 0.93/1.10 tff(64,plain,
% 0.93/1.10 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))),
% 0.93/1.10 inference(quant_intro,[status(thm)],[63])).
% 0.93/1.10 tff(65,plain,
% 0.93/1.10 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))))))))))),
% 0.93/1.10 inference(bind,[status(th)],[])).
% 0.93/1.10 tff(66,plain,
% 0.93/1.10 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))),
% 0.93/1.10 inference(quant_intro,[status(thm)],[65])).
% 0.93/1.10 tff(67,plain,
% 0.93/1.10 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))),
% 0.93/1.10 inference(transitivity,[status(thm)],[66, 64])).
% 0.93/1.10 tff(68,plain,
% 0.93/1.10 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), trans(monotonicity(rewrite(((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) <=> ((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))), rewrite((one_to_one(A) | (~((~(in(tptp_fun_B_47(A), relation_dom(A)) & in(tptp_fun_C_46(A), relation_dom(A)) & (apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))) | (tptp_fun_B_47(A) = tptp_fun_C_46(A))))) <=> (one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))), ((((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_47(A), relation_dom(A)) & in(tptp_fun_C_46(A), relation_dom(A)) & (apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))) | (tptp_fun_B_47(A) = tptp_fun_C_46(A)))))) <=> (((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))), rewrite((((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))))))))), ((((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_47(A), relation_dom(A)) & in(tptp_fun_C_46(A), relation_dom(A)) & (apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))) | (tptp_fun_B_47(A) = tptp_fun_C_46(A)))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))), (((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_47(A), relation_dom(A)) & in(tptp_fun_C_46(A), relation_dom(A)) & (apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))) | (tptp_fun_B_47(A) = tptp_fun_C_46(A))))))) <=> (((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))))))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))), (((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_47(A), relation_dom(A)) & in(tptp_fun_C_46(A), relation_dom(A)) & (apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))) | (tptp_fun_B_47(A) = tptp_fun_C_46(A))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))))),
% 0.93/1.10 inference(bind,[status(th)],[])).
% 0.93/1.10 tff(69,plain,
% 0.93/1.10 (![A: $i] : ((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_47(A), relation_dom(A)) & in(tptp_fun_C_46(A), relation_dom(A)) & (apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))) | (tptp_fun_B_47(A) = tptp_fun_C_46(A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))),
% 0.93/1.10 inference(quant_intro,[status(thm)],[68])).
% 0.93/1.10 tff(70,plain,
% 0.93/1.10 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(71,plain,
% 0.93/1.10 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))) <=> (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))))), rewrite(((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))))),
% 0.93/1.10 inference(bind,[status(th)],[])).
% 0.93/1.10 tff(72,plain,
% 0.93/1.10 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.93/1.10 inference(quant_intro,[status(thm)],[71])).
% 0.93/1.10 tff(73,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_funct_1')).
% 0.93/1.10 tff(74,plain,
% 0.93/1.10 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.93/1.10 tff(75,plain,
% 0.93/1.10 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.93/1.10 tff(76,plain,(
% 0.93/1.10 ![A: $i] : ((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_47(A), relation_dom(A)) & in(tptp_fun_C_46(A), relation_dom(A)) & (apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A))))) | (tptp_fun_B_47(A) = tptp_fun_C_46(A)))))))),
% 0.93/1.10 inference(skolemize,[status(sab)],[75])).
% 0.93/1.10 tff(77,plain,
% 0.93/1.10 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.93/1.10 tff(78,plain,
% 0.93/1.10 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.93/1.10 tff(79,plain,
% 0.93/1.10 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))) | ((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))) | (~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))))))))))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(80,plain,
% 0.93/1.10 (((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75)))))))))) <=> ((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))))))))))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(81,plain,
% 0.93/1.10 ((~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))))))))) <=> (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75)))))))))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(82,plain,
% 0.93/1.10 (((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))))))))) <=> ((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))))))))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[81])).
% 0.93/1.10 tff(83,plain,
% 0.93/1.10 (((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))))))))) <=> ((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))))))))))),
% 0.93/1.10 inference(transitivity,[status(thm)],[82, 80])).
% 0.93/1.10 tff(84,plain,
% 0.93/1.10 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))) | ((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))) | ((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75)))))))))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[83])).
% 0.93/1.10 tff(85,plain,
% 0.93/1.10 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))) | ((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))) | (~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))))))))))),
% 0.93/1.10 inference(transitivity,[status(thm)],[84, 79])).
% 0.93/1.10 tff(86,plain,
% 0.93/1.10 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))) | ((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))))))))))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(87,plain,
% 0.93/1.10 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_47(A) = tptp_fun_C_46(A)) | (~in(tptp_fun_B_47(A), relation_dom(A))) | (~in(tptp_fun_C_46(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_47(A)) = apply(A, tptp_fun_C_46(A)))))))))))) | (~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75)))))))))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.93/1.10 tff(88,plain,
% 0.93/1.10 ((~relation(function_inverse(A!75))) | (~function(function_inverse(A!75))) | (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75)))))))))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[87, 78])).
% 0.93/1.11 tff(89,plain,
% 0.93/1.11 (~((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))))))))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[88, 62, 60])).
% 0.93/1.11 tff(90,plain,
% 0.93/1.11 (((~((~one_to_one(function_inverse(A!75))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(function_inverse(A!75)))) | (~in(C, relation_dom(function_inverse(A!75)))) | (~(apply(function_inverse(A!75), B) = apply(function_inverse(A!75), C)))))) | (~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75)))))))) | (one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))))))),
% 0.93/1.11 inference(tautology,[status(thm)],[])).
% 0.93/1.11 tff(91,plain,
% 0.93/1.11 (one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75)))))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.93/1.11 tff(92,plain,
% 0.93/1.11 (~one_to_one(function_inverse(A!75))),
% 0.93/1.11 inference(or_elim,[status(thm)],[10])).
% 0.93/1.11 tff(93,plain,
% 0.93/1.11 ((~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))))))) | one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75)))))),
% 0.93/1.11 inference(tautology,[status(thm)],[])).
% 0.93/1.11 tff(94,plain,
% 0.93/1.11 ((~(one_to_one(function_inverse(A!75)) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))))))) | (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75)))))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.93/1.11 tff(95,plain,
% 0.93/1.11 (~((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[94, 91])).
% 0.93/1.11 tff(96,plain,
% 0.93/1.11 (((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75)))) | in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))),
% 0.93/1.11 inference(tautology,[status(thm)],[])).
% 0.93/1.11 tff(97,plain,
% 0.93/1.11 (in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.93/1.11 tff(98,plain,
% 0.93/1.11 (in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[97, 41])).
% 0.93/1.11 tff(99,plain,
% 0.93/1.11 (^[A: $i, B: $i] : refl(((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A)))))) <=> ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A)))))))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(100,plain,
% 0.93/1.11 (![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[99])).
% 0.93/1.11 tff(101,plain,
% 0.93/1.11 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) <=> (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A)))))), 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((one_to_one(B) & in(A, relation_rng(B))) <=> (~((~one_to_one(B)) | (~in(A, relation_rng(B)))))), ((~(one_to_one(B) & in(A, relation_rng(B)))) <=> (~(~((~one_to_one(B)) | (~in(A, relation_rng(B)))))))), rewrite((~(~((~one_to_one(B)) | (~in(A, relation_rng(B)))))) <=> ((~one_to_one(B)) | (~in(A, relation_rng(B))))), ((~(one_to_one(B) & in(A, relation_rng(B)))) <=> ((~one_to_one(B)) | (~in(A, relation_rng(B)))))), ((((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ((~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | ((~relation(B)) | (~function(B))) | ((~one_to_one(B)) | (~in(A, relation_rng(B))))))), rewrite(((~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | ((~relation(B)) | (~function(B))) | ((~one_to_one(B)) | (~in(A, relation_rng(B))))) <=> ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))), ((((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(102,plain,
% 0.93/1.11 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[101])).
% 0.93/1.11 tff(103,plain,
% 0.93/1.11 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(104,plain,
% 0.93/1.11 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A)))) <=> ((~(one_to_one(B) & in(A, relation_rng(B)))) | ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))), (((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> ((relation(B) & function(B)) => ((~(one_to_one(B) & in(A, relation_rng(B)))) | ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))))), rewrite(((relation(B) & function(B)) => ((~(one_to_one(B) & in(A, relation_rng(B)))) | ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))), (((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(105,plain,
% 0.93/1.11 (![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> ![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[104])).
% 0.93/1.11 tff(106,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t57_funct_1')).
% 0.93/1.11 tff(107,plain,
% 0.93/1.11 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.93/1.11 tff(108,plain,
% 0.93/1.11 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.93/1.11 tff(109,plain,(
% 0.93/1.11 ![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 0.93/1.11 inference(skolemize,[status(sab)],[108])).
% 0.93/1.11 tff(110,plain,
% 0.93/1.11 (![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.93/1.11 tff(111,plain,
% 0.93/1.11 (![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[110, 100])).
% 0.93/1.11 tff(112,plain,
% 0.93/1.11 (((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | ((~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | (~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75))))))))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(113,plain,
% 0.93/1.11 (((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75)))))))) <=> ((~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75))))))))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(114,plain,
% 0.93/1.11 ((~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75))))))) <=> (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75)))))))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(115,plain,
% 0.93/1.11 (((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75)))))))) <=> ((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75))))))))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[114])).
% 0.93/1.11 tff(116,plain,
% 0.93/1.11 (((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75)))))))) <=> ((~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75))))))))),
% 0.93/1.11 inference(transitivity,[status(thm)],[115, 113])).
% 0.93/1.11 tff(117,plain,
% 0.93/1.11 (((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | ((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | ((~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75)))))))))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[116])).
% 0.93/1.11 tff(118,plain,
% 0.93/1.11 (((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | ((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | (~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75))))))))),
% 0.93/1.11 inference(transitivity,[status(thm)],[117, 112])).
% 0.93/1.11 tff(119,plain,
% 0.93/1.11 ((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | ((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75))))))))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(120,plain,
% 0.93/1.11 ((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | (~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75)))))))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.93/1.11 tff(121,plain,
% 0.93/1.11 ((~in(tptp_fun_C_46(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75)))))))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[120, 111, 14, 13, 11])).
% 0.93/1.11 tff(122,plain,
% 0.93/1.11 (~((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75))))))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[121, 98])).
% 0.93/1.11 tff(123,plain,
% 0.93/1.11 (((~(tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (~(tptp_fun_C_46(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_C_46(function_inverse(A!75)))))) | (tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))))),
% 0.93/1.11 inference(tautology,[status(thm)],[])).
% 0.93/1.11 tff(124,plain,
% 0.93/1.11 (tptp_fun_C_46(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.93/1.11 tff(125,plain,
% 0.93/1.11 (apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))) = tptp_fun_C_46(function_inverse(A!75))),
% 0.93/1.11 inference(symmetry,[status(thm)],[124])).
% 0.93/1.11 tff(126,plain,
% 0.93/1.11 (((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75)))) | (apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))),
% 0.93/1.11 inference(tautology,[status(thm)],[])).
% 0.93/1.11 tff(127,plain,
% 0.93/1.11 (apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75)))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[126, 95])).
% 0.93/1.11 tff(128,plain,
% 0.93/1.11 (apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))) = apply(A!75, apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[127])).
% 0.93/1.11 tff(129,plain,
% 0.93/1.11 (in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75)) <=> in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[39])).
% 0.93/1.11 tff(130,plain,
% 0.93/1.11 (in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75))) <=> in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))),
% 0.93/1.11 inference(symmetry,[status(thm)],[129])).
% 0.93/1.11 tff(131,plain,
% 0.93/1.11 (((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75)))) | in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))),
% 0.93/1.11 inference(tautology,[status(thm)],[])).
% 0.93/1.11 tff(132,plain,
% 0.93/1.11 (in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[131, 95])).
% 0.93/1.11 tff(133,plain,
% 0.93/1.11 (in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[132, 130])).
% 0.93/1.11 tff(134,plain,
% 0.93/1.11 (((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | ((~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | (~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75))))))))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(135,plain,
% 0.93/1.11 (((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75)))))))) <=> ((~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75))))))))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(136,plain,
% 0.93/1.11 ((~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75))))))) <=> (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75)))))))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(137,plain,
% 0.93/1.11 (((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75)))))))) <=> ((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75))))))))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[136])).
% 0.93/1.11 tff(138,plain,
% 0.93/1.11 (((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75)))))))) <=> ((~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75))))))))),
% 0.93/1.11 inference(transitivity,[status(thm)],[137, 135])).
% 0.93/1.11 tff(139,plain,
% 0.93/1.11 (((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | ((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | ((~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75)))))))))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[138])).
% 0.93/1.11 tff(140,plain,
% 0.93/1.11 (((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | ((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | (~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75))))))))),
% 0.93/1.11 inference(transitivity,[status(thm)],[139, 134])).
% 0.93/1.11 tff(141,plain,
% 0.93/1.11 ((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | ((~relation(A!75)) | (~one_to_one(A!75)) | (~function(A!75)) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75))))))))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(142,plain,
% 0.93/1.11 ((~![A: $i, B: $i] : ((~relation(B)) | (~one_to_one(B)) | (~function(B)) | (~in(A, relation_rng(B))) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))))) | (~one_to_one(A!75)) | (~relation(A!75)) | (~function(A!75)) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75)))))))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.93/1.12 tff(143,plain,
% 0.93/1.12 ((~in(tptp_fun_B_47(function_inverse(A!75)), relation_rng(A!75))) | (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75)))))))),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[142, 111, 14, 13, 11])).
% 0.93/1.12 tff(144,plain,
% 0.93/1.12 (~((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75))))))),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[143, 133])).
% 0.93/1.12 tff(145,plain,
% 0.93/1.12 (((~(tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (~(tptp_fun_B_47(function_inverse(A!75)) = apply(relation_composition(function_inverse(A!75), A!75), tptp_fun_B_47(function_inverse(A!75)))))) | (tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75)))))),
% 0.93/1.12 inference(tautology,[status(thm)],[])).
% 0.93/1.12 tff(146,plain,
% 0.93/1.12 (tptp_fun_B_47(function_inverse(A!75)) = apply(A!75, apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))))),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.93/1.12 tff(147,plain,
% 0.93/1.12 (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))),
% 0.93/1.12 inference(transitivity,[status(thm)],[146, 128, 125])).
% 0.93/1.12 tff(148,plain,
% 0.93/1.12 (((~(apply(function_inverse(A!75), tptp_fun_B_47(function_inverse(A!75))) = apply(function_inverse(A!75), tptp_fun_C_46(function_inverse(A!75))))) | (~in(tptp_fun_C_46(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (~in(tptp_fun_B_47(function_inverse(A!75)), relation_dom(function_inverse(A!75)))) | (tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75)))) | (~(tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75))))),
% 0.93/1.12 inference(tautology,[status(thm)],[])).
% 0.93/1.12 tff(149,plain,
% 0.93/1.12 (~(tptp_fun_B_47(function_inverse(A!75)) = tptp_fun_C_46(function_inverse(A!75)))),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[148, 95])).
% 0.93/1.12 tff(150,plain,
% 0.93/1.12 ($false),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[149, 147])).
% 0.93/1.12 % SZS output end Proof
% 0.93/1.12 % E exiting
%------------------------------------------------------------------------------