%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU031+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:26:49 AM UTC 2025
% Result : Theorem 0.61s 0.79s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SEU031+1 : TPTP v9.0.0. Released v3.2.0.
% 0.09/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:57:17 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.61/0.79 % SZS status Theorem
% 0.61/0.79 % SZS output start Proof
% 0.61/0.79 tff(identity_relation_type, type, (
% 0.61/0.79 identity_relation: $i > $i)).
% 0.61/0.79 tff(relation_dom_type, type, (
% 0.61/0.79 relation_dom: $i > $i)).
% 0.61/0.79 tff(function_inverse_type, type, (
% 0.61/0.79 function_inverse: $i > $i)).
% 0.61/0.79 tff(tptp_fun_A_11_type, type, (
% 0.61/0.79 tptp_fun_A_11: $i)).
% 0.61/0.79 tff(relation_composition_type, type, (
% 0.61/0.79 relation_composition: ( $i * $i ) > $i)).
% 0.61/0.79 tff(tptp_fun_B_12_type, type, (
% 0.61/0.79 tptp_fun_B_12: $i)).
% 0.61/0.79 tff(relation_rng_type, type, (
% 0.61/0.79 relation_rng: $i > $i)).
% 0.61/0.79 tff(one_to_one_type, type, (
% 0.61/0.79 one_to_one: $i > $o)).
% 0.61/0.79 tff(function_type, type, (
% 0.61/0.79 function: $i > $o)).
% 0.61/0.79 tff(relation_type, type, (
% 0.61/0.79 relation: $i > $o)).
% 0.61/0.79 tff(1,plain,
% 0.61/0.79 (((relation(A!11) & function(A!11)) & (~((B!12 = function_inverse(A!11)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & (relation_rng(B!12) = relation_dom(A!11)) & (relation_composition(B!12, A!11) = identity_relation(relation_rng(A!11)))))))) <=> (relation(A!11) & function(A!11) & (~((B!12 = function_inverse(A!11)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & (relation_rng(B!12) = relation_dom(A!11)) & (relation_composition(B!12, A!11) = identity_relation(relation_rng(A!11))))))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(2,plain,
% 0.61/0.79 ((~((B!12 = function_inverse(A!11)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & (relation_rng(B!12) = relation_dom(A!11)) & (relation_composition(B!12, A!11) = identity_relation(relation_rng(A!11))))))) <=> (~((B!12 = function_inverse(A!11)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & (relation_rng(B!12) = relation_dom(A!11)) & (relation_composition(B!12, A!11) = identity_relation(relation_rng(A!11)))))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(3,plain,
% 0.61/0.79 (((relation(A!11) & function(A!11)) & (~((B!12 = function_inverse(A!11)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & (relation_rng(B!12) = relation_dom(A!11)) & (relation_composition(B!12, A!11) = identity_relation(relation_rng(A!11)))))))) <=> ((relation(A!11) & function(A!11)) & (~((B!12 = function_inverse(A!11)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & (relation_rng(B!12) = relation_dom(A!11)) & (relation_composition(B!12, A!11) = identity_relation(relation_rng(A!11))))))))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2])).
% 0.61/0.79 tff(4,plain,
% 0.61/0.79 (((relation(A!11) & function(A!11)) & (~((B!12 = function_inverse(A!11)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & (relation_rng(B!12) = relation_dom(A!11)) & (relation_composition(B!12, A!11) = identity_relation(relation_rng(A!11)))))))) <=> (relation(A!11) & function(A!11) & (~((B!12 = function_inverse(A!11)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & (relation_rng(B!12) = relation_dom(A!11)) & (relation_composition(B!12, A!11) = identity_relation(relation_rng(A!11))))))))),
% 0.61/0.79 inference(transitivity,[status(thm)],[3, 1])).
% 0.61/0.79 tff(5,plain,
% 0.61/0.79 ((~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(B) = relation_dom(A)) & (relation_composition(B, A) = identity_relation(relation_rng(A)))))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(B) = relation_dom(A)) & (relation_composition(B, A) = identity_relation(relation_rng(A))))))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(6,plain,
% 0.61/0.79 ((~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(B) = relation_dom(A))) & (relation_composition(B, A) = identity_relation(relation_rng(A)))) => (B = function_inverse(A)))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(B) = relation_dom(A)) & (relation_composition(B, A) = identity_relation(relation_rng(A))))))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(7,axiom,(~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(B) = relation_dom(A))) & (relation_composition(B, A) = identity_relation(relation_rng(A)))) => (B = function_inverse(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t64_funct_1')).
% 0.61/0.79 tff(8,plain,
% 0.61/0.79 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(B) = relation_dom(A)) & (relation_composition(B, A) = identity_relation(relation_rng(A)))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.61/0.79 tff(9,plain,
% 0.61/0.79 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(B) = relation_dom(A)) & (relation_composition(B, A) = identity_relation(relation_rng(A)))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.61/0.79 tff(10,plain,
% 0.61/0.79 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(B) = relation_dom(A)) & (relation_composition(B, A) = identity_relation(relation_rng(A)))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.61/0.79 tff(11,plain,
% 0.61/0.79 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(B) = relation_dom(A)) & (relation_composition(B, A) = identity_relation(relation_rng(A)))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.61/0.79 tff(12,plain,
% 0.61/0.79 (relation(A!11) & function(A!11) & (~((B!12 = function_inverse(A!11)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & (relation_rng(B!12) = relation_dom(A!11)) & (relation_composition(B!12, A!11) = identity_relation(relation_rng(A!11)))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.61/0.79 tff(13,plain,
% 0.61/0.79 (~((B!12 = function_inverse(A!11)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & (relation_rng(B!12) = relation_dom(A!11)) & (relation_composition(B!12, A!11) = identity_relation(relation_rng(A!11))))))),
% 0.61/0.79 inference(and_elim,[status(thm)],[12])).
% 0.61/0.79 tff(14,plain,
% 0.61/0.79 (one_to_one(A!11) & (relation_rng(B!12) = relation_dom(A!11)) & (relation_composition(B!12, A!11) = identity_relation(relation_rng(A!11)))),
% 0.61/0.79 inference(or_elim,[status(thm)],[13])).
% 0.61/0.79 tff(15,plain,
% 0.61/0.79 (one_to_one(A!11)),
% 0.61/0.79 inference(and_elim,[status(thm)],[14])).
% 0.61/0.79 tff(16,plain,
% 0.61/0.79 (function(A!11)),
% 0.61/0.79 inference(and_elim,[status(thm)],[12])).
% 0.61/0.79 tff(17,plain,
% 0.61/0.79 (relation(A!11)),
% 0.61/0.79 inference(and_elim,[status(thm)],[12])).
% 0.61/0.79 tff(18,plain,
% 0.61/0.79 (^[A: $i] : refl(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(19,plain,
% 0.61/0.79 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[18])).
% 0.61/0.79 tff(20,plain,
% 0.61/0.79 (^[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))) <=> ((~one_to_one(A)) | (~relation(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))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(21,plain,
% 0.61/0.79 (![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] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[20])).
% 0.61/0.79 tff(22,plain,
% 0.61/0.79 (![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)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(23,plain,
% 0.61/0.79 (^[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)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(24,plain,
% 0.61/0.79 (![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)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[23])).
% 0.61/0.79 tff(25,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')).
% 0.61/0.79 tff(26,plain,
% 0.61/0.79 (![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)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.61/0.79 tff(27,plain,
% 0.61/0.79 (![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)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.61/0.79 tff(28,plain,(
% 0.61/0.79 ![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)))),
% 0.61/0.79 inference(skolemize,[status(sab)],[27])).
% 0.61/0.79 tff(29,plain,
% 0.61/0.79 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.61/0.79 tff(30,plain,
% 0.61/0.79 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.61/0.79 tff(31,plain,
% 0.61/0.79 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(32,plain,
% 0.61/0.79 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(33,plain,
% 0.61/0.79 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.61/0.79 tff(34,plain,
% 0.61/0.79 (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[33, 30, 17, 16, 15])).
% 0.61/0.79 tff(35,plain,
% 0.61/0.79 (((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11))))) | (relation_rng(A!11) = relation_dom(function_inverse(A!11)))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(36,plain,
% 0.61/0.79 (relation_rng(A!11) = relation_dom(function_inverse(A!11))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.61/0.79 tff(37,plain,
% 0.61/0.79 (relation_dom(function_inverse(A!11)) = relation_rng(A!11)),
% 0.61/0.79 inference(symmetry,[status(thm)],[36])).
% 0.61/0.79 tff(38,plain,
% 0.61/0.79 (identity_relation(relation_dom(function_inverse(A!11))) = identity_relation(relation_rng(A!11))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[37])).
% 0.61/0.79 tff(39,plain,
% 0.61/0.79 (identity_relation(relation_rng(A!11)) = identity_relation(relation_dom(function_inverse(A!11)))),
% 0.61/0.79 inference(symmetry,[status(thm)],[38])).
% 0.61/0.79 tff(40,plain,
% 0.61/0.79 (relation_composition(B!12, A!11) = identity_relation(relation_rng(A!11))),
% 0.61/0.79 inference(and_elim,[status(thm)],[14])).
% 0.61/0.79 tff(41,plain,
% 0.61/0.79 (relation_composition(B!12, A!11) = identity_relation(relation_dom(function_inverse(A!11)))),
% 0.61/0.79 inference(transitivity,[status(thm)],[40, 39])).
% 0.61/0.79 tff(42,plain,
% 0.61/0.79 ((function_inverse(A!11) = B!12) <=> (B!12 = function_inverse(A!11))),
% 0.61/0.79 inference(commutativity,[status(thm)],[])).
% 0.61/0.79 tff(43,plain,
% 0.61/0.79 ((B!12 = function_inverse(A!11)) <=> (function_inverse(A!11) = B!12)),
% 0.61/0.79 inference(symmetry,[status(thm)],[42])).
% 0.61/0.79 tff(44,plain,
% 0.61/0.79 ((~(B!12 = function_inverse(A!11))) <=> (~(function_inverse(A!11) = B!12))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[43])).
% 0.61/0.79 tff(45,plain,
% 0.61/0.79 (~(B!12 = function_inverse(A!11))),
% 0.61/0.79 inference(or_elim,[status(thm)],[13])).
% 0.61/0.79 tff(46,plain,
% 0.61/0.79 (~(function_inverse(A!11) = B!12)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.61/0.79 tff(47,plain,
% 0.61/0.79 (relation(B!12) & function(B!12)),
% 0.61/0.79 inference(or_elim,[status(thm)],[13])).
% 0.61/0.79 tff(48,plain,
% 0.61/0.79 (function(B!12)),
% 0.61/0.79 inference(and_elim,[status(thm)],[47])).
% 0.61/0.79 tff(49,plain,
% 0.61/0.79 (relation(B!12)),
% 0.61/0.79 inference(and_elim,[status(thm)],[47])).
% 0.61/0.79 tff(50,plain,
% 0.61/0.79 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(51,plain,
% 0.61/0.79 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[50])).
% 0.61/0.79 tff(52,plain,
% 0.61/0.79 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(53,plain,
% 0.61/0.79 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[52])).
% 0.61/0.79 tff(54,plain,
% 0.61/0.79 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))),
% 0.61/0.79 inference(transitivity,[status(thm)],[53, 51])).
% 0.61/0.79 tff(55,plain,
% 0.61/0.79 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(D) & function(D)) <=> (~((~relation(D)) | (~function(D))))), ((~(relation(D) & function(D))) <=> (~(~((~relation(D)) | (~function(D))))))), rewrite((~(~((~relation(D)) | (~function(D))))) <=> ((~relation(D)) | (~function(D)))), ((~(relation(D) & function(D))) <=> ((~relation(D)) | (~function(D))))), trans(monotonicity(rewrite(((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))) <=> (~((~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))), ((~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))) <=> (~(~((~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))))), rewrite((~(~((~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))) <=> ((~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))), ((~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))) <=> ((~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))), (((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))))) <=> ((D = B) | ((~relation(D)) | (~function(D))) | ((~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))), rewrite(((D = B) | ((~relation(D)) | (~function(D))) | ((~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))) <=> ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))), (((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))))) <=> ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))), (![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))))) <=> ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))), (((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))) <=> (((~relation(C)) | (~function(C))) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))), rewrite((((~relation(C)) | (~function(C))) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))) <=> ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))), (((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))) <=> ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))))), (![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))), (((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A)))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))), (((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(56,plain,
% 0.61/0.79 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[55])).
% 0.61/0.79 tff(57,plain,
% 0.61/0.79 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(58,plain,
% 0.61/0.79 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite((((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D)))) & (relation_composition(C, D) = identity_relation(A))) <=> ((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))), (((((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D)))) & (relation_composition(C, D) = identity_relation(A))) => (D = B)) <=> (((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))) => (D = B)))), rewrite((((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))) => (D = B)) <=> ((~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))) | (D = B))), (((((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D)))) & (relation_composition(C, D) = identity_relation(A))) => (D = B)) <=> ((~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))) | (D = B)))), (((relation(D) & function(D)) => ((((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D)))) & (relation_composition(C, D) = identity_relation(A))) => (D = B))) <=> ((relation(D) & function(D)) => ((~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))) | (D = B))))), rewrite(((relation(D) & function(D)) => ((~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))) | (D = B))) <=> ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))), (((relation(D) & function(D)) => ((((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D)))) & (relation_composition(C, D) = identity_relation(A))) => (D = B))) <=> ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))))), (![D: $i] : ((relation(D) & function(D)) => ((((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D)))) & (relation_composition(C, D) = identity_relation(A))) => (D = B))) <=> ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))))))), (((relation(C) & function(C)) => ![D: $i] : ((relation(D) & function(D)) => ((((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D)))) & (relation_composition(C, D) = identity_relation(A))) => (D = B)))) <=> ((relation(C) & function(C)) => ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))))), rewrite(((relation(C) & function(C)) => ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))) <=> ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))))))), (((relation(C) & function(C)) => ![D: $i] : ((relation(D) & function(D)) => ((((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D)))) & (relation_composition(C, D) = identity_relation(A))) => (D = B)))) <=> ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))))))))), (![C: $i] : ((relation(C) & function(C)) => ![D: $i] : ((relation(D) & function(D)) => ((((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D)))) & (relation_composition(C, D) = identity_relation(A))) => (D = B)))) <=> ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => ![D: $i] : ((relation(D) & function(D)) => ((((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D)))) & (relation_composition(C, D) = identity_relation(A))) => (D = B))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A))))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => ![D: $i] : ((relation(D) & function(D)) => ((((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D)))) & (relation_composition(C, D) = identity_relation(A))) => (D = B))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(59,plain,
% 0.61/0.79 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => ![D: $i] : ((relation(D) & function(D)) => ((((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D)))) & (relation_composition(C, D) = identity_relation(A))) => (D = B))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[58])).
% 0.61/0.79 tff(60,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => ![D: $i] : ((relation(D) & function(D)) => ((((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D)))) & (relation_composition(C, D) = identity_relation(A))) => (D = B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l72_funct_1')).
% 0.61/0.79 tff(61,plain,
% 0.61/0.79 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.61/0.79 tff(62,plain,
% 0.61/0.79 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.61/0.79 tff(63,plain,(
% 0.61/0.79 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((D = B) | (~(relation(D) & function(D))) | (~((relation_rng(B) = A) & (relation_composition(B, C) = identity_relation(relation_dom(D))) & (relation_composition(C, D) = identity_relation(A)))))))),
% 0.61/0.79 inference(skolemize,[status(sab)],[62])).
% 0.61/0.79 tff(64,plain,
% 0.61/0.79 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.61/0.79 tff(65,plain,
% 0.61/0.79 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.61/0.79 tff(66,plain,
% 0.61/0.79 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))) | (~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11))))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(67,plain,
% 0.61/0.80 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))) <=> ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11))))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(68,plain,
% 0.61/0.80 (^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : rewrite(((D = B!12) | (~relation(D)) | (~function(D)) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11))))) <=> ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))), (![D: $i] : ((D = B!12) | (~relation(D)) | (~function(D)) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11))))) <=> ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))), (((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B!12) | (~relation(D)) | (~function(D)) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))))) <=> ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11))))))), rewrite(((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11))))) <=> ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))), (((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B!12) | (~relation(D)) | (~function(D)) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))))) <=> ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(69,plain,
% 0.61/0.80 (![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B!12) | (~relation(D)) | (~function(D)) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[68])).
% 0.61/0.80 tff(70,plain,
% 0.61/0.80 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B!12) | (~relation(D)) | (~function(D)) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11))))))) <=> ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11))))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[69])).
% 0.61/0.80 tff(71,plain,
% 0.61/0.80 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B!12) | (~relation(D)) | (~function(D)) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11))))))) <=> ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11))))))),
% 0.61/0.80 inference(transitivity,[status(thm)],[70, 67])).
% 0.61/0.80 tff(72,plain,
% 0.61/0.80 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B!12) | (~relation(D)) | (~function(D)) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[71])).
% 0.61/0.80 tff(73,plain,
% 0.61/0.80 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B!12) | (~relation(D)) | (~function(D)) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))) | (~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11))))))),
% 0.61/0.80 inference(transitivity,[status(thm)],[72, 66])).
% 0.61/0.80 tff(74,plain,
% 0.61/0.80 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B!12) | (~relation(D)) | (~function(D)) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))))))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(75,plain,
% 0.61/0.80 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = B) | (~relation(D)) | (~function(D)) | (~(relation_rng(B) = A)) | (~(relation_composition(B, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(A))))))) | (~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.61/0.80 tff(76,plain,
% 0.61/0.80 (![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[75, 65, 49, 48])).
% 0.61/0.80 tff(77,plain,
% 0.61/0.80 (((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))) | ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11))))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))) | (~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11))))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(78,plain,
% 0.61/0.80 (((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))))) <=> ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11))))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(79,plain,
% 0.61/0.80 (^[D: $i] : rewrite(((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))) <=> ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11))))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(80,plain,
% 0.61/0.80 (![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))) <=> ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[79])).
% 0.61/0.80 tff(81,plain,
% 0.61/0.80 (((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11))))) <=> ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11))))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[80])).
% 0.61/0.80 tff(82,plain,
% 0.61/0.80 (((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11))))) <=> ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11))))))),
% 0.61/0.80 inference(transitivity,[status(thm)],[81, 78])).
% 0.61/0.80 tff(83,plain,
% 0.61/0.80 (((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))) | ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))) | ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[82])).
% 0.61/0.80 tff(84,plain,
% 0.61/0.80 (((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))) | ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))) | (~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11))))))),
% 0.61/0.80 inference(transitivity,[status(thm)],[83, 77])).
% 0.61/0.80 tff(85,plain,
% 0.61/0.80 ((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))) | ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(86,plain,
% 0.61/0.80 ((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_composition(B!12, C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_dom(A!11)))) | (~(relation_rng(B!12) = relation_dom(A!11)))))) | (~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.61/0.80 tff(87,plain,
% 0.61/0.80 (![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[86, 17, 16, 76])).
% 0.61/0.80 tff(88,plain,
% 0.61/0.80 (^[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)))))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(89,plain,
% 0.61/0.80 (![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))))))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[88])).
% 0.61/0.80 tff(90,plain,
% 0.61/0.80 (^[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))))))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(91,plain,
% 0.61/0.80 (![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))))))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[90])).
% 0.61/0.80 tff(92,plain,
% 0.61/0.80 (![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))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(93,plain,
% 0.61/0.80 (^[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)))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(94,plain,
% 0.61/0.80 (![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))))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[93])).
% 0.61/0.80 tff(95,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')).
% 0.61/0.80 tff(96,plain,
% 0.61/0.80 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.61/0.80 tff(97,plain,
% 0.61/0.80 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.61/0.80 tff(98,plain,(
% 0.61/0.80 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.61/0.80 inference(skolemize,[status(sab)],[97])).
% 0.61/0.80 tff(99,plain,
% 0.61/0.80 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.61/0.80 tff(100,plain,
% 0.61/0.80 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.61/0.80 tff(101,plain,
% 0.61/0.80 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(102,plain,
% 0.61/0.80 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(103,plain,
% 0.61/0.80 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.61/0.80 tff(104,plain,
% 0.61/0.80 (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[103, 100, 17, 16])).
% 0.61/0.80 tff(105,plain,
% 0.61/0.80 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))) | function(function_inverse(A!11))),
% 0.61/0.80 inference(tautology,[status(thm)],[])).
% 0.61/0.80 tff(106,plain,
% 0.61/0.80 (function(function_inverse(A!11))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.61/0.80 tff(107,plain,
% 0.61/0.80 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))) | relation(function_inverse(A!11))),
% 0.61/0.80 inference(tautology,[status(thm)],[])).
% 0.61/0.80 tff(108,plain,
% 0.61/0.80 (relation(function_inverse(A!11))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[107, 104])).
% 0.61/0.80 tff(109,plain,
% 0.61/0.80 (^[A: $i] : refl(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(110,plain,
% 0.61/0.80 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[109])).
% 0.61/0.80 tff(111,plain,
% 0.61/0.80 (^[A: $i] : trans(monotonicity(rewrite(((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) <=> (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(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_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))))), rewrite(((~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))), ((((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(112,plain,
% 0.61/0.80 (![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[111])).
% 0.61/0.80 tff(113,plain,
% 0.61/0.80 (![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(114,plain,
% 0.61/0.80 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) => ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))) <=> ((~one_to_one(A)) | ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))) <=> (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))) <=> (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(115,plain,
% 0.61/0.80 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))) <=> ![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[114])).
% 0.61/0.80 tff(116,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t61_funct_1')).
% 0.61/0.80 tff(117,plain,
% 0.61/0.80 (![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.61/0.80 tff(118,plain,
% 0.61/0.80 (![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.61/0.80 tff(119,plain,(
% 0.61/0.80 ![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.61/0.80 inference(skolemize,[status(sab)],[118])).
% 0.61/0.80 tff(120,plain,
% 0.61/0.80 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.61/0.80 tff(121,plain,
% 0.61/0.80 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[120, 110])).
% 0.61/0.80 tff(122,plain,
% 0.61/0.80 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | ((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(123,plain,
% 0.61/0.80 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | ((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(124,plain,
% 0.61/0.80 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11))))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.61/0.81 tff(125,plain,
% 0.61/0.81 (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[124, 121, 17, 16, 15])).
% 0.61/0.81 tff(126,plain,
% 0.61/0.81 (((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11))))) | (relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))),
% 0.61/0.81 inference(tautology,[status(thm)],[])).
% 0.61/0.81 tff(127,plain,
% 0.61/0.81 (relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.61/0.81 tff(128,plain,
% 0.61/0.81 (relation_rng(B!12) = relation_dom(A!11)),
% 0.61/0.81 inference(and_elim,[status(thm)],[14])).
% 0.61/0.81 tff(129,plain,
% 0.61/0.81 (((~![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))))) | ((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | (~(relation_rng(B!12) = relation_dom(A!11))) | (function_inverse(A!11) = B!12) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(function_inverse(A!11))))))) <=> ((~![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))))) | (~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | (~(relation_rng(B!12) = relation_dom(A!11))) | (function_inverse(A!11) = B!12) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(130,plain,
% 0.61/0.81 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | (function_inverse(A!11) = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(function_inverse(A!11))))) | (~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11))))) <=> ((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | (~(relation_rng(B!12) = relation_dom(A!11))) | (function_inverse(A!11) = B!12) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(131,plain,
% 0.61/0.81 (((~![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))))) | ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | (function_inverse(A!11) = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(function_inverse(A!11))))) | (~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))))) <=> ((~![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))))) | ((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | (~(relation_rng(B!12) = relation_dom(A!11))) | (function_inverse(A!11) = B!12) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[130])).
% 0.61/0.81 tff(132,plain,
% 0.61/0.81 (((~![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))))) | ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | (function_inverse(A!11) = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(function_inverse(A!11))))) | (~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))))) <=> ((~![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))))) | (~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | (~(relation_rng(B!12) = relation_dom(A!11))) | (function_inverse(A!11) = B!12) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.61/0.81 inference(transitivity,[status(thm)],[131, 129])).
% 0.61/0.81 tff(133,plain,
% 0.61/0.81 ((~![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))))) | ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | (function_inverse(A!11) = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(function_inverse(A!11))))) | (~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))))),
% 0.61/0.81 inference(quant_inst,[status(thm)],[])).
% 0.61/0.81 tff(134,plain,
% 0.61/0.81 ((~![D: $i] : ((~relation(D)) | (~function(D)) | (D = B!12) | (~(relation_rng(B!12) = relation_dom(A!11))) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_dom(A!11)))))) | (~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | (~(relation_rng(B!12) = relation_dom(A!11))) | (function_inverse(A!11) = B!12) | (~(relation_composition(B!12, A!11) = identity_relation(relation_dom(function_inverse(A!11)))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.61/0.81 tff(135,plain,
% 0.61/0.81 ($false),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[134, 128, 127, 108, 106, 87, 46, 41])).
% 0.61/0.81 % SZS output end Proof
% 0.61/0.81 % E exiting
%------------------------------------------------------------------------------