%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU030+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.56s 0.74s
% Output : Proof 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU030+1 : TPTP v9.0.0. Released v3.2.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:57:09 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.56/0.74 % SZS status Theorem
% 0.56/0.74 % SZS output start Proof
% 0.56/0.74 tff(identity_relation_type, type, (
% 0.56/0.74 identity_relation: $i > $i)).
% 0.56/0.74 tff(relation_rng_type, type, (
% 0.56/0.74 relation_rng: $i > $i)).
% 0.56/0.74 tff(function_inverse_type, type, (
% 0.56/0.74 function_inverse: $i > $i)).
% 0.56/0.74 tff(tptp_fun_A_11_type, type, (
% 0.56/0.74 tptp_fun_A_11: $i)).
% 0.56/0.74 tff(relation_composition_type, type, (
% 0.56/0.74 relation_composition: ( $i * $i ) > $i)).
% 0.56/0.74 tff(tptp_fun_B_12_type, type, (
% 0.56/0.74 tptp_fun_B_12: $i)).
% 0.56/0.74 tff(relation_dom_type, type, (
% 0.56/0.74 relation_dom: $i > $i)).
% 0.56/0.74 tff(one_to_one_type, type, (
% 0.56/0.74 one_to_one: $i > $o)).
% 0.56/0.74 tff(function_type, type, (
% 0.56/0.74 function: $i > $o)).
% 0.56/0.74 tff(relation_type, type, (
% 0.56/0.74 relation: $i > $o)).
% 0.56/0.74 tff(1,plain,
% 0.56/0.74 (((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(A!11) = relation_dom(B!12)) & (relation_composition(A!11, B!12) = identity_relation(relation_dom(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(A!11) = relation_dom(B!12)) & (relation_composition(A!11, B!12) = identity_relation(relation_dom(A!11))))))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(2,plain,
% 0.56/0.74 ((~((B!12 = function_inverse(A!11)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & (relation_rng(A!11) = relation_dom(B!12)) & (relation_composition(A!11, B!12) = identity_relation(relation_dom(A!11))))))) <=> (~((B!12 = function_inverse(A!11)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & (relation_rng(A!11) = relation_dom(B!12)) & (relation_composition(A!11, B!12) = identity_relation(relation_dom(A!11)))))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(3,plain,
% 0.56/0.74 (((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(A!11) = relation_dom(B!12)) & (relation_composition(A!11, B!12) = identity_relation(relation_dom(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(A!11) = relation_dom(B!12)) & (relation_composition(A!11, B!12) = identity_relation(relation_dom(A!11))))))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2])).
% 0.56/0.74 tff(4,plain,
% 0.56/0.74 (((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(A!11) = relation_dom(B!12)) & (relation_composition(A!11, B!12) = identity_relation(relation_dom(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(A!11) = relation_dom(B!12)) & (relation_composition(A!11, B!12) = identity_relation(relation_dom(A!11))))))))),
% 0.56/0.74 inference(transitivity,[status(thm)],[3, 1])).
% 0.56/0.74 tff(5,plain,
% 0.56/0.74 ((~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(6,plain,
% 0.56/0.74 ((~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(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(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(7,axiom,(~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t63_funct_1')).
% 0.56/0.74 tff(8,plain,
% 0.56/0.74 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.56/0.74 tff(9,plain,
% 0.56/0.74 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.56/0.74 tff(10,plain,
% 0.56/0.74 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.56/0.74 tff(11,plain,
% 0.56/0.74 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.56/0.74 tff(12,plain,
% 0.56/0.74 (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(A!11) = relation_dom(B!12)) & (relation_composition(A!11, B!12) = identity_relation(relation_dom(A!11)))))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.56/0.74 tff(13,plain,
% 0.56/0.74 (~((B!12 = function_inverse(A!11)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & (relation_rng(A!11) = relation_dom(B!12)) & (relation_composition(A!11, B!12) = identity_relation(relation_dom(A!11))))))),
% 0.56/0.74 inference(and_elim,[status(thm)],[12])).
% 0.56/0.74 tff(14,plain,
% 0.56/0.74 (one_to_one(A!11) & (relation_rng(A!11) = relation_dom(B!12)) & (relation_composition(A!11, B!12) = identity_relation(relation_dom(A!11)))),
% 0.56/0.74 inference(or_elim,[status(thm)],[13])).
% 0.56/0.74 tff(15,plain,
% 0.56/0.74 (one_to_one(A!11)),
% 0.56/0.74 inference(and_elim,[status(thm)],[14])).
% 0.56/0.74 tff(16,plain,
% 0.56/0.74 (function(A!11)),
% 0.56/0.74 inference(and_elim,[status(thm)],[12])).
% 0.56/0.74 tff(17,plain,
% 0.56/0.74 (relation(A!11)),
% 0.56/0.74 inference(and_elim,[status(thm)],[12])).
% 0.56/0.74 tff(18,plain,
% 0.56/0.74 (^[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))))))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(19,plain,
% 0.56/0.74 (![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)))))))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[18])).
% 0.56/0.74 tff(20,plain,
% 0.56/0.74 (^[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)))))))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(21,plain,
% 0.56/0.74 (![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)))))))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[20])).
% 0.56/0.74 tff(22,plain,
% 0.56/0.74 (![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)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(23,plain,
% 0.56/0.74 (^[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)))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(24,plain,
% 0.56/0.74 (![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)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[23])).
% 0.56/0.74 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')).
% 0.56/0.74 tff(26,plain,
% 0.56/0.74 (![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)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.56/0.74 tff(27,plain,
% 0.56/0.74 (![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)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.56/0.74 tff(28,plain,(
% 0.56/0.74 ![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)))),
% 0.56/0.74 inference(skolemize,[status(sab)],[27])).
% 0.56/0.74 tff(29,plain,
% 0.56/0.74 (![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)))))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.56/0.74 tff(30,plain,
% 0.56/0.74 (![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)))))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.56/0.74 tff(31,plain,
% 0.56/0.74 (((~![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)))))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(32,plain,
% 0.56/0.74 ((~![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)))))))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(33,plain,
% 0.56/0.74 ((~![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))))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.56/0.74 tff(34,plain,
% 0.56/0.74 (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[33, 30, 17, 16, 15])).
% 0.56/0.74 tff(35,plain,
% 0.56/0.74 (((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11))))) | (relation_dom(A!11) = relation_rng(function_inverse(A!11)))),
% 0.56/0.74 inference(tautology,[status(thm)],[])).
% 0.56/0.74 tff(36,plain,
% 0.56/0.74 (relation_dom(A!11) = relation_rng(function_inverse(A!11))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.56/0.74 tff(37,plain,
% 0.56/0.74 (relation_rng(function_inverse(A!11)) = relation_dom(A!11)),
% 0.56/0.74 inference(symmetry,[status(thm)],[36])).
% 0.56/0.74 tff(38,plain,
% 0.56/0.74 (identity_relation(relation_rng(function_inverse(A!11))) = identity_relation(relation_dom(A!11))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[37])).
% 0.56/0.74 tff(39,plain,
% 0.56/0.74 (identity_relation(relation_dom(A!11)) = identity_relation(relation_rng(function_inverse(A!11)))),
% 0.56/0.74 inference(symmetry,[status(thm)],[38])).
% 0.56/0.74 tff(40,plain,
% 0.56/0.74 (relation_composition(A!11, B!12) = identity_relation(relation_dom(A!11))),
% 0.56/0.74 inference(and_elim,[status(thm)],[14])).
% 0.56/0.74 tff(41,plain,
% 0.56/0.74 (relation_composition(A!11, B!12) = identity_relation(relation_rng(function_inverse(A!11)))),
% 0.56/0.74 inference(transitivity,[status(thm)],[40, 39])).
% 0.56/0.74 tff(42,plain,
% 0.56/0.74 (relation_rng(A!11) = relation_dom(B!12)),
% 0.56/0.74 inference(and_elim,[status(thm)],[14])).
% 0.56/0.74 tff(43,plain,
% 0.56/0.74 (relation_dom(B!12) = relation_rng(A!11)),
% 0.56/0.74 inference(symmetry,[status(thm)],[42])).
% 0.56/0.74 tff(44,plain,
% 0.56/0.74 (identity_relation(relation_dom(B!12)) = identity_relation(relation_rng(A!11))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[43])).
% 0.56/0.74 tff(45,plain,
% 0.56/0.74 (identity_relation(relation_rng(A!11)) = identity_relation(relation_dom(B!12))),
% 0.56/0.74 inference(symmetry,[status(thm)],[44])).
% 0.56/0.74 tff(46,plain,
% 0.56/0.74 (^[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))))))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(47,plain,
% 0.56/0.74 (![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)))))))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[46])).
% 0.56/0.74 tff(48,plain,
% 0.56/0.74 (^[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)))))))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(49,plain,
% 0.56/0.74 (![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)))))))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[48])).
% 0.56/0.74 tff(50,plain,
% 0.56/0.74 (![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)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(51,plain,
% 0.56/0.74 (^[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)))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(52,plain,
% 0.56/0.74 (![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)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[51])).
% 0.56/0.74 tff(53,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')).
% 0.56/0.74 tff(54,plain,
% 0.56/0.74 (![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)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.56/0.74 tff(55,plain,
% 0.56/0.74 (![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)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.56/0.74 tff(56,plain,(
% 0.56/0.74 ![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)))),
% 0.56/0.74 inference(skolemize,[status(sab)],[55])).
% 0.56/0.74 tff(57,plain,
% 0.56/0.74 (![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)))))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.56/0.74 tff(58,plain,
% 0.56/0.74 (![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)))))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.56/0.74 tff(59,plain,
% 0.56/0.74 (((~![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)))))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(60,plain,
% 0.56/0.74 ((~![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)))))))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(61,plain,
% 0.56/0.74 ((~![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))))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.56/0.74 tff(62,plain,
% 0.56/0.74 (~((~(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)))))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[61, 58, 17, 16, 15])).
% 0.56/0.74 tff(63,plain,
% 0.56/0.74 (((~(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(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(64,plain,
% 0.56/0.75 (relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.56/0.75 tff(65,plain,
% 0.56/0.75 (relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(B!12))),
% 0.56/0.75 inference(transitivity,[status(thm)],[64, 45])).
% 0.56/0.75 tff(66,plain,
% 0.56/0.75 (^[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)))))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(67,plain,
% 0.56/0.75 (![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))))))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[66])).
% 0.56/0.75 tff(68,plain,
% 0.56/0.75 (^[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))))))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(69,plain,
% 0.56/0.75 (![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))))))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[68])).
% 0.56/0.75 tff(70,plain,
% 0.56/0.75 (![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))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(71,plain,
% 0.56/0.75 (^[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)))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(72,plain,
% 0.56/0.75 (![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))))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[71])).
% 0.56/0.75 tff(73,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')).
% 0.56/0.75 tff(74,plain,
% 0.56/0.75 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.56/0.75 tff(75,plain,
% 0.56/0.75 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.56/0.75 tff(76,plain,(
% 0.56/0.75 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.56/0.75 inference(skolemize,[status(sab)],[75])).
% 0.56/0.75 tff(77,plain,
% 0.56/0.75 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.56/0.75 tff(78,plain,
% 0.56/0.75 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.56/0.75 tff(79,plain,
% 0.56/0.75 (((~![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))))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(80,plain,
% 0.56/0.75 ((~![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))))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(81,plain,
% 0.56/0.75 ((~![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)))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.56/0.75 tff(82,plain,
% 0.56/0.75 (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[81, 78, 17, 16])).
% 0.56/0.75 tff(83,plain,
% 0.56/0.75 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))) | function(function_inverse(A!11))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(84,plain,
% 0.56/0.75 (function(function_inverse(A!11))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.56/0.75 tff(85,plain,
% 0.56/0.75 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))) | relation(function_inverse(A!11))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(86,plain,
% 0.56/0.75 (relation(function_inverse(A!11))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[85, 82])).
% 0.56/0.75 tff(87,plain,
% 0.56/0.75 (^[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)))))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(88,plain,
% 0.56/0.75 (![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))))))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[87])).
% 0.56/0.75 tff(89,plain,
% 0.56/0.75 (^[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)))))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(90,plain,
% 0.56/0.75 (![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))))))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[89])).
% 0.56/0.75 tff(91,plain,
% 0.56/0.75 (![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))))))),
% 0.56/0.75 inference(transitivity,[status(thm)],[90, 88])).
% 0.56/0.75 tff(92,plain,
% 0.56/0.75 (^[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))))))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(93,plain,
% 0.56/0.75 (![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))))))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[92])).
% 0.56/0.75 tff(94,plain,
% 0.56/0.75 (![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)))))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(95,plain,
% 0.56/0.75 (^[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)))))))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(96,plain,
% 0.56/0.75 (![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)))))))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[95])).
% 0.56/0.75 tff(97,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')).
% 0.56/0.75 tff(98,plain,
% 0.56/0.75 (![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)))))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.56/0.75 tff(99,plain,
% 0.56/0.75 (![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)))))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.56/0.75 tff(100,plain,(
% 0.56/0.75 ![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)))))))),
% 0.56/0.75 inference(skolemize,[status(sab)],[99])).
% 0.56/0.75 tff(101,plain,
% 0.56/0.75 (![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))))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.56/0.75 tff(102,plain,
% 0.56/0.75 (![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))))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[101, 91])).
% 0.56/0.75 tff(103,plain,
% 0.56/0.75 (((~![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(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(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(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11))))))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(104,plain,
% 0.56/0.75 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))) <=> ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11))))))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(105,plain,
% 0.56/0.75 (^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation_rng(function_inverse(A!11)) = relation_rng(function_inverse(A!11))) <=> $true), ((~(relation_rng(function_inverse(A!11)) = relation_rng(function_inverse(A!11)))) <=> (~$true))), rewrite((~$true) <=> $false), ((~(relation_rng(function_inverse(A!11)) = relation_rng(function_inverse(A!11)))) <=> $false)), (((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_rng(function_inverse(A!11)) = relation_rng(function_inverse(A!11)))) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))) <=> ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | $false | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))), rewrite(((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | $false | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))) <=> ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11))))))), (((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_rng(function_inverse(A!11)) = relation_rng(function_inverse(A!11)))) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))) <=> ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11))))))))), (![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_rng(function_inverse(A!11)) = relation_rng(function_inverse(A!11)))) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))) <=> ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))), (((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_rng(function_inverse(A!11)) = relation_rng(function_inverse(A!11)))) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11))))))) <=> ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11))))))))), rewrite(((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11))))))) <=> ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))), (((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_rng(function_inverse(A!11)) = relation_rng(function_inverse(A!11)))) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11))))))) <=> ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(106,plain,
% 0.56/0.75 (![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_rng(function_inverse(A!11)) = relation_rng(function_inverse(A!11)))) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11))))))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[105])).
% 0.56/0.75 tff(107,plain,
% 0.56/0.75 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_rng(function_inverse(A!11)) = relation_rng(function_inverse(A!11)))) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))) <=> ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11))))))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[106])).
% 0.56/0.75 tff(108,plain,
% 0.56/0.75 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_rng(function_inverse(A!11)) = relation_rng(function_inverse(A!11)))) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))) <=> ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11))))))))),
% 0.56/0.75 inference(transitivity,[status(thm)],[107, 104])).
% 0.56/0.75 tff(109,plain,
% 0.56/0.75 (((~![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(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_rng(function_inverse(A!11)) = relation_rng(function_inverse(A!11)))) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(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(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[108])).
% 0.56/0.75 tff(110,plain,
% 0.56/0.75 (((~![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(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_rng(function_inverse(A!11)) = relation_rng(function_inverse(A!11)))) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(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(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11))))))))),
% 0.56/0.75 inference(transitivity,[status(thm)],[109, 103])).
% 0.56/0.75 tff(111,plain,
% 0.56/0.75 ((~![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(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_rng(function_inverse(A!11)) = relation_rng(function_inverse(A!11)))) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11))))))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(112,plain,
% 0.56/0.75 ((~![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(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.56/0.75 tff(113,plain,
% 0.56/0.75 (![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[112, 102, 86, 84])).
% 0.56/0.75 tff(114,plain,
% 0.56/0.75 (((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))) | ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D))))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))) | (~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D))))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(115,plain,
% 0.56/0.76 (((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))))) <=> ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D))))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(116,plain,
% 0.56/0.76 (^[D: $i] : rewrite(((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11)))))) <=> ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D))))))),
% 0.56/0.76 inference(bind,[status(th)],[])).
% 0.56/0.76 tff(117,plain,
% 0.56/0.76 (![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11)))))) <=> ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))))),
% 0.56/0.76 inference(quant_intro,[status(thm)],[116])).
% 0.56/0.76 tff(118,plain,
% 0.56/0.76 (((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))))) <=> ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D))))))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[117])).
% 0.56/0.76 tff(119,plain,
% 0.56/0.76 (((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))))) <=> ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D))))))),
% 0.56/0.76 inference(transitivity,[status(thm)],[118, 115])).
% 0.56/0.76 tff(120,plain,
% 0.56/0.76 (((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))) | ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11)))))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))) | ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))))))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[119])).
% 0.56/0.76 tff(121,plain,
% 0.56/0.76 (((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))) | ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11)))))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))) | (~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D))))))),
% 0.56/0.76 inference(transitivity,[status(thm)],[120, 114])).
% 0.56/0.76 tff(122,plain,
% 0.56/0.76 ((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))) | ((~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11)))))))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(123,plain,
% 0.56/0.76 ((~![C: $i] : ((~relation(C)) | (~function(C)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(function_inverse(A!11), C) = identity_relation(relation_dom(D)))) | (~(relation_composition(C, D) = identity_relation(relation_rng(function_inverse(A!11)))))))) | (~relation(A!11)) | (~function(A!11)) | ![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.56/0.76 tff(124,plain,
% 0.56/0.76 (![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[123, 17, 16, 113])).
% 0.56/0.76 tff(125,plain,
% 0.56/0.76 (relation(B!12) & function(B!12)),
% 0.56/0.76 inference(or_elim,[status(thm)],[13])).
% 0.56/0.76 tff(126,plain,
% 0.56/0.76 (function(B!12)),
% 0.56/0.76 inference(and_elim,[status(thm)],[125])).
% 0.56/0.76 tff(127,plain,
% 0.56/0.76 (relation(B!12)),
% 0.56/0.76 inference(and_elim,[status(thm)],[125])).
% 0.56/0.76 tff(128,plain,
% 0.56/0.76 (~(B!12 = function_inverse(A!11))),
% 0.56/0.76 inference(or_elim,[status(thm)],[13])).
% 0.56/0.76 tff(129,plain,
% 0.56/0.76 (((~![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))))) | ((B!12 = function_inverse(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(B!12)))) | (~(relation_composition(A!11, B!12) = identity_relation(relation_rng(function_inverse(A!11))))))) <=> ((~![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))))) | (B!12 = function_inverse(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(B!12)))) | (~(relation_composition(A!11, B!12) = identity_relation(relation_rng(function_inverse(A!11))))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(130,plain,
% 0.56/0.76 (((B!12 = function_inverse(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(relation_composition(A!11, B!12) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(B!12))))) <=> ((B!12 = function_inverse(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(B!12)))) | (~(relation_composition(A!11, B!12) = identity_relation(relation_rng(function_inverse(A!11))))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(131,plain,
% 0.56/0.76 (((~![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))))) | ((B!12 = function_inverse(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(relation_composition(A!11, B!12) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(B!12)))))) <=> ((~![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))))) | ((B!12 = function_inverse(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(B!12)))) | (~(relation_composition(A!11, B!12) = identity_relation(relation_rng(function_inverse(A!11)))))))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[130])).
% 0.56/0.76 tff(132,plain,
% 0.56/0.76 (((~![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))))) | ((B!12 = function_inverse(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(relation_composition(A!11, B!12) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(B!12)))))) <=> ((~![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))))) | (B!12 = function_inverse(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(B!12)))) | (~(relation_composition(A!11, B!12) = identity_relation(relation_rng(function_inverse(A!11))))))),
% 0.56/0.76 inference(transitivity,[status(thm)],[131, 129])).
% 0.56/0.76 tff(133,plain,
% 0.56/0.76 ((~![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))))) | ((B!12 = function_inverse(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(relation_composition(A!11, B!12) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(B!12)))))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(134,plain,
% 0.56/0.76 ((~![D: $i] : ((D = function_inverse(A!11)) | (~relation(D)) | (~function(D)) | (~(relation_composition(A!11, D) = identity_relation(relation_rng(function_inverse(A!11))))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(D)))))) | (B!12 = function_inverse(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(B!12)))) | (~(relation_composition(A!11, B!12) = identity_relation(relation_rng(function_inverse(A!11)))))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.56/0.76 tff(135,plain,
% 0.56/0.76 ($false),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[134, 128, 127, 126, 124, 65, 41])).
% 0.56/0.76 % SZS output end Proof
% 0.56/0.76 % E exiting
%------------------------------------------------------------------------------