%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU368+1 : TPTP v9.0.0. Released v3.3.0.
% 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 05:27:43 AM UTC 2025
% Result : Theorem 127.45s 127.71s
% Output : Proof 127.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SEU368+1 : TPTP v9.0.0. Released v3.3.0.
% 0.09/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 06:54:39 EDT 2025
% 0.14/0.35 % CPUTime :
% 127.45/127.71 % SZS status Theorem
% 127.45/127.71 % SZS output start Proof
% 127.45/127.71 tff(tptp_fun_A_13_type, type, (
% 127.45/127.71 tptp_fun_A_13: $i)).
% 127.45/127.71 tff(the_carrier_type, type, (
% 127.45/127.71 the_carrier: $i > $i)).
% 127.45/127.71 tff(incl_POSet_type, type, (
% 127.45/127.71 incl_POSet: $i > $i)).
% 127.45/127.71 tff(rel_str_of_type, type, (
% 127.45/127.71 rel_str_of: ( $i * $i ) > $i)).
% 127.45/127.71 tff(inclusion_order_type, type, (
% 127.45/127.71 inclusion_order: $i > $i)).
% 127.45/127.71 tff(the_InternalRel_type, type, (
% 127.45/127.71 the_InternalRel: $i > $i)).
% 127.45/127.71 tff(inclusion_relation_type, type, (
% 127.45/127.71 inclusion_relation: $i > $i)).
% 127.45/127.71 tff(strict_rel_str_type, type, (
% 127.45/127.71 strict_rel_str: $i > $o)).
% 127.45/127.71 tff(antisymmetric_relstr_type, type, (
% 127.45/127.71 antisymmetric_relstr: $i > $o)).
% 127.45/127.71 tff(transitive_relstr_type, type, (
% 127.45/127.71 transitive_relstr: $i > $o)).
% 127.45/127.71 tff(reflexive_relstr_type, type, (
% 127.45/127.71 reflexive_relstr: $i > $o)).
% 127.45/127.71 tff(rel_str_type, type, (
% 127.45/127.71 rel_str: $i > $o)).
% 127.45/127.71 tff(relation_of2_type, type, (
% 127.45/127.71 relation_of2: ( $i * $i * $i ) > $o)).
% 127.45/127.71 tff(relation_of2_as_subset_type, type, (
% 127.45/127.71 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 127.45/127.71 tff(v1_partfun1_type, type, (
% 127.45/127.71 v1_partfun1: ( $i * $i * $i ) > $o)).
% 127.45/127.71 tff(transitive_type, type, (
% 127.45/127.71 transitive: $i > $o)).
% 127.45/127.71 tff(antisymmetric_type, type, (
% 127.45/127.71 antisymmetric: $i > $o)).
% 127.45/127.71 tff(reflexive_type, type, (
% 127.45/127.71 reflexive: $i > $o)).
% 127.45/127.71 tff(1,plain,
% 127.45/127.71 (^[A: $i] : refl((inclusion_order(A) = inclusion_relation(A)) <=> (inclusion_order(A) = inclusion_relation(A)))),
% 127.45/127.71 inference(bind,[status(th)],[])).
% 127.45/127.71 tff(2,plain,
% 127.45/127.71 (![A: $i] : (inclusion_order(A) = inclusion_relation(A)) <=> ![A: $i] : (inclusion_order(A) = inclusion_relation(A))),
% 127.45/127.71 inference(quant_intro,[status(thm)],[1])).
% 127.45/127.71 tff(3,plain,
% 127.45/127.71 (![A: $i] : (inclusion_order(A) = inclusion_relation(A)) <=> ![A: $i] : (inclusion_order(A) = inclusion_relation(A))),
% 127.45/127.71 inference(rewrite,[status(thm)],[])).
% 127.45/127.71 tff(4,axiom,(![A: $i] : (inclusion_order(A) = inclusion_relation(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k1_yellow_1')).
% 127.45/127.71 tff(5,plain,
% 127.45/127.71 (![A: $i] : (inclusion_order(A) = inclusion_relation(A))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[4, 3])).
% 127.45/127.71 tff(6,plain,(
% 127.45/127.71 ![A: $i] : (inclusion_order(A) = inclusion_relation(A))),
% 127.45/127.71 inference(skolemize,[status(sab)],[5])).
% 127.45/127.71 tff(7,plain,
% 127.45/127.71 (![A: $i] : (inclusion_order(A) = inclusion_relation(A))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[6, 2])).
% 127.45/127.71 tff(8,plain,
% 127.45/127.71 ((~![A: $i] : (inclusion_order(A) = inclusion_relation(A))) | (inclusion_order(A!13) = inclusion_relation(A!13))),
% 127.45/127.71 inference(quant_inst,[status(thm)],[])).
% 127.45/127.71 tff(9,plain,
% 127.45/127.71 (inclusion_order(A!13) = inclusion_relation(A!13)),
% 127.45/127.71 inference(unit_resolution,[status(thm)],[8, 7])).
% 127.45/127.71 tff(10,plain,
% 127.45/127.71 (inclusion_relation(A!13) = inclusion_order(A!13)),
% 127.45/127.71 inference(symmetry,[status(thm)],[9])).
% 127.45/127.71 tff(11,plain,
% 127.45/127.71 (rel_str_of(A!13, inclusion_relation(A!13)) = rel_str_of(A!13, inclusion_order(A!13))),
% 127.45/127.71 inference(monotonicity,[status(thm)],[10])).
% 127.45/127.71 tff(12,plain,
% 127.45/127.71 (rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(A!13, inclusion_relation(A!13))),
% 127.45/127.71 inference(symmetry,[status(thm)],[11])).
% 127.45/127.71 tff(13,plain,
% 127.45/127.71 (^[A: $i] : refl((incl_POSet(A) = rel_str_of(A, inclusion_order(A))) <=> (incl_POSet(A) = rel_str_of(A, inclusion_order(A))))),
% 127.45/127.71 inference(bind,[status(th)],[])).
% 127.45/127.71 tff(14,plain,
% 127.45/127.71 (![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A))) <=> ![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A)))),
% 127.45/127.71 inference(quant_intro,[status(thm)],[13])).
% 127.45/127.71 tff(15,plain,
% 127.45/127.71 (![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A))) <=> ![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A)))),
% 127.45/127.71 inference(rewrite,[status(thm)],[])).
% 127.45/127.71 tff(16,axiom,(![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_yellow_1')).
% 127.45/127.71 tff(17,plain,
% 127.45/127.71 (![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A)))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[16, 15])).
% 127.45/127.71 tff(18,plain,(
% 127.45/127.71 ![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A)))),
% 127.45/127.71 inference(skolemize,[status(sab)],[17])).
% 127.45/127.71 tff(19,plain,
% 127.45/127.71 (![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A)))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[18, 14])).
% 127.45/127.71 tff(20,plain,
% 127.45/127.71 ((~![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A)))) | (incl_POSet(A!13) = rel_str_of(A!13, inclusion_order(A!13)))),
% 127.45/127.71 inference(quant_inst,[status(thm)],[])).
% 127.45/127.71 tff(21,plain,
% 127.45/127.71 (incl_POSet(A!13) = rel_str_of(A!13, inclusion_order(A!13))),
% 127.45/127.71 inference(unit_resolution,[status(thm)],[20, 19])).
% 127.45/127.71 tff(22,plain,
% 127.45/127.71 (^[A: $i] : refl((~((~strict_rel_str(incl_POSet(A))) | (~reflexive_relstr(incl_POSet(A))) | (~transitive_relstr(incl_POSet(A))) | (~antisymmetric_relstr(incl_POSet(A))))) <=> (~((~strict_rel_str(incl_POSet(A))) | (~reflexive_relstr(incl_POSet(A))) | (~transitive_relstr(incl_POSet(A))) | (~antisymmetric_relstr(incl_POSet(A))))))),
% 127.45/127.71 inference(bind,[status(th)],[])).
% 127.45/127.71 tff(23,plain,
% 127.45/127.71 (![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~reflexive_relstr(incl_POSet(A))) | (~transitive_relstr(incl_POSet(A))) | (~antisymmetric_relstr(incl_POSet(A))))) <=> ![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~reflexive_relstr(incl_POSet(A))) | (~transitive_relstr(incl_POSet(A))) | (~antisymmetric_relstr(incl_POSet(A)))))),
% 127.45/127.71 inference(quant_intro,[status(thm)],[22])).
% 127.45/127.71 tff(24,plain,
% 127.45/127.71 (^[A: $i] : rewrite((strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A))) <=> (~((~strict_rel_str(incl_POSet(A))) | (~reflexive_relstr(incl_POSet(A))) | (~transitive_relstr(incl_POSet(A))) | (~antisymmetric_relstr(incl_POSet(A))))))),
% 127.45/127.71 inference(bind,[status(th)],[])).
% 127.45/127.71 tff(25,plain,
% 127.45/127.71 (![A: $i] : (strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A))) <=> ![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~reflexive_relstr(incl_POSet(A))) | (~transitive_relstr(incl_POSet(A))) | (~antisymmetric_relstr(incl_POSet(A)))))),
% 127.45/127.71 inference(quant_intro,[status(thm)],[24])).
% 127.45/127.71 tff(26,plain,
% 127.45/127.71 (![A: $i] : (strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A))) <=> ![A: $i] : (strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A)))),
% 127.45/127.71 inference(rewrite,[status(thm)],[])).
% 127.45/127.71 tff(27,plain,
% 127.45/127.71 (^[A: $i] : trans(monotonicity(rewrite(((strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A))) & transitive_relstr(incl_POSet(A))) <=> (strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)))), ((((strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A))) & transitive_relstr(incl_POSet(A))) & antisymmetric_relstr(incl_POSet(A))) <=> ((strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A))) & antisymmetric_relstr(incl_POSet(A))))), rewrite(((strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A))) & antisymmetric_relstr(incl_POSet(A))) <=> (strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A)))), ((((strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A))) & transitive_relstr(incl_POSet(A))) & antisymmetric_relstr(incl_POSet(A))) <=> (strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A)))))),
% 127.45/127.71 inference(bind,[status(th)],[])).
% 127.45/127.71 tff(28,plain,
% 127.45/127.71 (![A: $i] : (((strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A))) & transitive_relstr(incl_POSet(A))) & antisymmetric_relstr(incl_POSet(A))) <=> ![A: $i] : (strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A)))),
% 127.45/127.71 inference(quant_intro,[status(thm)],[27])).
% 127.45/127.71 tff(29,axiom,(![A: $i] : (((strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A))) & transitive_relstr(incl_POSet(A))) & antisymmetric_relstr(incl_POSet(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc5_yellow_1')).
% 127.45/127.71 tff(30,plain,
% 127.45/127.71 (![A: $i] : (strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A)))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[29, 28])).
% 127.45/127.71 tff(31,plain,
% 127.45/127.71 (![A: $i] : (strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A)))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[30, 26])).
% 127.45/127.71 tff(32,plain,(
% 127.45/127.71 ![A: $i] : (strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A)))),
% 127.45/127.71 inference(skolemize,[status(sab)],[31])).
% 127.45/127.71 tff(33,plain,
% 127.45/127.71 (![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~reflexive_relstr(incl_POSet(A))) | (~transitive_relstr(incl_POSet(A))) | (~antisymmetric_relstr(incl_POSet(A)))))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[32, 25])).
% 127.45/127.71 tff(34,plain,
% 127.45/127.71 (![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~reflexive_relstr(incl_POSet(A))) | (~transitive_relstr(incl_POSet(A))) | (~antisymmetric_relstr(incl_POSet(A)))))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[33, 23])).
% 127.45/127.71 tff(35,plain,
% 127.45/127.71 ((~![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~reflexive_relstr(incl_POSet(A))) | (~transitive_relstr(incl_POSet(A))) | (~antisymmetric_relstr(incl_POSet(A)))))) | (~((~strict_rel_str(incl_POSet(A!13))) | (~reflexive_relstr(incl_POSet(A!13))) | (~transitive_relstr(incl_POSet(A!13))) | (~antisymmetric_relstr(incl_POSet(A!13)))))),
% 127.45/127.71 inference(quant_inst,[status(thm)],[])).
% 127.45/127.71 tff(36,plain,
% 127.45/127.71 (~((~strict_rel_str(incl_POSet(A!13))) | (~reflexive_relstr(incl_POSet(A!13))) | (~transitive_relstr(incl_POSet(A!13))) | (~antisymmetric_relstr(incl_POSet(A!13))))),
% 127.45/127.71 inference(unit_resolution,[status(thm)],[35, 34])).
% 127.45/127.71 tff(37,plain,
% 127.45/127.71 (((~strict_rel_str(incl_POSet(A!13))) | (~reflexive_relstr(incl_POSet(A!13))) | (~transitive_relstr(incl_POSet(A!13))) | (~antisymmetric_relstr(incl_POSet(A!13)))) | strict_rel_str(incl_POSet(A!13))),
% 127.45/127.71 inference(tautology,[status(thm)],[])).
% 127.45/127.71 tff(38,plain,
% 127.45/127.71 (strict_rel_str(incl_POSet(A!13))),
% 127.45/127.71 inference(unit_resolution,[status(thm)],[37, 36])).
% 127.45/127.71 tff(39,plain,
% 127.45/127.71 (^[A: $i] : refl((~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A))))) <=> (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A))))))),
% 127.45/127.71 inference(bind,[status(th)],[])).
% 127.45/127.71 tff(40,plain,
% 127.45/127.71 (![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A))))) <=> ![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A)))))),
% 127.45/127.71 inference(quant_intro,[status(thm)],[39])).
% 127.45/127.71 tff(41,plain,
% 127.45/127.71 (^[A: $i] : rewrite((strict_rel_str(incl_POSet(A)) & rel_str(incl_POSet(A))) <=> (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A))))))),
% 127.45/127.71 inference(bind,[status(th)],[])).
% 127.45/127.71 tff(42,plain,
% 127.45/127.71 (![A: $i] : (strict_rel_str(incl_POSet(A)) & rel_str(incl_POSet(A))) <=> ![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A)))))),
% 127.45/127.71 inference(quant_intro,[status(thm)],[41])).
% 127.45/127.71 tff(43,plain,
% 127.45/127.71 (![A: $i] : (strict_rel_str(incl_POSet(A)) & rel_str(incl_POSet(A))) <=> ![A: $i] : (strict_rel_str(incl_POSet(A)) & rel_str(incl_POSet(A)))),
% 127.45/127.71 inference(rewrite,[status(thm)],[])).
% 127.45/127.71 tff(44,axiom,(![A: $i] : (strict_rel_str(incl_POSet(A)) & rel_str(incl_POSet(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_yellow_1')).
% 127.45/127.71 tff(45,plain,
% 127.45/127.71 (![A: $i] : (strict_rel_str(incl_POSet(A)) & rel_str(incl_POSet(A)))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[44, 43])).
% 127.45/127.71 tff(46,plain,(
% 127.45/127.71 ![A: $i] : (strict_rel_str(incl_POSet(A)) & rel_str(incl_POSet(A)))),
% 127.45/127.71 inference(skolemize,[status(sab)],[45])).
% 127.45/127.71 tff(47,plain,
% 127.45/127.71 (![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A)))))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[46, 42])).
% 127.45/127.71 tff(48,plain,
% 127.45/127.71 (![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A)))))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[47, 40])).
% 127.45/127.71 tff(49,plain,
% 127.45/127.71 (((~![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A)))))) | (~((~rel_str(incl_POSet(A!13))) | (~strict_rel_str(incl_POSet(A!13)))))) <=> ((~![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A)))))) | (~((~rel_str(incl_POSet(A!13))) | (~strict_rel_str(incl_POSet(A!13))))))),
% 127.45/127.71 inference(rewrite,[status(thm)],[])).
% 127.45/127.71 tff(50,plain,
% 127.45/127.71 ((~((~strict_rel_str(incl_POSet(A!13))) | (~rel_str(incl_POSet(A!13))))) <=> (~((~rel_str(incl_POSet(A!13))) | (~strict_rel_str(incl_POSet(A!13)))))),
% 127.45/127.71 inference(rewrite,[status(thm)],[])).
% 127.45/127.71 tff(51,plain,
% 127.45/127.71 (((~![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A)))))) | (~((~strict_rel_str(incl_POSet(A!13))) | (~rel_str(incl_POSet(A!13)))))) <=> ((~![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A)))))) | (~((~rel_str(incl_POSet(A!13))) | (~strict_rel_str(incl_POSet(A!13))))))),
% 127.45/127.71 inference(monotonicity,[status(thm)],[50])).
% 127.45/127.71 tff(52,plain,
% 127.45/127.71 (((~![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A)))))) | (~((~strict_rel_str(incl_POSet(A!13))) | (~rel_str(incl_POSet(A!13)))))) <=> ((~![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A)))))) | (~((~rel_str(incl_POSet(A!13))) | (~strict_rel_str(incl_POSet(A!13))))))),
% 127.45/127.71 inference(transitivity,[status(thm)],[51, 49])).
% 127.45/127.71 tff(53,plain,
% 127.45/127.71 ((~![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A)))))) | (~((~strict_rel_str(incl_POSet(A!13))) | (~rel_str(incl_POSet(A!13)))))),
% 127.45/127.71 inference(quant_inst,[status(thm)],[])).
% 127.45/127.71 tff(54,plain,
% 127.45/127.71 ((~![A: $i] : (~((~strict_rel_str(incl_POSet(A))) | (~rel_str(incl_POSet(A)))))) | (~((~rel_str(incl_POSet(A!13))) | (~strict_rel_str(incl_POSet(A!13)))))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[53, 52])).
% 127.45/127.71 tff(55,plain,
% 127.45/127.71 (~((~rel_str(incl_POSet(A!13))) | (~strict_rel_str(incl_POSet(A!13))))),
% 127.45/127.71 inference(unit_resolution,[status(thm)],[54, 48])).
% 127.45/127.71 tff(56,plain,
% 127.45/127.71 (((~rel_str(incl_POSet(A!13))) | (~strict_rel_str(incl_POSet(A!13)))) | rel_str(incl_POSet(A!13))),
% 127.45/127.71 inference(tautology,[status(thm)],[])).
% 127.45/127.71 tff(57,plain,
% 127.45/127.71 (rel_str(incl_POSet(A!13))),
% 127.45/127.71 inference(unit_resolution,[status(thm)],[56, 55])).
% 127.45/127.71 tff(58,plain,
% 127.45/127.71 (^[A: $i] : refl(((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))) <=> ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))))),
% 127.45/127.71 inference(bind,[status(th)],[])).
% 127.45/127.71 tff(59,plain,
% 127.45/127.71 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))) <=> ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 127.45/127.71 inference(quant_intro,[status(thm)],[58])).
% 127.45/127.71 tff(60,plain,
% 127.45/127.71 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))) <=> ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 127.45/127.71 inference(rewrite,[status(thm)],[])).
% 127.45/127.71 tff(61,plain,
% 127.45/127.71 (^[A: $i] : trans(monotonicity(rewrite((strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A)))) <=> ((~strict_rel_str(A)) | (A = rel_str_of(the_carrier(A), the_InternalRel(A))))), ((rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> (rel_str(A) => ((~strict_rel_str(A)) | (A = rel_str_of(the_carrier(A), the_InternalRel(A))))))), rewrite((rel_str(A) => ((~strict_rel_str(A)) | (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))), ((rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))))),
% 127.45/127.71 inference(bind,[status(th)],[])).
% 127.45/127.71 tff(62,plain,
% 127.45/127.71 (![A: $i] : (rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 127.45/127.71 inference(quant_intro,[status(thm)],[61])).
% 127.45/127.71 tff(63,axiom,(![A: $i] : (rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','abstractness_v1_orders_2')).
% 127.45/127.71 tff(64,plain,
% 127.45/127.71 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[63, 62])).
% 127.45/127.71 tff(65,plain,
% 127.45/127.71 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[64, 60])).
% 127.45/127.71 tff(66,plain,(
% 127.45/127.71 ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 127.45/127.71 inference(skolemize,[status(sab)],[65])).
% 127.45/127.71 tff(67,plain,
% 127.45/127.71 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 127.45/127.71 inference(modus_ponens,[status(thm)],[66, 59])).
% 127.45/127.71 tff(68,plain,
% 127.45/127.71 (((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((~rel_str(incl_POSet(A!13))) | (incl_POSet(A!13) = rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13)))) | (~strict_rel_str(incl_POSet(A!13))))) <=> ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | (~rel_str(incl_POSet(A!13))) | (incl_POSet(A!13) = rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13)))) | (~strict_rel_str(incl_POSet(A!13))))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(69,plain,
% 127.45/127.72 (((incl_POSet(A!13) = rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13)))) | (~strict_rel_str(incl_POSet(A!13))) | (~rel_str(incl_POSet(A!13)))) <=> ((~rel_str(incl_POSet(A!13))) | (incl_POSet(A!13) = rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13)))) | (~strict_rel_str(incl_POSet(A!13))))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(70,plain,
% 127.45/127.72 (((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((incl_POSet(A!13) = rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13)))) | (~strict_rel_str(incl_POSet(A!13))) | (~rel_str(incl_POSet(A!13))))) <=> ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((~rel_str(incl_POSet(A!13))) | (incl_POSet(A!13) = rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13)))) | (~strict_rel_str(incl_POSet(A!13)))))),
% 127.45/127.72 inference(monotonicity,[status(thm)],[69])).
% 127.45/127.72 tff(71,plain,
% 127.45/127.72 (((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((incl_POSet(A!13) = rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13)))) | (~strict_rel_str(incl_POSet(A!13))) | (~rel_str(incl_POSet(A!13))))) <=> ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | (~rel_str(incl_POSet(A!13))) | (incl_POSet(A!13) = rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13)))) | (~strict_rel_str(incl_POSet(A!13))))),
% 127.45/127.72 inference(transitivity,[status(thm)],[70, 68])).
% 127.45/127.72 tff(72,plain,
% 127.45/127.72 ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((incl_POSet(A!13) = rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13)))) | (~strict_rel_str(incl_POSet(A!13))) | (~rel_str(incl_POSet(A!13))))),
% 127.45/127.72 inference(quant_inst,[status(thm)],[])).
% 127.45/127.72 tff(73,plain,
% 127.45/127.72 ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | (~rel_str(incl_POSet(A!13))) | (incl_POSet(A!13) = rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13)))) | (~strict_rel_str(incl_POSet(A!13)))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[72, 71])).
% 127.45/127.72 tff(74,plain,
% 127.45/127.72 ((~rel_str(incl_POSet(A!13))) | (incl_POSet(A!13) = rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13)))) | (~strict_rel_str(incl_POSet(A!13)))),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[73, 67])).
% 127.45/127.72 tff(75,plain,
% 127.45/127.72 (incl_POSet(A!13) = rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13)))),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[74, 57, 38])).
% 127.45/127.72 tff(76,plain,
% 127.45/127.72 (rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = incl_POSet(A!13)),
% 127.45/127.72 inference(symmetry,[status(thm)],[75])).
% 127.45/127.72 tff(77,plain,
% 127.45/127.72 (rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(A!13, inclusion_relation(A!13))),
% 127.45/127.72 inference(transitivity,[status(thm)],[76, 21, 12])).
% 127.45/127.72 tff(78,plain,
% 127.45/127.72 (^[A: $i, B: $i, C: $i] : refl((relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)))),
% 127.45/127.72 inference(bind,[status(th)],[])).
% 127.45/127.72 tff(79,plain,
% 127.45/127.72 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 127.45/127.72 inference(quant_intro,[status(thm)],[78])).
% 127.45/127.72 tff(80,plain,
% 127.45/127.72 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(81,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 127.45/127.72 tff(82,plain,
% 127.45/127.72 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[81, 80])).
% 127.45/127.72 tff(83,plain,(
% 127.45/127.72 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 127.45/127.72 inference(skolemize,[status(sab)],[82])).
% 127.45/127.72 tff(84,plain,
% 127.45/127.72 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[83, 79])).
% 127.45/127.72 tff(85,plain,
% 127.45/127.72 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13))) <=> relation_of2(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13))))),
% 127.45/127.72 inference(quant_inst,[status(thm)],[])).
% 127.45/127.72 tff(86,plain,
% 127.45/127.72 (relation_of2_as_subset(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13))) <=> relation_of2(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)))),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[85, 84])).
% 127.45/127.72 tff(87,plain,
% 127.45/127.72 (^[A: $i] : refl(((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))))),
% 127.45/127.72 inference(bind,[status(th)],[])).
% 127.45/127.72 tff(88,plain,
% 127.45/127.72 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 127.45/127.72 inference(quant_intro,[status(thm)],[87])).
% 127.45/127.72 tff(89,plain,
% 127.45/127.72 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(90,plain,
% 127.45/127.72 (^[A: $i] : rewrite((rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))))),
% 127.45/127.72 inference(bind,[status(th)],[])).
% 127.45/127.72 tff(91,plain,
% 127.45/127.72 (![A: $i] : (rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 127.45/127.72 inference(quant_intro,[status(thm)],[90])).
% 127.45/127.72 tff(92,axiom,(![A: $i] : (rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u1_orders_2')).
% 127.45/127.72 tff(93,plain,
% 127.45/127.72 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[92, 91])).
% 127.45/127.72 tff(94,plain,
% 127.45/127.72 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[93, 89])).
% 127.45/127.72 tff(95,plain,(
% 127.45/127.72 ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 127.45/127.72 inference(skolemize,[status(sab)],[94])).
% 127.45/127.72 tff(96,plain,
% 127.45/127.72 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[95, 88])).
% 127.45/127.72 tff(97,plain,
% 127.45/127.72 (((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | ((~rel_str(incl_POSet(A!13))) | relation_of2_as_subset(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13))))) <=> ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | (~rel_str(incl_POSet(A!13))) | relation_of2_as_subset(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13))))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(98,plain,
% 127.45/127.72 ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | ((~rel_str(incl_POSet(A!13))) | relation_of2_as_subset(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13))))),
% 127.45/127.72 inference(quant_inst,[status(thm)],[])).
% 127.45/127.72 tff(99,plain,
% 127.45/127.72 ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | (~rel_str(incl_POSet(A!13))) | relation_of2_as_subset(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[98, 97])).
% 127.45/127.72 tff(100,plain,
% 127.45/127.72 ((~rel_str(incl_POSet(A!13))) | relation_of2_as_subset(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)))),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[99, 96])).
% 127.45/127.72 tff(101,plain,
% 127.45/127.72 (relation_of2_as_subset(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)))),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[100, 57])).
% 127.45/127.72 tff(102,plain,
% 127.45/127.72 ((~(relation_of2_as_subset(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13))) <=> relation_of2(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13))))) | (~relation_of2_as_subset(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)))) | relation_of2(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)))),
% 127.45/127.72 inference(tautology,[status(thm)],[])).
% 127.45/127.72 tff(103,plain,
% 127.45/127.72 ((~(relation_of2_as_subset(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13))) <=> relation_of2(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13))))) | relation_of2(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)))),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[102, 101])).
% 127.45/127.72 tff(104,plain,
% 127.45/127.72 (relation_of2(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)))),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[103, 86])).
% 127.45/127.72 tff(105,plain,
% 127.45/127.72 (^[A: $i, B: $i] : refl(((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 127.45/127.72 inference(bind,[status(th)],[])).
% 127.45/127.72 tff(106,plain,
% 127.45/127.72 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 127.45/127.72 inference(quant_intro,[status(thm)],[105])).
% 127.45/127.72 tff(107,plain,
% 127.45/127.72 (^[A: $i, B: $i] : rewrite(((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 127.45/127.72 inference(bind,[status(th)],[])).
% 127.45/127.72 tff(108,plain,
% 127.45/127.72 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 127.45/127.72 inference(quant_intro,[status(thm)],[107])).
% 127.45/127.72 tff(109,plain,
% 127.45/127.72 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 127.45/127.72 inference(transitivity,[status(thm)],[108, 106])).
% 127.45/127.72 tff(110,plain,
% 127.45/127.72 (^[A: $i, B: $i] : rewrite(((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 127.45/127.72 inference(bind,[status(th)],[])).
% 127.45/127.72 tff(111,plain,
% 127.45/127.72 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 127.45/127.72 inference(quant_intro,[status(thm)],[110])).
% 127.45/127.72 tff(112,plain,
% 127.45/127.72 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(113,plain,
% 127.45/127.72 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i, D: $i] : rewrite(((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D))) <=> ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))), (![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D))) <=> ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))), ((relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D)))) <=> (relation_of2(B, A, A) => ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))))), rewrite((relation_of2(B, A, A) => ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))), ((relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D)))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))))),
% 127.45/127.72 inference(bind,[status(th)],[])).
% 127.45/127.72 tff(114,plain,
% 127.45/127.72 (![A: $i, B: $i] : (relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 127.45/127.72 inference(quant_intro,[status(thm)],[113])).
% 127.45/127.72 tff(115,axiom,(![A: $i, B: $i] : (relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','free_g1_orders_2')).
% 127.45/127.72 tff(116,plain,
% 127.45/127.72 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[115, 114])).
% 127.45/127.72 tff(117,plain,
% 127.45/127.72 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[116, 112])).
% 127.45/127.72 tff(118,plain,(
% 127.45/127.72 ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 127.45/127.72 inference(skolemize,[status(sab)],[117])).
% 127.45/127.72 tff(119,plain,
% 127.45/127.72 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[118, 111])).
% 127.45/127.72 tff(120,plain,
% 127.45/127.72 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[119, 109])).
% 127.45/127.72 tff(121,plain,
% 127.45/127.72 (((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~relation_of2(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(C, D))) | (~((~(the_carrier(incl_POSet(A!13)) = C)) | (~(the_InternalRel(incl_POSet(A!13)) = D))))))) <=> ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~relation_of2(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(C, D))) | (~((~(the_carrier(incl_POSet(A!13)) = C)) | (~(the_InternalRel(incl_POSet(A!13)) = D))))))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(122,plain,
% 127.45/127.72 ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~relation_of2(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(C, D))) | (~((~(the_carrier(incl_POSet(A!13)) = C)) | (~(the_InternalRel(incl_POSet(A!13)) = D))))))),
% 127.45/127.72 inference(quant_inst,[status(thm)],[])).
% 127.45/127.72 tff(123,plain,
% 127.45/127.72 ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~relation_of2(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(C, D))) | (~((~(the_carrier(incl_POSet(A!13)) = C)) | (~(the_InternalRel(incl_POSet(A!13)) = D)))))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[122, 121])).
% 127.45/127.72 tff(124,plain,
% 127.45/127.72 ((~relation_of2(the_InternalRel(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)), the_carrier(incl_POSet(A!13)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(C, D))) | (~((~(the_carrier(incl_POSet(A!13)) = C)) | (~(the_InternalRel(incl_POSet(A!13)) = D)))))),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[123, 120])).
% 127.45/127.72 tff(125,plain,
% 127.45/127.72 (![C: $i, D: $i] : ((~(rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(C, D))) | (~((~(the_carrier(incl_POSet(A!13)) = C)) | (~(the_InternalRel(incl_POSet(A!13)) = D)))))),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[124, 104])).
% 127.45/127.72 tff(126,plain,
% 127.45/127.72 (((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(C, D))) | (~((~(the_carrier(incl_POSet(A!13)) = C)) | (~(the_InternalRel(incl_POSet(A!13)) = D)))))) | ((~(rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(A!13, inclusion_relation(A!13)))) | (~((~(the_carrier(incl_POSet(A!13)) = A!13)) | (~(the_InternalRel(incl_POSet(A!13)) = inclusion_relation(A!13))))))) <=> ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(C, D))) | (~((~(the_carrier(incl_POSet(A!13)) = C)) | (~(the_InternalRel(incl_POSet(A!13)) = D)))))) | (~(rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(A!13, inclusion_relation(A!13)))) | (~((~(the_carrier(incl_POSet(A!13)) = A!13)) | (~(the_InternalRel(incl_POSet(A!13)) = inclusion_relation(A!13))))))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(127,plain,
% 127.45/127.72 ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(C, D))) | (~((~(the_carrier(incl_POSet(A!13)) = C)) | (~(the_InternalRel(incl_POSet(A!13)) = D)))))) | ((~(rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(A!13, inclusion_relation(A!13)))) | (~((~(the_carrier(incl_POSet(A!13)) = A!13)) | (~(the_InternalRel(incl_POSet(A!13)) = inclusion_relation(A!13))))))),
% 127.45/127.72 inference(quant_inst,[status(thm)],[])).
% 127.45/127.72 tff(128,plain,
% 127.45/127.72 ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(C, D))) | (~((~(the_carrier(incl_POSet(A!13)) = C)) | (~(the_InternalRel(incl_POSet(A!13)) = D)))))) | (~(rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(A!13, inclusion_relation(A!13)))) | (~((~(the_carrier(incl_POSet(A!13)) = A!13)) | (~(the_InternalRel(incl_POSet(A!13)) = inclusion_relation(A!13)))))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[127, 126])).
% 127.45/127.72 tff(129,plain,
% 127.45/127.72 (~((~(the_carrier(incl_POSet(A!13)) = A!13)) | (~(the_InternalRel(incl_POSet(A!13)) = inclusion_relation(A!13))))),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[128, 125, 77])).
% 127.45/127.72 tff(130,plain,
% 127.45/127.72 (((~(the_carrier(incl_POSet(A!13)) = A!13)) | (~(the_InternalRel(incl_POSet(A!13)) = inclusion_relation(A!13)))) | (the_InternalRel(incl_POSet(A!13)) = inclusion_relation(A!13))),
% 127.45/127.72 inference(tautology,[status(thm)],[])).
% 127.45/127.72 tff(131,plain,
% 127.45/127.72 (the_InternalRel(incl_POSet(A!13)) = inclusion_relation(A!13)),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[130, 129])).
% 127.45/127.72 tff(132,plain,
% 127.45/127.72 (the_InternalRel(incl_POSet(A!13)) = inclusion_order(A!13)),
% 127.45/127.72 inference(transitivity,[status(thm)],[131, 10])).
% 127.45/127.72 tff(133,assumption,(~(the_InternalRel(incl_POSet(A!13)) = inclusion_order(A!13))), introduced(assumption)).
% 127.45/127.72 tff(134,plain,
% 127.45/127.72 ($false),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[133, 132])).
% 127.45/127.72 tff(135,plain,(the_InternalRel(incl_POSet(A!13)) = inclusion_order(A!13)), inference(lemma,lemma(discharge,[]))).
% 127.45/127.72 tff(136,plain,
% 127.45/127.72 (inclusion_order(A!13) = the_InternalRel(incl_POSet(A!13))),
% 127.45/127.72 inference(symmetry,[status(thm)],[135])).
% 127.45/127.72 tff(137,plain,
% 127.45/127.72 (rel_str_of(the_carrier(incl_POSet(A!13)), inclusion_order(A!13)) = rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13)))),
% 127.45/127.72 inference(monotonicity,[status(thm)],[136])).
% 127.45/127.72 tff(138,plain,
% 127.45/127.72 (rel_str_of(the_carrier(incl_POSet(A!13)), the_InternalRel(incl_POSet(A!13))) = rel_str_of(the_carrier(incl_POSet(A!13)), inclusion_order(A!13))),
% 127.45/127.72 inference(symmetry,[status(thm)],[137])).
% 127.45/127.72 tff(139,plain,
% 127.45/127.72 (rel_str_of(A!13, inclusion_order(A!13)) = incl_POSet(A!13)),
% 127.45/127.72 inference(symmetry,[status(thm)],[21])).
% 127.45/127.72 tff(140,plain,
% 127.45/127.72 (rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(the_carrier(incl_POSet(A!13)), inclusion_order(A!13))),
% 127.45/127.72 inference(transitivity,[status(thm)],[139, 75, 138])).
% 127.45/127.72 tff(141,plain,
% 127.45/127.72 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(inclusion_order(A!13), A!13, A!13) <=> relation_of2(inclusion_order(A!13), A!13, A!13))),
% 127.45/127.72 inference(quant_inst,[status(thm)],[])).
% 127.45/127.72 tff(142,plain,
% 127.45/127.72 (relation_of2_as_subset(inclusion_order(A!13), A!13, A!13) <=> relation_of2(inclusion_order(A!13), A!13, A!13)),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[141, 84])).
% 127.45/127.72 tff(143,plain,
% 127.45/127.72 (^[A: $i] : refl((~((~reflexive(inclusion_order(A))) | (~antisymmetric(inclusion_order(A))) | (~transitive(inclusion_order(A))) | (~v1_partfun1(inclusion_order(A), A, A)) | (~relation_of2_as_subset(inclusion_order(A), A, A)))) <=> (~((~reflexive(inclusion_order(A))) | (~antisymmetric(inclusion_order(A))) | (~transitive(inclusion_order(A))) | (~v1_partfun1(inclusion_order(A), A, A)) | (~relation_of2_as_subset(inclusion_order(A), A, A)))))),
% 127.45/127.72 inference(bind,[status(th)],[])).
% 127.45/127.72 tff(144,plain,
% 127.45/127.72 (![A: $i] : (~((~reflexive(inclusion_order(A))) | (~antisymmetric(inclusion_order(A))) | (~transitive(inclusion_order(A))) | (~v1_partfun1(inclusion_order(A), A, A)) | (~relation_of2_as_subset(inclusion_order(A), A, A)))) <=> ![A: $i] : (~((~reflexive(inclusion_order(A))) | (~antisymmetric(inclusion_order(A))) | (~transitive(inclusion_order(A))) | (~v1_partfun1(inclusion_order(A), A, A)) | (~relation_of2_as_subset(inclusion_order(A), A, A))))),
% 127.45/127.72 inference(quant_intro,[status(thm)],[143])).
% 127.45/127.72 tff(145,plain,
% 127.45/127.72 (^[A: $i] : rewrite((reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A), A, A) & relation_of2_as_subset(inclusion_order(A), A, A)) <=> (~((~reflexive(inclusion_order(A))) | (~antisymmetric(inclusion_order(A))) | (~transitive(inclusion_order(A))) | (~v1_partfun1(inclusion_order(A), A, A)) | (~relation_of2_as_subset(inclusion_order(A), A, A)))))),
% 127.45/127.72 inference(bind,[status(th)],[])).
% 127.45/127.72 tff(146,plain,
% 127.45/127.72 (![A: $i] : (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A), A, A) & relation_of2_as_subset(inclusion_order(A), A, A)) <=> ![A: $i] : (~((~reflexive(inclusion_order(A))) | (~antisymmetric(inclusion_order(A))) | (~transitive(inclusion_order(A))) | (~v1_partfun1(inclusion_order(A), A, A)) | (~relation_of2_as_subset(inclusion_order(A), A, A))))),
% 127.45/127.72 inference(quant_intro,[status(thm)],[145])).
% 127.45/127.72 tff(147,plain,
% 127.45/127.72 (![A: $i] : (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A), A, A) & relation_of2_as_subset(inclusion_order(A), A, A)) <=> ![A: $i] : (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A), A, A) & relation_of2_as_subset(inclusion_order(A), A, A))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(148,plain,
% 127.45/127.72 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A))) & transitive(inclusion_order(A))) <=> (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)))), ((((reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A))) & transitive(inclusion_order(A))) & v1_partfun1(inclusion_order(A), A, A)) <=> ((reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A))) & v1_partfun1(inclusion_order(A), A, A)))), rewrite(((reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A))) & v1_partfun1(inclusion_order(A), A, A)) <=> (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A), A, A))), ((((reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A))) & transitive(inclusion_order(A))) & v1_partfun1(inclusion_order(A), A, A)) <=> (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A), A, A)))), (((((reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A))) & transitive(inclusion_order(A))) & v1_partfun1(inclusion_order(A), A, A)) & relation_of2_as_subset(inclusion_order(A), A, A)) <=> ((reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A), A, A)) & relation_of2_as_subset(inclusion_order(A), A, A)))), rewrite(((reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A), A, A)) & relation_of2_as_subset(inclusion_order(A), A, A)) <=> (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A), A, A) & relation_of2_as_subset(inclusion_order(A), A, A))), (((((reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A))) & transitive(inclusion_order(A))) & v1_partfun1(inclusion_order(A), A, A)) & relation_of2_as_subset(inclusion_order(A), A, A)) <=> (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A), A, A) & relation_of2_as_subset(inclusion_order(A), A, A))))),
% 127.45/127.72 inference(bind,[status(th)],[])).
% 127.45/127.72 tff(149,plain,
% 127.45/127.72 (![A: $i] : ((((reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A))) & transitive(inclusion_order(A))) & v1_partfun1(inclusion_order(A), A, A)) & relation_of2_as_subset(inclusion_order(A), A, A)) <=> ![A: $i] : (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A), A, A) & relation_of2_as_subset(inclusion_order(A), A, A))),
% 127.45/127.72 inference(quant_intro,[status(thm)],[148])).
% 127.45/127.72 tff(150,axiom,(![A: $i] : ((((reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A))) & transitive(inclusion_order(A))) & v1_partfun1(inclusion_order(A), A, A)) & relation_of2_as_subset(inclusion_order(A), A, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_yellow_1')).
% 127.45/127.72 tff(151,plain,
% 127.45/127.72 (![A: $i] : (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A), A, A) & relation_of2_as_subset(inclusion_order(A), A, A))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[150, 149])).
% 127.45/127.72 tff(152,plain,
% 127.45/127.72 (![A: $i] : (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A), A, A) & relation_of2_as_subset(inclusion_order(A), A, A))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[151, 147])).
% 127.45/127.72 tff(153,plain,(
% 127.45/127.72 ![A: $i] : (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A), A, A) & relation_of2_as_subset(inclusion_order(A), A, A))),
% 127.45/127.72 inference(skolemize,[status(sab)],[152])).
% 127.45/127.72 tff(154,plain,
% 127.45/127.72 (![A: $i] : (~((~reflexive(inclusion_order(A))) | (~antisymmetric(inclusion_order(A))) | (~transitive(inclusion_order(A))) | (~v1_partfun1(inclusion_order(A), A, A)) | (~relation_of2_as_subset(inclusion_order(A), A, A))))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[153, 146])).
% 127.45/127.72 tff(155,plain,
% 127.45/127.72 (![A: $i] : (~((~reflexive(inclusion_order(A))) | (~antisymmetric(inclusion_order(A))) | (~transitive(inclusion_order(A))) | (~v1_partfun1(inclusion_order(A), A, A)) | (~relation_of2_as_subset(inclusion_order(A), A, A))))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[154, 144])).
% 127.45/127.72 tff(156,plain,
% 127.45/127.72 ((~![A: $i] : (~((~reflexive(inclusion_order(A))) | (~antisymmetric(inclusion_order(A))) | (~transitive(inclusion_order(A))) | (~v1_partfun1(inclusion_order(A), A, A)) | (~relation_of2_as_subset(inclusion_order(A), A, A))))) | (~((~reflexive(inclusion_order(A!13))) | (~antisymmetric(inclusion_order(A!13))) | (~transitive(inclusion_order(A!13))) | (~v1_partfun1(inclusion_order(A!13), A!13, A!13)) | (~relation_of2_as_subset(inclusion_order(A!13), A!13, A!13))))),
% 127.45/127.72 inference(quant_inst,[status(thm)],[])).
% 127.45/127.72 tff(157,plain,
% 127.45/127.72 (~((~reflexive(inclusion_order(A!13))) | (~antisymmetric(inclusion_order(A!13))) | (~transitive(inclusion_order(A!13))) | (~v1_partfun1(inclusion_order(A!13), A!13, A!13)) | (~relation_of2_as_subset(inclusion_order(A!13), A!13, A!13)))),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[156, 155])).
% 127.45/127.72 tff(158,plain,
% 127.45/127.72 (((~reflexive(inclusion_order(A!13))) | (~antisymmetric(inclusion_order(A!13))) | (~transitive(inclusion_order(A!13))) | (~v1_partfun1(inclusion_order(A!13), A!13, A!13)) | (~relation_of2_as_subset(inclusion_order(A!13), A!13, A!13))) | relation_of2_as_subset(inclusion_order(A!13), A!13, A!13)),
% 127.45/127.72 inference(tautology,[status(thm)],[])).
% 127.45/127.72 tff(159,plain,
% 127.45/127.72 (relation_of2_as_subset(inclusion_order(A!13), A!13, A!13)),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[158, 157])).
% 127.45/127.72 tff(160,plain,
% 127.45/127.72 ((~(relation_of2_as_subset(inclusion_order(A!13), A!13, A!13) <=> relation_of2(inclusion_order(A!13), A!13, A!13))) | (~relation_of2_as_subset(inclusion_order(A!13), A!13, A!13)) | relation_of2(inclusion_order(A!13), A!13, A!13)),
% 127.45/127.72 inference(tautology,[status(thm)],[])).
% 127.45/127.72 tff(161,plain,
% 127.45/127.72 ((~(relation_of2_as_subset(inclusion_order(A!13), A!13, A!13) <=> relation_of2(inclusion_order(A!13), A!13, A!13))) | relation_of2(inclusion_order(A!13), A!13, A!13)),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[160, 159])).
% 127.45/127.72 tff(162,plain,
% 127.45/127.72 (relation_of2(inclusion_order(A!13), A!13, A!13)),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[161, 142])).
% 127.45/127.72 tff(163,plain,
% 127.45/127.72 (((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~relation_of2(inclusion_order(A!13), A!13, A!13)) | ![C: $i, D: $i] : ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(C, D))) | (~((~(A!13 = C)) | (~(inclusion_order(A!13) = D))))))) <=> ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~relation_of2(inclusion_order(A!13), A!13, A!13)) | ![C: $i, D: $i] : ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(C, D))) | (~((~(A!13 = C)) | (~(inclusion_order(A!13) = D))))))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(164,plain,
% 127.45/127.72 ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~relation_of2(inclusion_order(A!13), A!13, A!13)) | ![C: $i, D: $i] : ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(C, D))) | (~((~(A!13 = C)) | (~(inclusion_order(A!13) = D))))))),
% 127.45/127.72 inference(quant_inst,[status(thm)],[])).
% 127.45/127.72 tff(165,plain,
% 127.45/127.72 ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~relation_of2(inclusion_order(A!13), A!13, A!13)) | ![C: $i, D: $i] : ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(C, D))) | (~((~(A!13 = C)) | (~(inclusion_order(A!13) = D)))))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[164, 163])).
% 127.45/127.72 tff(166,plain,
% 127.45/127.72 ((~relation_of2(inclusion_order(A!13), A!13, A!13)) | ![C: $i, D: $i] : ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(C, D))) | (~((~(A!13 = C)) | (~(inclusion_order(A!13) = D)))))),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[165, 120])).
% 127.45/127.72 tff(167,plain,
% 127.45/127.72 (![C: $i, D: $i] : ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(C, D))) | (~((~(A!13 = C)) | (~(inclusion_order(A!13) = D)))))),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[166, 162])).
% 127.45/127.72 tff(168,plain,
% 127.45/127.72 (((~![C: $i, D: $i] : ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(C, D))) | (~((~(A!13 = C)) | (~(inclusion_order(A!13) = D)))))) | ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(the_carrier(incl_POSet(A!13)), inclusion_order(A!13)))) | (A!13 = the_carrier(incl_POSet(A!13))))) <=> ((~![C: $i, D: $i] : ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(C, D))) | (~((~(A!13 = C)) | (~(inclusion_order(A!13) = D)))))) | (~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(the_carrier(incl_POSet(A!13)), inclusion_order(A!13)))) | (A!13 = the_carrier(incl_POSet(A!13))))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(169,plain,
% 127.45/127.72 (((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(the_carrier(incl_POSet(A!13)), inclusion_order(A!13)))) | (~((~(A!13 = the_carrier(incl_POSet(A!13)))) | (~(inclusion_order(A!13) = inclusion_order(A!13)))))) <=> ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(the_carrier(incl_POSet(A!13)), inclusion_order(A!13)))) | (A!13 = the_carrier(incl_POSet(A!13))))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(170,plain,
% 127.45/127.72 (((~![C: $i, D: $i] : ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(C, D))) | (~((~(A!13 = C)) | (~(inclusion_order(A!13) = D)))))) | ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(the_carrier(incl_POSet(A!13)), inclusion_order(A!13)))) | (~((~(A!13 = the_carrier(incl_POSet(A!13)))) | (~(inclusion_order(A!13) = inclusion_order(A!13))))))) <=> ((~![C: $i, D: $i] : ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(C, D))) | (~((~(A!13 = C)) | (~(inclusion_order(A!13) = D)))))) | ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(the_carrier(incl_POSet(A!13)), inclusion_order(A!13)))) | (A!13 = the_carrier(incl_POSet(A!13)))))),
% 127.45/127.72 inference(monotonicity,[status(thm)],[169])).
% 127.45/127.72 tff(171,plain,
% 127.45/127.72 (((~![C: $i, D: $i] : ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(C, D))) | (~((~(A!13 = C)) | (~(inclusion_order(A!13) = D)))))) | ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(the_carrier(incl_POSet(A!13)), inclusion_order(A!13)))) | (~((~(A!13 = the_carrier(incl_POSet(A!13)))) | (~(inclusion_order(A!13) = inclusion_order(A!13))))))) <=> ((~![C: $i, D: $i] : ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(C, D))) | (~((~(A!13 = C)) | (~(inclusion_order(A!13) = D)))))) | (~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(the_carrier(incl_POSet(A!13)), inclusion_order(A!13)))) | (A!13 = the_carrier(incl_POSet(A!13))))),
% 127.45/127.72 inference(transitivity,[status(thm)],[170, 168])).
% 127.45/127.72 tff(172,plain,
% 127.45/127.72 ((~![C: $i, D: $i] : ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(C, D))) | (~((~(A!13 = C)) | (~(inclusion_order(A!13) = D)))))) | ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(the_carrier(incl_POSet(A!13)), inclusion_order(A!13)))) | (~((~(A!13 = the_carrier(incl_POSet(A!13)))) | (~(inclusion_order(A!13) = inclusion_order(A!13))))))),
% 127.45/127.72 inference(quant_inst,[status(thm)],[])).
% 127.45/127.72 tff(173,plain,
% 127.45/127.72 ((~![C: $i, D: $i] : ((~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(C, D))) | (~((~(A!13 = C)) | (~(inclusion_order(A!13) = D)))))) | (~(rel_str_of(A!13, inclusion_order(A!13)) = rel_str_of(the_carrier(incl_POSet(A!13)), inclusion_order(A!13)))) | (A!13 = the_carrier(incl_POSet(A!13)))),
% 127.45/127.72 inference(modus_ponens,[status(thm)],[172, 171])).
% 127.45/127.72 tff(174,plain,
% 127.45/127.72 (A!13 = the_carrier(incl_POSet(A!13))),
% 127.45/127.72 inference(unit_resolution,[status(thm)],[173, 167, 140])).
% 127.45/127.72 tff(175,plain,
% 127.45/127.72 (the_carrier(incl_POSet(A!13)) = A!13),
% 127.45/127.72 inference(symmetry,[status(thm)],[174])).
% 127.45/127.72 tff(176,plain,
% 127.45/127.72 ((~(~((~(the_carrier(incl_POSet(A!13)) = A!13)) | (~(the_InternalRel(incl_POSet(A!13)) = inclusion_order(A!13)))))) <=> ((~(the_carrier(incl_POSet(A!13)) = A!13)) | (~(the_InternalRel(incl_POSet(A!13)) = inclusion_order(A!13))))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(177,plain,
% 127.45/127.72 (((the_carrier(incl_POSet(A!13)) = A!13) & (the_InternalRel(incl_POSet(A!13)) = inclusion_order(A!13))) <=> (~((~(the_carrier(incl_POSet(A!13)) = A!13)) | (~(the_InternalRel(incl_POSet(A!13)) = inclusion_order(A!13)))))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(178,plain,
% 127.45/127.72 ((~((the_carrier(incl_POSet(A!13)) = A!13) & (the_InternalRel(incl_POSet(A!13)) = inclusion_order(A!13)))) <=> (~(~((~(the_carrier(incl_POSet(A!13)) = A!13)) | (~(the_InternalRel(incl_POSet(A!13)) = inclusion_order(A!13))))))),
% 127.45/127.72 inference(monotonicity,[status(thm)],[177])).
% 127.45/127.72 tff(179,plain,
% 127.45/127.72 ((~((the_carrier(incl_POSet(A!13)) = A!13) & (the_InternalRel(incl_POSet(A!13)) = inclusion_order(A!13)))) <=> ((~(the_carrier(incl_POSet(A!13)) = A!13)) | (~(the_InternalRel(incl_POSet(A!13)) = inclusion_order(A!13))))),
% 127.45/127.72 inference(transitivity,[status(thm)],[178, 176])).
% 127.45/127.72 tff(180,plain,
% 127.45/127.72 ((~![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A)))) <=> (~![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A))))),
% 127.45/127.72 inference(rewrite,[status(thm)],[])).
% 127.45/127.72 tff(181,axiom,(~![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_yellow_1')).
% 127.45/127.72 tff(182,plain,
% 127.45/127.72 (~![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A)))),
% 127.97/128.25 inference(modus_ponens,[status(thm)],[181, 180])).
% 127.97/128.25 tff(183,plain,
% 127.97/128.25 (~![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A)))),
% 127.97/128.25 inference(modus_ponens,[status(thm)],[182, 180])).
% 127.97/128.25 tff(184,plain,
% 127.97/128.25 (~![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A)))),
% 127.97/128.25 inference(modus_ponens,[status(thm)],[183, 180])).
% 127.97/128.25 tff(185,plain,
% 127.97/128.25 (~![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A)))),
% 127.97/128.25 inference(modus_ponens,[status(thm)],[184, 180])).
% 127.97/128.25 tff(186,plain,(
% 127.97/128.25 ~((the_carrier(incl_POSet(A!13)) = A!13) & (the_InternalRel(incl_POSet(A!13)) = inclusion_order(A!13)))),
% 127.97/128.25 inference(skolemize,[status(sab)],[185])).
% 127.97/128.25 tff(187,plain,
% 127.97/128.25 ((~(the_carrier(incl_POSet(A!13)) = A!13)) | (~(the_InternalRel(incl_POSet(A!13)) = inclusion_order(A!13)))),
% 127.97/128.25 inference(modus_ponens,[status(thm)],[186, 179])).
% 127.97/128.25 tff(188,plain,
% 127.97/128.25 (~(the_carrier(incl_POSet(A!13)) = A!13)),
% 127.97/128.25 inference(unit_resolution,[status(thm)],[187, 135])).
% 127.97/128.25 tff(189,plain,
% 127.97/128.25 ($false),
% 127.97/128.25 inference(unit_resolution,[status(thm)],[188, 175])).
% 127.97/128.25 % SZS output end Proof
% 128.07/128.33 % E exiting
%------------------------------------------------------------------------------