%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU363+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU363+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 06:52:48 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(in_type, type, (
% 0.19/0.39 in: ( $i * $i ) > $o)).
% 0.19/0.39 tff(relation_restriction_type, type, (
% 0.19/0.39 relation_restriction: ( $i * $i ) > $i)).
% 0.19/0.39 tff(the_carrier_type, type, (
% 0.19/0.39 the_carrier: $i > $i)).
% 0.19/0.39 tff(tptp_fun_B_11_type, type, (
% 0.19/0.39 tptp_fun_B_11: $i)).
% 0.19/0.39 tff(the_InternalRel_type, type, (
% 0.19/0.39 the_InternalRel: $i > $i)).
% 0.19/0.39 tff(tptp_fun_A_10_type, type, (
% 0.19/0.39 tptp_fun_A_10: $i)).
% 0.19/0.39 tff(ordered_pair_type, type, (
% 0.19/0.39 ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_D_13_type, type, (
% 0.19/0.39 tptp_fun_D_13: $i)).
% 0.19/0.39 tff(tptp_fun_C_12_type, type, (
% 0.19/0.39 tptp_fun_C_12: $i)).
% 0.19/0.39 tff(relation_restriction_as_relation_of_type, type, (
% 0.19/0.39 relation_restriction_as_relation_of: ( $i * $i ) > $i)).
% 0.19/0.39 tff(full_subrelstr_type, type, (
% 0.19/0.39 full_subrelstr: ( $i * $i ) > $o)).
% 0.19/0.39 tff(subrelstr_type, type, (
% 0.19/0.39 subrelstr: ( $i * $i ) > $o)).
% 0.19/0.39 tff(rel_str_type, type, (
% 0.19/0.39 rel_str: $i > $o)).
% 0.19/0.39 tff(related_type, type, (
% 0.19/0.39 related: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(element_type, type, (
% 0.19/0.39 element: ( $i * $i ) > $o)).
% 0.19/0.39 tff(relation_type, type, (
% 0.19/0.39 relation: $i > $o)).
% 0.19/0.39 tff(powerset_type, type, (
% 0.19/0.39 powerset: $i > $i)).
% 0.19/0.39 tff(cartesian_product2_type, type, (
% 0.19/0.39 cartesian_product2: ( $i * $i ) > $i)).
% 0.19/0.39 tff(relation_of2_as_subset_type, type, (
% 0.19/0.39 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 ((rel_str(A!10) & (full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10) & element(C!12, the_carrier(A!10)) & (~((~element(C!12, the_carrier(B!11))) | (~in(C!12, the_carrier(B!11))) | related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13)))))) <=> (rel_str(A!10) & full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10) & element(C!12, the_carrier(A!10)) & (~((~element(C!12, the_carrier(B!11))) | (~in(C!12, the_carrier(B!11))) | related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (((full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10)) & (element(C!12, the_carrier(A!10)) & (~((~element(C!12, the_carrier(B!11))) | (~in(C!12, the_carrier(B!11))) | related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13)))))) <=> (full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10) & element(C!12, the_carrier(A!10)) & (~((~element(C!12, the_carrier(B!11))) | (~in(C!12, the_carrier(B!11))) | related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 ((element(C!12, the_carrier(A!10)) & (~(related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~element(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13)) | (~in(C!12, the_carrier(B!11)))))) <=> (element(C!12, the_carrier(A!10)) & (~((~element(C!12, the_carrier(B!11))) | (~in(C!12, the_carrier(B!11))) | related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (((full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10)) & (element(C!12, the_carrier(A!10)) & (~(related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~element(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13)) | (~in(C!12, the_carrier(B!11))))))) <=> ((full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10)) & (element(C!12, the_carrier(A!10)) & (~((~element(C!12, the_carrier(B!11))) | (~in(C!12, the_carrier(B!11))) | related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (((full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10)) & (element(C!12, the_carrier(A!10)) & (~(related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~element(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13)) | (~in(C!12, the_carrier(B!11))))))) <=> (full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10) & element(C!12, the_carrier(A!10)) & (~((~element(C!12, the_carrier(B!11))) | (~in(C!12, the_carrier(B!11))) | related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13)))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 ((rel_str(A!10) & ((full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10)) & (element(C!12, the_carrier(A!10)) & (~(related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~element(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13)) | (~in(C!12, the_carrier(B!11)))))))) <=> (rel_str(A!10) & (full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10) & element(C!12, the_carrier(A!10)) & (~((~element(C!12, the_carrier(B!11))) | (~in(C!12, the_carrier(B!11))) | related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 ((rel_str(A!10) & ((full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10)) & (element(C!12, the_carrier(A!10)) & (~(related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~element(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13)) | (~in(C!12, the_carrier(B!11)))))))) <=> (rel_str(A!10) & full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10) & element(C!12, the_carrier(A!10)) & (~((~element(C!12, the_carrier(B!11))) | (~in(C!12, the_carrier(B!11))) | related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13)))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[6, 1])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : (related(B, C, D) | (~element(D, the_carrier(B))) | (~element(D, the_carrier(A))) | (~element(C, the_carrier(B))) | (~in(D, the_carrier(B))) | (~related(A, C, D)) | (~in(C, the_carrier(B)))))))) <=> (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : (related(B, C, D) | (~element(D, the_carrier(B))) | (~element(D, the_carrier(A))) | (~element(C, the_carrier(B))) | (~in(D, the_carrier(B))) | (~related(A, C, D)) | (~in(C, the_carrier(B))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 ((~![A: $i] : (rel_str(A) => ![B: $i] : ((full_subrelstr(B, A) & subrelstr(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F))))))))) <=> (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : (related(B, C, D) | (~element(D, the_carrier(B))) | (~element(D, the_carrier(A))) | (~element(C, the_carrier(B))) | (~in(D, the_carrier(B))) | (~related(A, C, D)) | (~in(C, the_carrier(B))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(10,axiom,(~![A: $i] : (rel_str(A) => ![B: $i] : ((full_subrelstr(B, A) & subrelstr(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t61_yellow_0')).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : (related(B, C, D) | (~element(D, the_carrier(B))) | (~element(D, the_carrier(A))) | (~element(C, the_carrier(B))) | (~in(D, the_carrier(B))) | (~related(A, C, D)) | (~in(C, the_carrier(B)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : (related(B, C, D) | (~element(D, the_carrier(B))) | (~element(D, the_carrier(A))) | (~element(C, the_carrier(B))) | (~in(D, the_carrier(B))) | (~related(A, C, D)) | (~in(C, the_carrier(B)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : (related(B, C, D) | (~element(D, the_carrier(B))) | (~element(D, the_carrier(A))) | (~element(C, the_carrier(B))) | (~in(D, the_carrier(B))) | (~related(A, C, D)) | (~in(C, the_carrier(B)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : (related(B, C, D) | (~element(D, the_carrier(B))) | (~element(D, the_carrier(A))) | (~element(C, the_carrier(B))) | (~in(D, the_carrier(B))) | (~related(A, C, D)) | (~in(C, the_carrier(B)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (rel_str(A!10) & full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10) & element(C!12, the_carrier(A!10)) & (~((~element(C!12, the_carrier(B!11))) | (~in(C!12, the_carrier(B!11))) | related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (rel_str(A!10)),
% 0.19/0.40 inference(and_elim,[status(thm)],[15])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[20, 18])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((subrelstr(B, A) => (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))) <=> ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))), (![B: $i] : (subrelstr(B, A) => (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))) <=> ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))), ((rel_str(A) => ![B: $i] : (subrelstr(B, A) => (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> (rel_str(A) => ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))))), rewrite((rel_str(A) => ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))), ((rel_str(A) => ![B: $i] : (subrelstr(B, A) => (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![A: $i] : (rel_str(A) => ![B: $i] : (subrelstr(B, A) => (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.40 tff(25,axiom,(![A: $i] : (rel_str(A) => ![B: $i] : (subrelstr(B, A) => (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d14_yellow_0')).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.40 tff(28,plain,(
% 0.19/0.40 ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[27])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))) | ((~rel_str(A!10)) | ![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))) | (~rel_str(A!10)) | ![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))) | ((~rel_str(A!10)) | ![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))) | (~rel_str(A!10)) | ![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[32, 29, 16])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (subrelstr(B!11, A!10)),
% 0.19/0.40 inference(and_elim,[status(thm)],[15])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (((~![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B)))))) | ((~subrelstr(B!11, A!10)) | (full_subrelstr(B!11, A!10) <=> (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)))))) <=> ((~![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B)))))) | (~subrelstr(B!11, A!10)) | (full_subrelstr(B!11, A!10) <=> (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 ((~![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B)))))) | ((~subrelstr(B!11, A!10)) | (full_subrelstr(B!11, A!10) <=> (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 ((~![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B)))))) | (~subrelstr(B!11, A!10)) | (full_subrelstr(B!11, A!10) <=> (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (full_subrelstr(B!11, A!10) <=> (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[37, 34, 33])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (full_subrelstr(B!11, A!10)),
% 0.19/0.40 inference(and_elim,[status(thm)],[15])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 ((~(full_subrelstr(B!11, A!10) <=> (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11))))) | (~full_subrelstr(B!11, A!10)) | (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 ((~(full_subrelstr(B!11, A!10) <=> (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11))))) | (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)) = the_InternalRel(B!11)),
% 0.19/0.40 inference(symmetry,[status(thm)],[42])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.40 tff(49,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')).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.40 tff(52,plain,(
% 0.19/0.40 ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[51])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | ((~rel_str(A!10)) | relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10)))) <=> ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | (~rel_str(A!10)) | relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | ((~rel_str(A!10)) | relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | (~rel_str(A!10)) | relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[56, 53, 16])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.40 tff(63,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.19/0.40 tff(66,plain,(
% 0.19/0.40 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[65])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10))) | element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10))) | element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10))) | element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10))) | element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[70, 67, 57])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (^[A: $i, B: $i, C: $i] : refl((relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : rewrite((element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.41 tff(77,axiom,(![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_relset_1')).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.41 tff(80,plain,(
% 0.19/0.41 ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[79])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(the_InternalRel(A!10)) | (~element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10))))))) <=> ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(the_InternalRel(A!10)) | (~element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(the_InternalRel(A!10)) | (~element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(the_InternalRel(A!10)) | (~element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (relation(the_InternalRel(A!10))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[84, 81, 71])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (^[A: $i, B: $i] : refl(((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B))) <=> ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (^[A: $i, B: $i] : rewrite((relation(A) => (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B))) <=> ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (![A: $i, B: $i] : (relation(A) => (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[89])).
% 0.19/0.41 tff(91,axiom,(![A: $i, B: $i] : (relation(A) => (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k1_toler_1')).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.19/0.41 tff(94,plain,(
% 0.19/0.41 ![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[93])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))) | ((~relation(the_InternalRel(A!10))) | (relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)) = relation_restriction(the_InternalRel(A!10), the_carrier(B!11))))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))) | (~relation(the_InternalRel(A!10))) | (relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)) = relation_restriction(the_InternalRel(A!10), the_carrier(B!11))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))) | ((~relation(the_InternalRel(A!10))) | (relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)) = relation_restriction(the_InternalRel(A!10), the_carrier(B!11))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))) | (~relation(the_InternalRel(A!10))) | (relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)) = relation_restriction(the_InternalRel(A!10), the_carrier(B!11)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)) = relation_restriction(the_InternalRel(A!10), the_carrier(B!11))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[98, 95, 85])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (relation_restriction(the_InternalRel(A!10), the_carrier(B!11)) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11))),
% 0.19/0.41 inference(symmetry,[status(thm)],[99])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (relation_restriction(the_InternalRel(A!10), the_carrier(B!11)) = the_InternalRel(B!11)),
% 0.19/0.41 inference(transitivity,[status(thm)],[100, 43])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (in(ordered_pair(C!12, D!13), the_InternalRel(B!11)) <=> in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[102])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 ((~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))) <=> (~in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[103])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))) <=> ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))) <=> ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[108, 106])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((subrelstr(B, A) => rel_str(B)) <=> (rel_str(B) | (~subrelstr(B, A))))), (![B: $i] : (subrelstr(B, A) => rel_str(B)) <=> ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))), ((rel_str(A) => ![B: $i] : (subrelstr(B, A) => rel_str(B))) <=> (rel_str(A) => ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))))), rewrite((rel_str(A) => ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))) <=> ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))), ((rel_str(A) => ![B: $i] : (subrelstr(B, A) => rel_str(B))) <=> ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (![A: $i] : (rel_str(A) => ![B: $i] : (subrelstr(B, A) => rel_str(B))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[111])).
% 0.19/0.41 tff(113,axiom,(![A: $i] : (rel_str(A) => ![B: $i] : (subrelstr(B, A) => rel_str(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_yellow_0')).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.19/0.41 tff(116,plain,(
% 0.19/0.41 ![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[115])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))) | ((~rel_str(A!10)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A!10))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))) | (~rel_str(A!10)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A!10))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))) | ((~rel_str(A!10)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A!10))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))) | (~rel_str(A!10)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[120, 117, 16])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (((~![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))) | (rel_str(B!11) | (~subrelstr(B!11, A!10)))) <=> ((~![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))) | rel_str(B!11) | (~subrelstr(B!11, A!10)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 ((~![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))) | (rel_str(B!11) | (~subrelstr(B!11, A!10)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 ((~![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))) | rel_str(B!11) | (~subrelstr(B!11, A!10))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (rel_str(B!11)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[124, 34, 121])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[128])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[129, 127])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))) <=> ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))), (![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> (element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), ((rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> (rel_str(A) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))), rewrite((rel_str(A) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), ((rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 (![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[132])).
% 0.19/0.41 tff(134,axiom,(![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_orders_2')).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.19/0.41 tff(136,plain,
% 0.19/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.19/0.41 tff(137,plain,(
% 0.19/0.41 ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[136])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | ((~rel_str(B!11)) | ![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | (~rel_str(B!11)) | ![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | ((~rel_str(B!11)) | ![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | (~rel_str(B!11)) | ![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 ((~rel_str(B!11)) | ![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[141, 138])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[142, 125])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 (~((~element(C!12, the_carrier(B!11))) | (~in(C!12, the_carrier(B!11))) | related(B!11, C!12, D!13) | (~element(D!13, the_carrier(B!11))) | (~element(D!13, the_carrier(A!10))) | (~in(D!13, the_carrier(B!11))) | (~related(A!10, C!12, D!13)))),
% 0.19/0.42 inference(and_elim,[status(thm)],[15])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (element(C!12, the_carrier(B!11))),
% 0.19/0.42 inference(or_elim,[status(thm)],[144])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 (((~![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11)))))) | ((~element(C!12, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11)))))) | (~element(C!12, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 ((~![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11)))))) | ((~element(C!12, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 ((~![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11)))))) | (~element(C!12, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 (![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[148, 145, 143])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (element(D!13, the_carrier(B!11))),
% 0.19/0.42 inference(or_elim,[status(thm)],[144])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 (((~![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11))))) | ((~element(D!13, the_carrier(B!11))) | (related(B!11, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11))))) <=> ((~![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11))))) | (~element(D!13, the_carrier(B!11))) | (related(B!11, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 ((~![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11))))) | ((~element(D!13, the_carrier(B!11))) | (related(B!11, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 ((~![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11))))) | (~element(D!13, the_carrier(B!11))) | (related(B!11, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 (related(B!11, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[153, 150, 149])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 (~related(B!11, C!12, D!13)),
% 0.19/0.42 inference(or_elim,[status(thm)],[144])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 ((~(related(B!11, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11)))) | related(B!11, C!12, D!13) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 ((~(related(B!11, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11)))) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.19/0.42 tff(158,plain,
% 0.19/0.42 (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[157, 154])).
% 0.19/0.42 tff(159,plain,
% 0.19/0.42 (~in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[158, 104])).
% 0.19/0.42 tff(160,plain,
% 0.19/0.42 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))) <=> ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[160])).
% 0.19/0.42 tff(162,plain,
% 0.19/0.42 (^[A: $i, B: $i, C: $i] : rewrite(((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(163,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[162])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 (^[A: $i, B: $i, C: $i] : rewrite((relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(166,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[165])).
% 0.19/0.42 tff(167,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t16_wellord1')).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.19/0.42 tff(169,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.19/0.42 tff(170,plain,(
% 0.19/0.42 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[169])).
% 0.19/0.42 tff(171,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.19/0.42 tff(172,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[171, 161])).
% 0.19/0.42 tff(173,plain,
% 0.19/0.42 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(the_InternalRel(A!10))) | (~(((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))) <=> in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(the_InternalRel(A!10))) | (~(((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))) <=> in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(174,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(the_InternalRel(A!10))) | (~(((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))) <=> in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(175,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(the_InternalRel(A!10))) | (~(((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))) <=> in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.19/0.42 tff(176,plain,
% 0.19/0.42 (~(((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))) <=> in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[175, 172, 85])).
% 0.19/0.42 tff(177,plain,
% 0.19/0.42 (^[A: $i, B: $i, C: $i, D: $i] : refl((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(178,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[177])).
% 0.19/0.42 tff(179,plain,
% 0.19/0.42 (^[A: $i, B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((in(A, C) & in(B, D)) <=> (~((~in(A, C)) | (~in(B, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))), rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))), rewrite((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(180,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[179])).
% 0.19/0.42 tff(181,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(182,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t106_zfmisc_1')).
% 0.19/0.42 tff(183,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.19/0.42 tff(184,plain,(
% 0.19/0.42 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[183])).
% 0.19/0.42 tff(185,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.19/0.42 tff(186,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.19/0.42 tff(187,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11)))) <=> in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(188,plain,
% 0.19/0.42 (~(((~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11)))) <=> in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.19/0.43 tff(189,plain,
% 0.19/0.43 (in(D!13, the_carrier(B!11))),
% 0.19/0.43 inference(or_elim,[status(thm)],[144])).
% 0.19/0.43 tff(190,plain,
% 0.19/0.43 (in(C!12, the_carrier(B!11))),
% 0.19/0.43 inference(or_elim,[status(thm)],[144])).
% 0.19/0.43 tff(191,plain,
% 0.19/0.43 ((~((~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11))))) | (~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(192,plain,
% 0.19/0.43 (~((~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[191, 190, 189])).
% 0.19/0.43 tff(193,plain,
% 0.19/0.43 ((((~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11)))) <=> in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))) | ((~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11)))) | in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(194,plain,
% 0.19/0.43 ((((~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11)))) <=> in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))) | in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.19/0.43 tff(195,plain,
% 0.19/0.43 (in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[194, 188])).
% 0.19/0.43 tff(196,plain,
% 0.19/0.43 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | ((~rel_str(A!10)) | ![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | (~rel_str(A!10)) | ![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(197,plain,
% 0.19/0.43 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | ((~rel_str(A!10)) | ![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(198,plain,
% 0.19/0.43 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | (~rel_str(A!10)) | ![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.19/0.43 tff(199,plain,
% 0.19/0.43 (![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[198, 138, 16])).
% 0.19/0.43 tff(200,plain,
% 0.19/0.43 (element(C!12, the_carrier(A!10))),
% 0.19/0.43 inference(and_elim,[status(thm)],[15])).
% 0.19/0.43 tff(201,plain,
% 0.19/0.43 (((~![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10)))))) | ((~element(C!12, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10)))))) | (~element(C!12, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(202,plain,
% 0.19/0.43 ((~![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10)))))) | ((~element(C!12, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(203,plain,
% 0.19/0.43 ((~![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10)))))) | (~element(C!12, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.19/0.43 tff(204,plain,
% 0.19/0.43 (![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[203, 200, 199])).
% 0.19/0.43 tff(205,plain,
% 0.19/0.43 (element(D!13, the_carrier(A!10))),
% 0.19/0.43 inference(or_elim,[status(thm)],[144])).
% 0.19/0.43 tff(206,plain,
% 0.19/0.43 (((~![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10))))) | ((~element(D!13, the_carrier(A!10))) | (related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10))))) | (~element(D!13, the_carrier(A!10))) | (related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(207,plain,
% 0.19/0.43 ((~![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10))))) | ((~element(D!13, the_carrier(A!10))) | (related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(208,plain,
% 0.19/0.43 ((~![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10))))) | (~element(D!13, the_carrier(A!10))) | (related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.19/0.43 tff(209,plain,
% 0.19/0.43 (related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[208, 205, 204])).
% 0.19/0.43 tff(210,plain,
% 0.19/0.43 (related(A!10, C!12, D!13)),
% 0.19/0.43 inference(or_elim,[status(thm)],[144])).
% 0.19/0.43 tff(211,plain,
% 0.19/0.43 ((~(related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10)))) | (~related(A!10, C!12, D!13)) | in(ordered_pair(C!12, D!13), the_InternalRel(A!10))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(212,plain,
% 0.19/0.43 ((~(related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10)))) | in(ordered_pair(C!12, D!13), the_InternalRel(A!10))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.19/0.43 tff(213,plain,
% 0.19/0.43 (in(ordered_pair(C!12, D!13), the_InternalRel(A!10))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[212, 209])).
% 0.19/0.43 tff(214,plain,
% 0.19/0.43 ((~((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))))) | (~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(215,plain,
% 0.19/0.43 ((~((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.19/0.43 tff(216,plain,
% 0.19/0.43 (~((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[215, 195])).
% 0.19/0.43 tff(217,plain,
% 0.19/0.43 ((((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))) <=> in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11)))) | ((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))) | in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(218,plain,
% 0.19/0.43 (in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[217, 216, 176])).
% 0.19/0.43 tff(219,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[218, 159])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------