%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU340+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:39 AM UTC 2025
% Result : Theorem 1.68s 1.90s
% Output : Proof 1.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU340+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:48:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.68/1.90 % SZS status Theorem
% 1.68/1.90 % SZS output start Proof
% 1.68/1.90 tff(empty_type, type, (
% 1.68/1.90 empty: $i > $o)).
% 1.68/1.90 tff(the_carrier_type, type, (
% 1.68/1.90 the_carrier: $i > $i)).
% 1.68/1.90 tff(tptp_fun_A_12_type, type, (
% 1.68/1.90 tptp_fun_A_12: $i)).
% 1.68/1.90 tff(in_type, type, (
% 1.68/1.90 in: ( $i * $i ) > $o)).
% 1.68/1.90 tff(tptp_fun_B_13_type, type, (
% 1.68/1.90 tptp_fun_B_13: $i)).
% 1.68/1.90 tff(tptp_fun_C_14_type, type, (
% 1.68/1.90 tptp_fun_C_14: $i)).
% 1.68/1.90 tff(cartesian_product2_type, type, (
% 1.68/1.90 cartesian_product2: ( $i * $i ) > $i)).
% 1.68/1.90 tff(ordered_pair_type, type, (
% 1.68/1.90 ordered_pair: ( $i * $i ) > $i)).
% 1.68/1.90 tff(unordered_pair_type, type, (
% 1.68/1.90 unordered_pair: ( $i * $i ) > $i)).
% 1.68/1.90 tff(singleton_type, type, (
% 1.68/1.90 singleton: $i > $i)).
% 1.68/1.90 tff(element_type, type, (
% 1.68/1.90 element: ( $i * $i ) > $o)).
% 1.68/1.90 tff(the_InternalRel_type, type, (
% 1.68/1.90 the_InternalRel: $i > $i)).
% 1.68/1.90 tff(related_type, type, (
% 1.68/1.90 related: ( $i * $i * $i ) > $o)).
% 1.68/1.90 tff(rel_str_type, type, (
% 1.68/1.90 rel_str: $i > $o)).
% 1.68/1.90 tff(tptp_fun_D_15_type, type, (
% 1.68/1.90 tptp_fun_D_15: $i)).
% 1.68/1.90 tff(transitive_relstr_type, type, (
% 1.68/1.90 transitive_relstr: $i > $o)).
% 1.68/1.90 tff(powerset_type, type, (
% 1.68/1.90 powerset: $i > $i)).
% 1.68/1.90 tff(relation_of2_as_subset_type, type, (
% 1.68/1.90 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 1.68/1.90 tff(is_transitive_in_type, type, (
% 1.68/1.90 is_transitive_in: ( $i * $i ) > $o)).
% 1.68/1.90 tff(tptp_fun_E_0_type, type, (
% 1.68/1.90 tptp_fun_E_0: ( $i * $i ) > $i)).
% 1.68/1.90 tff(tptp_fun_D_1_type, type, (
% 1.68/1.90 tptp_fun_D_1: ( $i * $i ) > $i)).
% 1.68/1.90 tff(tptp_fun_C_2_type, type, (
% 1.68/1.90 tptp_fun_C_2: ( $i * $i ) > $i)).
% 1.68/1.90 tff(relation_type, type, (
% 1.68/1.90 relation: $i > $o)).
% 1.68/1.90 tff(1,plain,
% 1.68/1.90 (^[A: $i, B: $i] : refl((ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))) <=> (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))))),
% 1.68/1.90 inference(bind,[status(th)],[])).
% 1.68/1.90 tff(2,plain,
% 1.68/1.90 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))) <=> ![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 1.68/1.90 inference(quant_intro,[status(thm)],[1])).
% 1.68/1.90 tff(3,plain,
% 1.68/1.90 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))) <=> ![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(4,axiom,(![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_tarski')).
% 1.68/1.90 tff(5,plain,
% 1.68/1.90 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.68/1.90 tff(6,plain,(
% 1.68/1.90 ![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 1.68/1.90 inference(skolemize,[status(sab)],[5])).
% 1.68/1.90 tff(7,plain,
% 1.68/1.90 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.68/1.90 tff(8,plain,
% 1.68/1.90 ((~![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))) | (ordered_pair(B!13, C!14) = unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(9,plain,
% 1.68/1.90 (ordered_pair(B!13, C!14) = unordered_pair(unordered_pair(B!13, C!14), singleton(B!13))),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.68/1.90 tff(10,plain,
% 1.68/1.90 (unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)) = ordered_pair(B!13, C!14)),
% 1.68/1.90 inference(symmetry,[status(thm)],[9])).
% 1.68/1.90 tff(11,plain,
% 1.68/1.90 (in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) <=> in(ordered_pair(B!13, C!14), cartesian_product2(the_carrier(A!12), the_carrier(A!12)))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[10])).
% 1.68/1.90 tff(12,plain,
% 1.68/1.90 (in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12)) <=> in(ordered_pair(B!13, C!14), the_InternalRel(A!12))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[10])).
% 1.68/1.90 tff(13,plain,
% 1.68/1.90 (in(ordered_pair(B!13, C!14), the_InternalRel(A!12)) <=> in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12))),
% 1.68/1.90 inference(symmetry,[status(thm)],[12])).
% 1.68/1.90 tff(14,plain,
% 1.68/1.90 (((transitive_relstr(A!12) & rel_str(A!12)) & (element(B!13, the_carrier(A!12)) & element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12))))))) <=> (transitive_relstr(A!12) & rel_str(A!12) & element(B!13, the_carrier(A!12)) & element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12))))))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(15,plain,
% 1.68/1.90 ((element(B!13, the_carrier(A!12)) & (element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12))))))) <=> (element(B!13, the_carrier(A!12)) & element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12))))))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(16,plain,
% 1.68/1.90 ((~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12))))) <=> (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12)))))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(17,plain,
% 1.68/1.90 ((element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12)))))) <=> (element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12))))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[16])).
% 1.68/1.90 tff(18,plain,
% 1.68/1.90 ((element(B!13, the_carrier(A!12)) & (element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12))))))) <=> (element(B!13, the_carrier(A!12)) & (element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12)))))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[17])).
% 1.68/1.90 tff(19,plain,
% 1.68/1.90 ((element(B!13, the_carrier(A!12)) & (element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12))))))) <=> (element(B!13, the_carrier(A!12)) & element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12))))))),
% 1.68/1.90 inference(transitivity,[status(thm)],[18, 15])).
% 1.68/1.90 tff(20,plain,
% 1.68/1.90 (((transitive_relstr(A!12) & rel_str(A!12)) & (element(B!13, the_carrier(A!12)) & (element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12)))))))) <=> ((transitive_relstr(A!12) & rel_str(A!12)) & (element(B!13, the_carrier(A!12)) & element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12)))))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[19])).
% 1.68/1.90 tff(21,plain,
% 1.68/1.90 (((transitive_relstr(A!12) & rel_str(A!12)) & (element(B!13, the_carrier(A!12)) & (element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12)))))))) <=> (transitive_relstr(A!12) & rel_str(A!12) & element(B!13, the_carrier(A!12)) & element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12))))))),
% 1.68/1.90 inference(transitivity,[status(thm)],[20, 14])).
% 1.68/1.90 tff(22,plain,
% 1.68/1.90 ((~![A: $i] : ((~(transitive_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : (related(A, B, D) | (~(related(A, B, C) & related(A, C, D))) | (~element(D, the_carrier(A)))))))) <=> (~![A: $i] : ((~(transitive_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : (related(A, B, D) | (~(related(A, B, C) & related(A, C, D))) | (~element(D, the_carrier(A))))))))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(23,plain,
% 1.68/1.90 ((~![A: $i] : ((transitive_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ((related(A, B, C) & related(A, C, D)) => related(A, B, D))))))) <=> (~![A: $i] : ((~(transitive_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : (related(A, B, D) | (~(related(A, B, C) & related(A, C, D))) | (~element(D, the_carrier(A))))))))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(24,axiom,(~![A: $i] : ((transitive_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ((related(A, B, C) & related(A, C, D)) => related(A, B, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t26_orders_2')).
% 1.68/1.90 tff(25,plain,
% 1.68/1.90 (~![A: $i] : ((~(transitive_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : (related(A, B, D) | (~(related(A, B, C) & related(A, C, D))) | (~element(D, the_carrier(A)))))))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.68/1.90 tff(26,plain,
% 1.68/1.90 (~![A: $i] : ((~(transitive_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : (related(A, B, D) | (~(related(A, B, C) & related(A, C, D))) | (~element(D, the_carrier(A)))))))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[25, 22])).
% 1.68/1.90 tff(27,plain,
% 1.68/1.90 (~![A: $i] : ((~(transitive_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : (related(A, B, D) | (~(related(A, B, C) & related(A, C, D))) | (~element(D, the_carrier(A)))))))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[26, 22])).
% 1.68/1.90 tff(28,plain,
% 1.68/1.90 (~![A: $i] : ((~(transitive_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : (related(A, B, D) | (~(related(A, B, C) & related(A, C, D))) | (~element(D, the_carrier(A)))))))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[27, 22])).
% 1.68/1.90 tff(29,plain,
% 1.68/1.90 (transitive_relstr(A!12) & rel_str(A!12) & element(B!13, the_carrier(A!12)) & element(C!14, the_carrier(A!12)) & (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12)))))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[28, 21])).
% 1.68/1.90 tff(30,plain,
% 1.68/1.90 (rel_str(A!12)),
% 1.68/1.90 inference(and_elim,[status(thm)],[29])).
% 1.68/1.90 tff(31,plain,
% 1.68/1.90 (^[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)))))))),
% 1.68/1.90 inference(bind,[status(th)],[])).
% 1.68/1.90 tff(32,plain,
% 1.68/1.90 (![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))))))),
% 1.68/1.90 inference(quant_intro,[status(thm)],[31])).
% 1.68/1.90 tff(33,plain,
% 1.68/1.90 (^[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)))))))),
% 1.68/1.90 inference(bind,[status(th)],[])).
% 1.68/1.90 tff(34,plain,
% 1.68/1.90 (![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))))))),
% 1.68/1.90 inference(quant_intro,[status(thm)],[33])).
% 1.68/1.90 tff(35,plain,
% 1.68/1.90 (![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))))))),
% 1.68/1.90 inference(transitivity,[status(thm)],[34, 32])).
% 1.68/1.90 tff(36,plain,
% 1.68/1.90 (![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))))))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(37,plain,
% 1.68/1.90 (^[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))))))))),
% 1.68/1.90 inference(bind,[status(th)],[])).
% 1.68/1.90 tff(38,plain,
% 1.68/1.90 (![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))))))),
% 1.68/1.90 inference(quant_intro,[status(thm)],[37])).
% 1.68/1.90 tff(39,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')).
% 1.68/1.90 tff(40,plain,
% 1.68/1.90 (![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))))))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.68/1.90 tff(41,plain,
% 1.68/1.90 (![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))))))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.68/1.90 tff(42,plain,(
% 1.68/1.90 ![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))))))),
% 1.68/1.90 inference(skolemize,[status(sab)],[41])).
% 1.68/1.90 tff(43,plain,
% 1.68/1.90 (![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))))))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[42, 35])).
% 1.68/1.90 tff(44,plain,
% 1.68/1.90 (((~![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!12)) | ![B: $i] : ((~element(B, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!12))))))) <=> ((~![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!12)) | ![B: $i] : ((~element(B, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!12))))))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(45,plain,
% 1.68/1.90 ((~![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!12)) | ![B: $i] : ((~element(B, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!12))))))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(46,plain,
% 1.68/1.90 ((~![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!12)) | ![B: $i] : ((~element(B, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!12)))))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.68/1.90 tff(47,plain,
% 1.68/1.90 (![B: $i] : ((~element(B, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!12)))))),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[46, 43, 30])).
% 1.68/1.90 tff(48,plain,
% 1.68/1.90 (element(B!13, the_carrier(A!12))),
% 1.68/1.90 inference(and_elim,[status(thm)],[29])).
% 1.68/1.90 tff(49,plain,
% 1.68/1.90 (((~![B: $i] : ((~element(B, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!12)))))) | ((~element(B!13, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B!13, C) <=> in(ordered_pair(B!13, C), the_InternalRel(A!12)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!12)))))) | (~element(B!13, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B!13, C) <=> in(ordered_pair(B!13, C), the_InternalRel(A!12)))))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(50,plain,
% 1.68/1.90 ((~![B: $i] : ((~element(B, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!12)))))) | ((~element(B!13, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B!13, C) <=> in(ordered_pair(B!13, C), the_InternalRel(A!12)))))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(51,plain,
% 1.68/1.90 ((~![B: $i] : ((~element(B, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!12)))))) | (~element(B!13, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B!13, C) <=> in(ordered_pair(B!13, C), the_InternalRel(A!12))))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.68/1.90 tff(52,plain,
% 1.68/1.90 (![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B!13, C) <=> in(ordered_pair(B!13, C), the_InternalRel(A!12))))),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[51, 48, 47])).
% 1.68/1.90 tff(53,plain,
% 1.68/1.90 (element(C!14, the_carrier(A!12))),
% 1.68/1.90 inference(and_elim,[status(thm)],[29])).
% 1.68/1.90 tff(54,plain,
% 1.68/1.90 (((~![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B!13, C) <=> in(ordered_pair(B!13, C), the_InternalRel(A!12))))) | ((~element(C!14, the_carrier(A!12))) | (related(A!12, B!13, C!14) <=> in(ordered_pair(B!13, C!14), the_InternalRel(A!12))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B!13, C) <=> in(ordered_pair(B!13, C), the_InternalRel(A!12))))) | (~element(C!14, the_carrier(A!12))) | (related(A!12, B!13, C!14) <=> in(ordered_pair(B!13, C!14), the_InternalRel(A!12))))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(55,plain,
% 1.68/1.90 ((~![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B!13, C) <=> in(ordered_pair(B!13, C), the_InternalRel(A!12))))) | ((~element(C!14, the_carrier(A!12))) | (related(A!12, B!13, C!14) <=> in(ordered_pair(B!13, C!14), the_InternalRel(A!12))))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(56,plain,
% 1.68/1.90 ((~![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B!13, C) <=> in(ordered_pair(B!13, C), the_InternalRel(A!12))))) | (~element(C!14, the_carrier(A!12))) | (related(A!12, B!13, C!14) <=> in(ordered_pair(B!13, C!14), the_InternalRel(A!12)))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.68/1.90 tff(57,plain,
% 1.68/1.90 (related(A!12, B!13, C!14) <=> in(ordered_pair(B!13, C!14), the_InternalRel(A!12))),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[56, 53, 52])).
% 1.68/1.90 tff(58,plain,
% 1.68/1.90 (~(related(A!12, B!13, D!15) | (~(related(A!12, B!13, C!14) & related(A!12, C!14, D!15))) | (~element(D!15, the_carrier(A!12))))),
% 1.68/1.90 inference(and_elim,[status(thm)],[29])).
% 1.68/1.90 tff(59,plain,
% 1.68/1.90 (related(A!12, B!13, C!14) & related(A!12, C!14, D!15)),
% 1.68/1.90 inference(or_elim,[status(thm)],[58])).
% 1.68/1.90 tff(60,plain,
% 1.68/1.90 (related(A!12, B!13, C!14)),
% 1.68/1.90 inference(and_elim,[status(thm)],[59])).
% 1.68/1.90 tff(61,plain,
% 1.68/1.90 ((~(related(A!12, B!13, C!14) <=> in(ordered_pair(B!13, C!14), the_InternalRel(A!12)))) | (~related(A!12, B!13, C!14)) | in(ordered_pair(B!13, C!14), the_InternalRel(A!12))),
% 1.68/1.90 inference(tautology,[status(thm)],[])).
% 1.68/1.90 tff(62,plain,
% 1.68/1.90 ((~(related(A!12, B!13, C!14) <=> in(ordered_pair(B!13, C!14), the_InternalRel(A!12)))) | in(ordered_pair(B!13, C!14), the_InternalRel(A!12))),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[61, 60])).
% 1.68/1.90 tff(63,plain,
% 1.68/1.90 (in(ordered_pair(B!13, C!14), the_InternalRel(A!12))),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[62, 57])).
% 1.68/1.90 tff(64,plain,
% 1.68/1.90 (in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[63, 13])).
% 1.68/1.90 tff(65,assumption,(~in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12))), introduced(assumption)).
% 1.68/1.90 tff(66,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[65, 64])).
% 1.68/1.90 tff(67,plain,(in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(68,assumption,(~element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12)))), introduced(assumption)).
% 1.68/1.90 tff(69,plain,
% 1.68/1.90 (^[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))))),
% 1.68/1.90 inference(bind,[status(th)],[])).
% 1.68/1.90 tff(70,plain,
% 1.68/1.90 (![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)))),
% 1.68/1.90 inference(quant_intro,[status(thm)],[69])).
% 1.68/1.90 tff(71,plain,
% 1.68/1.90 (![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)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(72,plain,
% 1.68/1.90 (^[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))))),
% 1.68/1.90 inference(bind,[status(th)],[])).
% 1.68/1.90 tff(73,plain,
% 1.68/1.90 (![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)))),
% 1.68/1.90 inference(quant_intro,[status(thm)],[72])).
% 1.68/1.90 tff(74,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')).
% 1.68/1.90 tff(75,plain,
% 1.68/1.90 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.68/1.90 tff(76,plain,
% 1.68/1.90 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[75, 71])).
% 1.68/1.90 tff(77,plain,(
% 1.68/1.90 ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 1.68/1.90 inference(skolemize,[status(sab)],[76])).
% 1.68/1.90 tff(78,plain,
% 1.68/1.90 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[77, 70])).
% 1.68/1.90 tff(79,plain,
% 1.68/1.90 (((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | ((~rel_str(A!12)) | relation_of2_as_subset(the_InternalRel(A!12), the_carrier(A!12), the_carrier(A!12)))) <=> ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | (~rel_str(A!12)) | relation_of2_as_subset(the_InternalRel(A!12), the_carrier(A!12), the_carrier(A!12)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(80,plain,
% 1.68/1.90 ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | ((~rel_str(A!12)) | relation_of2_as_subset(the_InternalRel(A!12), the_carrier(A!12), the_carrier(A!12)))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(81,plain,
% 1.68/1.90 ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | (~rel_str(A!12)) | relation_of2_as_subset(the_InternalRel(A!12), the_carrier(A!12), the_carrier(A!12))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.68/1.91 tff(82,plain,
% 1.68/1.91 (relation_of2_as_subset(the_InternalRel(A!12), the_carrier(A!12), the_carrier(A!12))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[81, 78, 30])).
% 1.68/1.91 tff(83,plain,
% 1.68/1.91 (^[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)))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(84,plain,
% 1.68/1.91 (![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))))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[83])).
% 1.68/1.91 tff(85,plain,
% 1.68/1.91 (![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))))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(86,plain,
% 1.68/1.91 (^[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)))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(87,plain,
% 1.68/1.91 (![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))))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[86])).
% 1.68/1.91 tff(88,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')).
% 1.68/1.91 tff(89,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[88, 87])).
% 1.68/1.91 tff(90,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[89, 85])).
% 1.68/1.91 tff(91,plain,(
% 1.68/1.91 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 1.68/1.91 inference(skolemize,[status(sab)],[90])).
% 1.68/1.91 tff(92,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[91, 84])).
% 1.68/1.91 tff(93,plain,
% 1.68/1.91 (((~![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!12), the_carrier(A!12), the_carrier(A!12))) | element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))))) <=> ((~![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!12), the_carrier(A!12), the_carrier(A!12))) | element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(94,plain,
% 1.68/1.91 ((~![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!12), the_carrier(A!12), the_carrier(A!12))) | element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(95,plain,
% 1.68/1.91 ((~![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!12), the_carrier(A!12), the_carrier(A!12))) | element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[94, 93])).
% 1.68/1.91 tff(96,plain,
% 1.68/1.91 (element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[95, 92, 82])).
% 1.68/1.91 tff(97,plain,
% 1.68/1.91 (^[A: $i, B: $i, C: $i] : refl((element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(98,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[97])).
% 1.68/1.91 tff(99,plain,
% 1.68/1.91 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C))) <=> (~((~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)))) <=> (~(~((~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)))) <=> ((~in(A, B)) | (~element(B, powerset(C)))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)))), rewrite((((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(100,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[99])).
% 1.68/1.91 tff(101,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(102,plain,
% 1.68/1.91 (^[A: $i, B: $i, C: $i] : rewrite(((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(103,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[102])).
% 1.68/1.91 tff(104,axiom,(![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_subset')).
% 1.68/1.91 tff(105,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.68/1.91 tff(106,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[105, 101])).
% 1.68/1.91 tff(107,plain,(
% 1.68/1.91 ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.68/1.91 inference(skolemize,[status(sab)],[106])).
% 1.68/1.91 tff(108,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[107, 100])).
% 1.68/1.91 tff(109,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[108, 98])).
% 1.68/1.91 tff(110,plain,
% 1.68/1.91 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))) | element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))) | element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12))))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(111,plain,
% 1.68/1.91 ((element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12))) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))))) <=> ((~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))) | element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12))))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(112,plain,
% 1.68/1.91 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12))) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))) | element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12)))))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[111])).
% 1.68/1.91 tff(113,plain,
% 1.68/1.91 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12))) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))) | element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12))))),
% 1.68/1.91 inference(transitivity,[status(thm)],[112, 110])).
% 1.68/1.91 tff(114,plain,
% 1.68/1.91 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12))) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(115,plain,
% 1.68/1.91 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))) | element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), the_InternalRel(A!12)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.68/1.91 tff(116,plain,
% 1.68/1.91 ($false),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[115, 109, 96, 68, 67])).
% 1.68/1.91 tff(117,plain,(element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12)))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.91 tff(118,plain,
% 1.68/1.91 (^[A: $i, B: $i, C: $i] : refl(((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(119,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[118])).
% 1.68/1.91 tff(120,plain,
% 1.68/1.91 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C)) & empty(C)) <=> (~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> (~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(121,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[120])).
% 1.68/1.91 tff(122,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(123,plain,
% 1.68/1.91 (^[A: $i, B: $i, C: $i] : rewrite((~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> (~(in(A, B) & element(B, powerset(C)) & empty(C))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(124,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[123])).
% 1.68/1.91 tff(125,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_subset')).
% 1.68/1.91 tff(126,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.68/1.91 tff(127,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[126, 122])).
% 1.68/1.91 tff(128,plain,(
% 1.68/1.91 ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.68/1.91 inference(skolemize,[status(sab)],[127])).
% 1.68/1.91 tff(129,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[128, 121])).
% 1.68/1.91 tff(130,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[129, 119])).
% 1.68/1.91 tff(131,plain,
% 1.68/1.91 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))) | (~empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))) | (~empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(132,plain,
% 1.68/1.91 (((~empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))))) <=> ((~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))) | (~empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(133,plain,
% 1.68/1.91 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))) | (~empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12)))))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[132])).
% 1.68/1.91 tff(134,plain,
% 1.68/1.91 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))) | (~empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))))),
% 1.68/1.91 inference(transitivity,[status(thm)],[133, 131])).
% 1.68/1.91 tff(135,plain,
% 1.68/1.91 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(136,plain,
% 1.68/1.91 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))) | (~empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.68/1.91 tff(137,plain,
% 1.68/1.91 (~empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[136, 130, 96, 63])).
% 1.68/1.91 tff(138,plain,
% 1.68/1.91 (^[A: $i, B: $i] : refl((in(A, B) | empty(B) | (~element(A, B))) <=> (in(A, B) | empty(B) | (~element(A, B))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(139,plain,
% 1.68/1.91 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[138])).
% 1.68/1.91 tff(140,plain,
% 1.68/1.91 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(141,plain,
% 1.68/1.91 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (in(A, B) | empty(B) | (~element(A, B))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(142,plain,
% 1.68/1.91 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[141])).
% 1.68/1.91 tff(143,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 1.68/1.91 tff(144,plain,
% 1.68/1.91 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.68/1.91 tff(145,plain,
% 1.68/1.91 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[144, 140])).
% 1.68/1.91 tff(146,plain,(
% 1.68/1.91 ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 1.68/1.91 inference(skolemize,[status(sab)],[145])).
% 1.68/1.91 tff(147,plain,
% 1.68/1.91 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[146, 139])).
% 1.68/1.91 tff(148,plain,
% 1.68/1.91 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12)))))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12)))))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(149,plain,
% 1.68/1.91 ((in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))))) <=> (empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12)))))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(150,plain,
% 1.68/1.91 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12)))))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))))))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[149])).
% 1.68/1.91 tff(151,plain,
% 1.68/1.91 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12)))))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12)))))),
% 1.68/1.91 inference(transitivity,[status(thm)],[150, 148])).
% 1.68/1.91 tff(152,plain,
% 1.68/1.91 ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12)))))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(153,plain,
% 1.68/1.91 ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | empty(cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.68/1.91 tff(154,plain,
% 1.68/1.91 (in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))) | (~element(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12))))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[153, 147, 137])).
% 1.68/1.91 tff(155,plain,
% 1.68/1.91 (in(unordered_pair(unordered_pair(B!13, C!14), singleton(B!13)), cartesian_product2(the_carrier(A!12), the_carrier(A!12)))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[154, 117])).
% 1.68/1.91 tff(156,plain,
% 1.68/1.91 (in(ordered_pair(B!13, C!14), cartesian_product2(the_carrier(A!12), the_carrier(A!12)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[155, 11])).
% 1.68/1.91 tff(157,plain,
% 1.68/1.91 (^[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)))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(158,plain,
% 1.68/1.91 (![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))))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[157])).
% 1.68/1.91 tff(159,plain,
% 1.68/1.91 (^[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))))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(160,plain,
% 1.68/1.91 (![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))))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[159])).
% 1.68/1.91 tff(161,plain,
% 1.68/1.91 (![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)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(162,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')).
% 1.68/1.91 tff(163,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[162, 161])).
% 1.68/1.91 tff(164,plain,(
% 1.68/1.91 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 1.68/1.91 inference(skolemize,[status(sab)],[163])).
% 1.68/1.91 tff(165,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[164, 160])).
% 1.68/1.91 tff(166,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[165, 158])).
% 1.68/1.91 tff(167,plain,
% 1.68/1.91 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12)))) <=> in(ordered_pair(B!13, C!14), cartesian_product2(the_carrier(A!12), the_carrier(A!12)))))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(168,plain,
% 1.68/1.91 (~(((~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12)))) <=> in(ordered_pair(B!13, C!14), cartesian_product2(the_carrier(A!12), the_carrier(A!12))))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[167, 166])).
% 1.68/1.91 tff(169,plain,
% 1.68/1.91 ((((~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12)))) <=> in(ordered_pair(B!13, C!14), cartesian_product2(the_carrier(A!12), the_carrier(A!12)))) | (~((~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12))))) | (~in(ordered_pair(B!13, C!14), cartesian_product2(the_carrier(A!12), the_carrier(A!12))))),
% 1.68/1.91 inference(tautology,[status(thm)],[])).
% 1.68/1.91 tff(170,plain,
% 1.68/1.91 ((~((~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12))))) | (~in(ordered_pair(B!13, C!14), cartesian_product2(the_carrier(A!12), the_carrier(A!12))))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[169, 168])).
% 1.68/1.91 tff(171,plain,
% 1.68/1.91 (~((~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12))))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[170, 156])).
% 1.68/1.91 tff(172,plain,
% 1.68/1.91 (((~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12)))) | in(B!13, the_carrier(A!12))),
% 1.68/1.91 inference(tautology,[status(thm)],[])).
% 1.68/1.91 tff(173,plain,
% 1.68/1.91 (in(B!13, the_carrier(A!12))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[172, 171])).
% 1.68/1.91 tff(174,plain,
% 1.68/1.91 (^[A: $i, B: $i] : refl(((~empty(B)) | (~in(A, B))) <=> ((~empty(B)) | (~in(A, B))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(175,plain,
% 1.68/1.91 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[174])).
% 1.68/1.91 tff(176,plain,
% 1.68/1.91 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~empty(B)) | (~in(A, B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~empty(B)) | (~in(A, B))))))), rewrite((~(~((~empty(B)) | (~in(A, B))))) <=> ((~empty(B)) | (~in(A, B)))), ((~(in(A, B) & empty(B))) <=> ((~empty(B)) | (~in(A, B)))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(177,plain,
% 1.68/1.91 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[176])).
% 1.68/1.91 tff(178,plain,
% 1.68/1.91 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(179,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_boole')).
% 1.68/1.91 tff(180,plain,
% 1.68/1.91 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[179, 178])).
% 1.68/1.91 tff(181,plain,(
% 1.68/1.91 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 1.68/1.91 inference(skolemize,[status(sab)],[180])).
% 1.68/1.91 tff(182,plain,
% 1.68/1.91 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[181, 177])).
% 1.68/1.91 tff(183,plain,
% 1.68/1.91 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[182, 175])).
% 1.68/1.91 tff(184,plain,
% 1.68/1.91 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(the_carrier(A!12))) | (~in(B!13, the_carrier(A!12))))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(the_carrier(A!12))) | (~in(B!13, the_carrier(A!12))))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(185,plain,
% 1.68/1.91 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(the_carrier(A!12))) | (~in(B!13, the_carrier(A!12))))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(186,plain,
% 1.68/1.91 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(the_carrier(A!12))) | (~in(B!13, the_carrier(A!12)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.68/1.91 tff(187,plain,
% 1.68/1.91 ((~empty(the_carrier(A!12))) | (~in(B!13, the_carrier(A!12)))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[186, 183])).
% 1.68/1.91 tff(188,plain,
% 1.68/1.91 (~empty(the_carrier(A!12))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[187, 173])).
% 1.68/1.91 tff(189,plain,
% 1.68/1.91 (((~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12)))) | in(C!14, the_carrier(A!12))),
% 1.68/1.91 inference(tautology,[status(thm)],[])).
% 1.68/1.91 tff(190,plain,
% 1.68/1.91 (in(C!14, the_carrier(A!12))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[189, 171])).
% 1.68/1.91 tff(191,plain,
% 1.68/1.91 (^[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))))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(192,plain,
% 1.68/1.91 (![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)))))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[191])).
% 1.68/1.91 tff(193,plain,
% 1.68/1.91 (![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)))))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(194,plain,
% 1.68/1.91 (^[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))))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(195,plain,
% 1.68/1.91 (![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)))))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[194])).
% 1.68/1.91 tff(196,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')).
% 1.68/1.91 tff(197,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[196, 195])).
% 1.68/1.91 tff(198,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[197, 193])).
% 1.68/1.91 tff(199,plain,(
% 1.68/1.91 ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 1.68/1.91 inference(skolemize,[status(sab)],[198])).
% 1.68/1.91 tff(200,plain,
% 1.68/1.91 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[199, 192])).
% 1.68/1.91 tff(201,plain,
% 1.68/1.91 (((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(the_InternalRel(A!12)) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))))) <=> ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(the_InternalRel(A!12)) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(202,plain,
% 1.68/1.91 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(the_InternalRel(A!12)) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12))))))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(203,plain,
% 1.68/1.91 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(the_InternalRel(A!12)) | (~element(the_InternalRel(A!12), powerset(cartesian_product2(the_carrier(A!12), the_carrier(A!12)))))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[202, 201])).
% 1.68/1.91 tff(204,plain,
% 1.68/1.91 (relation(the_InternalRel(A!12))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[203, 200, 96])).
% 1.68/1.91 tff(205,plain,
% 1.68/1.91 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(206,plain,
% 1.68/1.91 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[205])).
% 1.68/1.91 tff(207,plain,
% 1.68/1.91 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(208,plain,
% 1.68/1.91 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[207])).
% 1.68/1.91 tff(209,plain,
% 1.68/1.91 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 1.68/1.92 inference(transitivity,[status(thm)],[208, 206])).
% 1.68/1.92 tff(210,plain,
% 1.68/1.92 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))) & (is_transitive_in(A, B) | (~((~(in(tptp_fun_C_2(B, A), B) & in(tptp_fun_D_1(B, A), B) & in(tptp_fun_E_0(B, A), B) & in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A) & in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A)))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))))),
% 1.68/1.92 inference(bind,[status(th)],[])).
% 1.68/1.92 tff(211,plain,
% 1.68/1.92 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))) & (is_transitive_in(A, B) | (~((~(in(tptp_fun_C_2(B, A), B) & in(tptp_fun_D_1(B, A), B) & in(tptp_fun_E_0(B, A), B) & in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A) & in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 1.68/1.92 inference(quant_intro,[status(thm)],[210])).
% 1.68/1.92 tff(212,plain,
% 1.68/1.92 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 1.68/1.92 inference(rewrite,[status(thm)],[])).
% 1.68/1.92 tff(213,plain,
% 1.68/1.92 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A))) <=> (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))), (![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A))) <=> ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))), ((relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A)))) <=> (relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A)))))), rewrite((relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A)))) <=> ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))), ((relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A)))) <=> ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))))),
% 1.68/1.92 inference(bind,[status(th)],[])).
% 1.68/1.92 tff(214,plain,
% 1.68/1.92 (![A: $i] : (relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 1.68/1.92 inference(quant_intro,[status(thm)],[213])).
% 1.68/1.92 tff(215,axiom,(![A: $i] : (relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_relat_2')).
% 1.68/1.92 tff(216,plain,
% 1.68/1.92 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 1.68/1.92 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.68/1.92 tff(217,plain,
% 1.68/1.92 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 1.68/1.92 inference(modus_ponens,[status(thm)],[216, 212])).
% 1.68/1.92 tff(218,plain,(
% 1.68/1.92 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))) & (is_transitive_in(A, B) | (~((~(in(tptp_fun_C_2(B, A), B) & in(tptp_fun_D_1(B, A), B) & in(tptp_fun_E_0(B, A), B) & in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A) & in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A))))))),
% 1.68/1.92 inference(skolemize,[status(sab)],[217])).
% 1.68/1.92 tff(219,plain,
% 1.68/1.92 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 1.68/1.92 inference(modus_ponens,[status(thm)],[218, 211])).
% 1.68/1.92 tff(220,plain,
% 1.68/1.92 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 1.68/1.92 inference(modus_ponens,[status(thm)],[219, 209])).
% 1.68/1.92 tff(221,plain,
% 1.68/1.92 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | ((~relation(the_InternalRel(A!12))) | ![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | (~relation(the_InternalRel(A!12))) | ![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12)))))))))),
% 1.68/1.92 inference(rewrite,[status(thm)],[])).
% 1.68/1.92 tff(222,plain,
% 1.68/1.92 (((~relation(the_InternalRel(A!12))) | ![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~(in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12)))))))))) <=> ((~relation(the_InternalRel(A!12))) | ![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12)))))))))),
% 1.68/1.92 inference(rewrite,[status(thm)],[])).
% 1.68/1.92 tff(223,plain,
% 1.68/1.92 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | ((~relation(the_InternalRel(A!12))) | ![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~(in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | ((~relation(the_InternalRel(A!12))) | ![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))))))))))),
% 1.68/1.92 inference(monotonicity,[status(thm)],[222])).
% 1.68/1.92 tff(224,plain,
% 1.68/1.92 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | ((~relation(the_InternalRel(A!12))) | ![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~(in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | (~relation(the_InternalRel(A!12))) | ![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12)))))))))),
% 1.68/1.92 inference(transitivity,[status(thm)],[223, 221])).
% 1.68/1.92 tff(225,plain,
% 1.68/1.92 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | ((~relation(the_InternalRel(A!12))) | ![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~(in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))))))))))),
% 1.68/1.92 inference(quant_inst,[status(thm)],[])).
% 1.68/1.92 tff(226,plain,
% 1.68/1.92 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | (~relation(the_InternalRel(A!12))) | ![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))))))))),
% 1.68/1.92 inference(modus_ponens,[status(thm)],[225, 224])).
% 1.68/1.92 tff(227,plain,
% 1.68/1.92 (![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))))))))),
% 1.68/1.92 inference(unit_resolution,[status(thm)],[226, 220, 204])).
% 1.68/1.92 tff(228,plain,
% 1.68/1.92 (((~![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))))))))) | (~((~((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)) | (~(in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12)) | (~in(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12)))))))))) <=> ((~![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))))))))) | (~((~((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)) | (~(in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12)) | (~in(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))))))))))),
% 1.68/1.92 inference(rewrite,[status(thm)],[])).
% 1.68/1.92 tff(229,plain,
% 1.68/1.92 ((~((~((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : ((~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)) | (~((~in(ordered_pair(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12)))))))) <=> (~((~((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)) | (~(in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12)) | (~in(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12)))))))))),
% 1.68/1.92 inference(rewrite,[status(thm)],[])).
% 1.68/1.92 tff(230,plain,
% 1.68/1.92 (((~![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))))))))) | (~((~((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : ((~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)) | (~((~in(ordered_pair(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))))))))) <=> ((~![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))))))))) | (~((~((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)) | (~(in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12)) | (~in(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))))))))))),
% 1.77/1.92 inference(monotonicity,[status(thm)],[229])).
% 1.77/1.92 tff(231,plain,
% 1.77/1.92 (((~![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))))))))) | (~((~((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : ((~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)) | (~((~in(ordered_pair(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))))))))) <=> ((~![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))))))))) | (~((~((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)) | (~(in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12)) | (~in(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))))))))))),
% 1.77/1.93 inference(transitivity,[status(thm)],[230, 228])).
% 1.77/1.93 tff(232,plain,
% 1.77/1.93 ((~![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))))))))) | (~((~((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : ((~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)) | (~((~in(ordered_pair(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))))))))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(233,plain,
% 1.77/1.93 ((~![B: $i] : (~((~((~is_transitive_in(the_InternalRel(A!12), B)) | ![C: $i, D: $i, E: $i] : ((~in(C, B)) | (~in(D, B)) | (~in(E, B)) | in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), B) | (~((~in(ordered_pair(tptp_fun_D_1(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_D_1(B, the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(tptp_fun_E_0(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_D_1(B, the_InternalRel(A!12)), B)) | (~in(tptp_fun_C_2(B, the_InternalRel(A!12)), B)) | in(ordered_pair(tptp_fun_C_2(B, the_InternalRel(A!12)), tptp_fun_E_0(B, the_InternalRel(A!12))), the_InternalRel(A!12))))))))) | (~((~((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)) | (~(in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12)) | (~in(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12)))))))))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[232, 231])).
% 1.77/1.93 tff(234,plain,
% 1.77/1.93 (~((~((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)) | (~(in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12)) | (~in(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))))))))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[233, 227])).
% 1.77/1.93 tff(235,plain,
% 1.77/1.93 (((~((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12)))))) | (~(is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)) | (~(in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12)) | (~in(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12)), the_carrier(A!12))) | (~in(ordered_pair(tptp_fun_C_2(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12))) | (~in(ordered_pair(tptp_fun_D_1(the_carrier(A!12), the_InternalRel(A!12)), tptp_fun_E_0(the_carrier(A!12), the_InternalRel(A!12))), the_InternalRel(A!12)))))))) | ((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12)))))),
% 1.77/1.93 inference(tautology,[status(thm)],[])).
% 1.77/1.93 tff(236,plain,
% 1.77/1.93 ((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[235, 234])).
% 1.77/1.93 tff(237,plain,
% 1.77/1.93 (^[A: $i] : refl(((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A)))) <=> ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A)))))),
% 1.77/1.93 inference(bind,[status(th)],[])).
% 1.77/1.93 tff(238,plain,
% 1.77/1.93 (![A: $i] : ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A)))) <=> ![A: $i] : ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A))))),
% 1.77/1.93 inference(quant_intro,[status(thm)],[237])).
% 1.77/1.93 tff(239,plain,
% 1.77/1.93 (![A: $i] : ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A)))) <=> ![A: $i] : ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A))))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(240,plain,
% 1.77/1.93 (^[A: $i] : rewrite((rel_str(A) => (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A)))) <=> ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A)))))),
% 1.77/1.93 inference(bind,[status(th)],[])).
% 1.77/1.93 tff(241,plain,
% 1.77/1.93 (![A: $i] : (rel_str(A) => (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A)))) <=> ![A: $i] : ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A))))),
% 1.77/1.93 inference(quant_intro,[status(thm)],[240])).
% 1.77/1.93 tff(242,axiom,(![A: $i] : (rel_str(A) => (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_orders_2')).
% 1.77/1.93 tff(243,plain,
% 1.77/1.93 (![A: $i] : ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A))))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[242, 241])).
% 1.77/1.93 tff(244,plain,
% 1.77/1.93 (![A: $i] : ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A))))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[243, 239])).
% 1.77/1.93 tff(245,plain,(
% 1.77/1.93 ![A: $i] : ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A))))),
% 1.77/1.93 inference(skolemize,[status(sab)],[244])).
% 1.77/1.93 tff(246,plain,
% 1.77/1.93 (![A: $i] : ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A))))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[245, 238])).
% 1.77/1.93 tff(247,plain,
% 1.77/1.93 (((~![A: $i] : ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A))))) | ((~rel_str(A!12)) | (transitive_relstr(A!12) <=> is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))))) <=> ((~![A: $i] : ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A))))) | (~rel_str(A!12)) | (transitive_relstr(A!12) <=> is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(248,plain,
% 1.77/1.93 ((~![A: $i] : ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A))))) | ((~rel_str(A!12)) | (transitive_relstr(A!12) <=> is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(249,plain,
% 1.77/1.93 ((~![A: $i] : ((~rel_str(A)) | (transitive_relstr(A) <=> is_transitive_in(the_InternalRel(A), the_carrier(A))))) | (~rel_str(A!12)) | (transitive_relstr(A!12) <=> is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[248, 247])).
% 1.77/1.93 tff(250,plain,
% 1.77/1.93 (transitive_relstr(A!12) <=> is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[249, 246, 30])).
% 1.77/1.93 tff(251,plain,
% 1.77/1.93 (transitive_relstr(A!12)),
% 1.77/1.93 inference(and_elim,[status(thm)],[29])).
% 1.77/1.93 tff(252,plain,
% 1.77/1.93 ((~(transitive_relstr(A!12) <=> is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)))) | (~transitive_relstr(A!12)) | is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))),
% 1.77/1.93 inference(tautology,[status(thm)],[])).
% 1.77/1.93 tff(253,plain,
% 1.77/1.93 ((~(transitive_relstr(A!12) <=> is_transitive_in(the_InternalRel(A!12), the_carrier(A!12)))) | is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[252, 251])).
% 1.77/1.93 tff(254,plain,
% 1.77/1.93 (is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[253, 250])).
% 1.77/1.93 tff(255,plain,
% 1.77/1.93 ((~((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12)))))) | (~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))))),
% 1.77/1.93 inference(tautology,[status(thm)],[])).
% 1.77/1.93 tff(256,plain,
% 1.77/1.93 ((~((~is_transitive_in(the_InternalRel(A!12), the_carrier(A!12))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12)))))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[255, 254])).
% 1.77/1.93 tff(257,plain,
% 1.77/1.93 (![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[256, 236])).
% 1.77/1.93 tff(258,plain,
% 1.77/1.93 (((~![B: $i] : ((~element(B, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!12)))))) | ((~element(C!14, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, C!14, C) <=> in(ordered_pair(C!14, C), the_InternalRel(A!12)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!12)))))) | (~element(C!14, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, C!14, C) <=> in(ordered_pair(C!14, C), the_InternalRel(A!12)))))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(259,plain,
% 1.77/1.93 ((~![B: $i] : ((~element(B, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!12)))))) | ((~element(C!14, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, C!14, C) <=> in(ordered_pair(C!14, C), the_InternalRel(A!12)))))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(260,plain,
% 1.77/1.93 ((~![B: $i] : ((~element(B, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!12)))))) | (~element(C!14, the_carrier(A!12))) | ![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, C!14, C) <=> in(ordered_pair(C!14, C), the_InternalRel(A!12))))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[259, 258])).
% 1.77/1.93 tff(261,plain,
% 1.77/1.93 (![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, C!14, C) <=> in(ordered_pair(C!14, C), the_InternalRel(A!12))))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[260, 53, 47])).
% 1.77/1.93 tff(262,plain,
% 1.77/1.93 (element(D!15, the_carrier(A!12))),
% 1.77/1.93 inference(or_elim,[status(thm)],[58])).
% 1.77/1.93 tff(263,plain,
% 1.77/1.93 (((~![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, C!14, C) <=> in(ordered_pair(C!14, C), the_InternalRel(A!12))))) | ((~element(D!15, the_carrier(A!12))) | (related(A!12, C!14, D!15) <=> in(ordered_pair(C!14, D!15), the_InternalRel(A!12))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, C!14, C) <=> in(ordered_pair(C!14, C), the_InternalRel(A!12))))) | (~element(D!15, the_carrier(A!12))) | (related(A!12, C!14, D!15) <=> in(ordered_pair(C!14, D!15), the_InternalRel(A!12))))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(264,plain,
% 1.77/1.93 ((~![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, C!14, C) <=> in(ordered_pair(C!14, C), the_InternalRel(A!12))))) | ((~element(D!15, the_carrier(A!12))) | (related(A!12, C!14, D!15) <=> in(ordered_pair(C!14, D!15), the_InternalRel(A!12))))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(265,plain,
% 1.77/1.93 ((~![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, C!14, C) <=> in(ordered_pair(C!14, C), the_InternalRel(A!12))))) | (~element(D!15, the_carrier(A!12))) | (related(A!12, C!14, D!15) <=> in(ordered_pair(C!14, D!15), the_InternalRel(A!12)))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[264, 263])).
% 1.77/1.93 tff(266,plain,
% 1.77/1.93 (related(A!12, C!14, D!15) <=> in(ordered_pair(C!14, D!15), the_InternalRel(A!12))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[265, 262, 261])).
% 1.77/1.93 tff(267,plain,
% 1.77/1.93 (related(A!12, C!14, D!15)),
% 1.77/1.93 inference(and_elim,[status(thm)],[59])).
% 1.77/1.93 tff(268,plain,
% 1.77/1.93 ((~(related(A!12, C!14, D!15) <=> in(ordered_pair(C!14, D!15), the_InternalRel(A!12)))) | (~related(A!12, C!14, D!15)) | in(ordered_pair(C!14, D!15), the_InternalRel(A!12))),
% 1.77/1.93 inference(tautology,[status(thm)],[])).
% 1.77/1.93 tff(269,plain,
% 1.77/1.93 ((~(related(A!12, C!14, D!15) <=> in(ordered_pair(C!14, D!15), the_InternalRel(A!12)))) | in(ordered_pair(C!14, D!15), the_InternalRel(A!12))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[268, 267])).
% 1.77/1.93 tff(270,plain,
% 1.77/1.93 (in(ordered_pair(C!14, D!15), the_InternalRel(A!12))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[269, 266])).
% 1.77/1.93 tff(271,plain,
% 1.77/1.93 (((~![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B!13, C) <=> in(ordered_pair(B!13, C), the_InternalRel(A!12))))) | ((~element(D!15, the_carrier(A!12))) | (related(A!12, B!13, D!15) <=> in(ordered_pair(B!13, D!15), the_InternalRel(A!12))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B!13, C) <=> in(ordered_pair(B!13, C), the_InternalRel(A!12))))) | (~element(D!15, the_carrier(A!12))) | (related(A!12, B!13, D!15) <=> in(ordered_pair(B!13, D!15), the_InternalRel(A!12))))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(272,plain,
% 1.77/1.93 ((~![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B!13, C) <=> in(ordered_pair(B!13, C), the_InternalRel(A!12))))) | ((~element(D!15, the_carrier(A!12))) | (related(A!12, B!13, D!15) <=> in(ordered_pair(B!13, D!15), the_InternalRel(A!12))))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(273,plain,
% 1.77/1.93 ((~![C: $i] : ((~element(C, the_carrier(A!12))) | (related(A!12, B!13, C) <=> in(ordered_pair(B!13, C), the_InternalRel(A!12))))) | (~element(D!15, the_carrier(A!12))) | (related(A!12, B!13, D!15) <=> in(ordered_pair(B!13, D!15), the_InternalRel(A!12)))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[272, 271])).
% 1.77/1.93 tff(274,plain,
% 1.77/1.93 (related(A!12, B!13, D!15) <=> in(ordered_pair(B!13, D!15), the_InternalRel(A!12))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[273, 262, 52])).
% 1.77/1.93 tff(275,plain,
% 1.77/1.93 (~related(A!12, B!13, D!15)),
% 1.77/1.93 inference(or_elim,[status(thm)],[58])).
% 1.77/1.93 tff(276,plain,
% 1.77/1.93 ((~(related(A!12, B!13, D!15) <=> in(ordered_pair(B!13, D!15), the_InternalRel(A!12)))) | related(A!12, B!13, D!15) | (~in(ordered_pair(B!13, D!15), the_InternalRel(A!12)))),
% 1.77/1.93 inference(tautology,[status(thm)],[])).
% 1.77/1.93 tff(277,plain,
% 1.77/1.93 ((~(related(A!12, B!13, D!15) <=> in(ordered_pair(B!13, D!15), the_InternalRel(A!12)))) | (~in(ordered_pair(B!13, D!15), the_InternalRel(A!12)))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[276, 275])).
% 1.77/1.93 tff(278,plain,
% 1.77/1.93 (~in(ordered_pair(B!13, D!15), the_InternalRel(A!12))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[277, 274])).
% 1.77/1.93 tff(279,plain,
% 1.77/1.93 (((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))))) | ((~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))) | in(ordered_pair(B!13, D!15), the_InternalRel(A!12)) | (~in(ordered_pair(C!14, D!15), the_InternalRel(A!12))) | (~in(D!15, the_carrier(A!12))) | (~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12))))) <=> ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))))) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))) | in(ordered_pair(B!13, D!15), the_InternalRel(A!12)) | (~in(ordered_pair(C!14, D!15), the_InternalRel(A!12))) | (~in(D!15, the_carrier(A!12))) | (~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12))))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(280,plain,
% 1.77/1.93 ((in(ordered_pair(B!13, D!15), the_InternalRel(A!12)) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))) | (~in(ordered_pair(C!14, D!15), the_InternalRel(A!12))) | (~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12))) | (~in(D!15, the_carrier(A!12)))) <=> ((~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))) | in(ordered_pair(B!13, D!15), the_InternalRel(A!12)) | (~in(ordered_pair(C!14, D!15), the_InternalRel(A!12))) | (~in(D!15, the_carrier(A!12))) | (~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12))))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(281,plain,
% 1.77/1.93 (((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))))) | (in(ordered_pair(B!13, D!15), the_InternalRel(A!12)) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))) | (~in(ordered_pair(C!14, D!15), the_InternalRel(A!12))) | (~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12))) | (~in(D!15, the_carrier(A!12))))) <=> ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))))) | ((~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))) | in(ordered_pair(B!13, D!15), the_InternalRel(A!12)) | (~in(ordered_pair(C!14, D!15), the_InternalRel(A!12))) | (~in(D!15, the_carrier(A!12))) | (~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12)))))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[280])).
% 1.77/1.93 tff(282,plain,
% 1.77/1.93 (((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))))) | (in(ordered_pair(B!13, D!15), the_InternalRel(A!12)) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))) | (~in(ordered_pair(C!14, D!15), the_InternalRel(A!12))) | (~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12))) | (~in(D!15, the_carrier(A!12))))) <=> ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))))) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))) | in(ordered_pair(B!13, D!15), the_InternalRel(A!12)) | (~in(ordered_pair(C!14, D!15), the_InternalRel(A!12))) | (~in(D!15, the_carrier(A!12))) | (~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12))))),
% 1.77/1.93 inference(transitivity,[status(thm)],[281, 279])).
% 1.77/1.93 tff(283,plain,
% 1.77/1.93 ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))))) | (in(ordered_pair(B!13, D!15), the_InternalRel(A!12)) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))) | (~in(ordered_pair(C!14, D!15), the_InternalRel(A!12))) | (~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12))) | (~in(D!15, the_carrier(A!12))))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(284,plain,
% 1.77/1.93 ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), the_InternalRel(A!12)) | (~in(ordered_pair(C, D), the_InternalRel(A!12))) | (~in(ordered_pair(D, E), the_InternalRel(A!12))) | (~in(C, the_carrier(A!12))) | (~in(D, the_carrier(A!12))) | (~in(E, the_carrier(A!12))))) | (~in(ordered_pair(B!13, C!14), the_InternalRel(A!12))) | in(ordered_pair(B!13, D!15), the_InternalRel(A!12)) | (~in(ordered_pair(C!14, D!15), the_InternalRel(A!12))) | (~in(D!15, the_carrier(A!12))) | (~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12)))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[283, 282])).
% 1.77/1.93 tff(285,plain,
% 1.77/1.93 ((~in(D!15, the_carrier(A!12))) | (~in(B!13, the_carrier(A!12))) | (~in(C!14, the_carrier(A!12)))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[284, 63, 278, 270, 257])).
% 1.77/1.93 tff(286,plain,
% 1.77/1.93 (~in(D!15, the_carrier(A!12))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[285, 190, 173])).
% 1.77/1.93 tff(287,plain,
% 1.77/1.93 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | ((~element(D!15, the_carrier(A!12))) | empty(the_carrier(A!12)) | in(D!15, the_carrier(A!12)))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (~element(D!15, the_carrier(A!12))) | empty(the_carrier(A!12)) | in(D!15, the_carrier(A!12)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(288,plain,
% 1.77/1.93 ((in(D!15, the_carrier(A!12)) | empty(the_carrier(A!12)) | (~element(D!15, the_carrier(A!12)))) <=> ((~element(D!15, the_carrier(A!12))) | empty(the_carrier(A!12)) | in(D!15, the_carrier(A!12)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(289,plain,
% 1.77/1.93 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(D!15, the_carrier(A!12)) | empty(the_carrier(A!12)) | (~element(D!15, the_carrier(A!12))))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | ((~element(D!15, the_carrier(A!12))) | empty(the_carrier(A!12)) | in(D!15, the_carrier(A!12))))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[288])).
% 1.77/1.93 tff(290,plain,
% 1.77/1.93 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(D!15, the_carrier(A!12)) | empty(the_carrier(A!12)) | (~element(D!15, the_carrier(A!12))))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (~element(D!15, the_carrier(A!12))) | empty(the_carrier(A!12)) | in(D!15, the_carrier(A!12)))),
% 1.77/1.93 inference(transitivity,[status(thm)],[289, 287])).
% 1.77/1.93 tff(291,plain,
% 1.77/1.93 ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(D!15, the_carrier(A!12)) | empty(the_carrier(A!12)) | (~element(D!15, the_carrier(A!12))))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(292,plain,
% 1.77/1.93 ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (~element(D!15, the_carrier(A!12))) | empty(the_carrier(A!12)) | in(D!15, the_carrier(A!12))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[291, 290])).
% 1.77/1.94 tff(293,plain,
% 1.77/1.94 (empty(the_carrier(A!12)) | in(D!15, the_carrier(A!12))),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[292, 262, 147])).
% 1.77/1.94 tff(294,plain,
% 1.77/1.94 ($false),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[293, 286, 188])).
% 1.77/1.94 % SZS output end Proof
% 1.77/1.95 % E exiting
%------------------------------------------------------------------------------