%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU339+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:27:38 AM UTC 2025
% Result : Theorem 0.79s 1.00s
% Output : Proof 0.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU339+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:48:25 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.79/1.00 % SZS status Theorem
% 0.79/1.00 % SZS output start Proof
% 0.79/1.00 tff(in_type, type, (
% 0.79/1.00 in: ( $i * $i ) > $o)).
% 0.79/1.00 tff(the_carrier_type, type, (
% 0.79/1.00 the_carrier: $i > $i)).
% 0.79/1.00 tff(tptp_fun_A_11_type, type, (
% 0.79/1.00 tptp_fun_A_11: $i)).
% 0.79/1.00 tff(tptp_fun_B_12_type, type, (
% 0.79/1.00 tptp_fun_B_12: $i)).
% 0.79/1.00 tff(tptp_fun_C_13_type, type, (
% 0.79/1.00 tptp_fun_C_13: $i)).
% 0.79/1.00 tff(cartesian_product2_type, type, (
% 0.79/1.00 cartesian_product2: ( $i * $i ) > $i)).
% 0.79/1.00 tff(ordered_pair_type, type, (
% 0.79/1.00 ordered_pair: ( $i * $i ) > $i)).
% 0.79/1.00 tff(unordered_pair_type, type, (
% 0.79/1.00 unordered_pair: ( $i * $i ) > $i)).
% 0.79/1.00 tff(singleton_type, type, (
% 0.79/1.00 singleton: $i > $i)).
% 0.79/1.00 tff(element_type, type, (
% 0.79/1.00 element: ( $i * $i ) > $o)).
% 0.79/1.00 tff(the_InternalRel_type, type, (
% 0.79/1.00 the_InternalRel: $i > $i)).
% 0.79/1.00 tff(related_type, type, (
% 0.79/1.00 related: ( $i * $i * $i ) > $o)).
% 0.79/1.00 tff(rel_str_type, type, (
% 0.79/1.00 rel_str: $i > $o)).
% 0.79/1.00 tff(antisymmetric_relstr_type, type, (
% 0.79/1.00 antisymmetric_relstr: $i > $o)).
% 0.79/1.00 tff(powerset_type, type, (
% 0.79/1.00 powerset: $i > $i)).
% 0.79/1.00 tff(relation_of2_as_subset_type, type, (
% 0.79/1.00 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 0.79/1.00 tff(empty_type, type, (
% 0.79/1.00 empty: $i > $o)).
% 0.79/1.00 tff(is_antisymmetric_in_type, type, (
% 0.79/1.00 is_antisymmetric_in: ( $i * $i ) > $o)).
% 0.79/1.00 tff(tptp_fun_C_1_type, type, (
% 0.79/1.00 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.79/1.00 tff(tptp_fun_D_0_type, type, (
% 0.79/1.00 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.79/1.00 tff(relation_type, type, (
% 0.79/1.00 relation: $i > $o)).
% 0.79/1.00 tff(1,plain,
% 0.79/1.00 (^[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))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(2,plain,
% 0.79/1.00 (![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)))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[1])).
% 0.79/1.00 tff(3,plain,
% 0.79/1.00 (![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)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 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')).
% 0.79/1.00 tff(5,plain,
% 0.79/1.00 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.79/1.00 tff(6,plain,(
% 0.79/1.00 ![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 0.79/1.00 inference(skolemize,[status(sab)],[5])).
% 0.79/1.00 tff(7,plain,
% 0.79/1.00 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.79/1.00 tff(8,plain,
% 0.79/1.00 ((~![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))) | (ordered_pair(C!13, B!12) = unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(9,plain,
% 0.79/1.00 (ordered_pair(C!13, B!12) = unordered_pair(unordered_pair(C!13, B!12), singleton(C!13))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.79/1.00 tff(10,plain,
% 0.79/1.00 (unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)) = ordered_pair(C!13, B!12)),
% 0.79/1.00 inference(symmetry,[status(thm)],[9])).
% 0.79/1.00 tff(11,plain,
% 0.79/1.00 (in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[10])).
% 0.79/1.00 tff(12,plain,
% 0.79/1.00 (in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11)) <=> in(ordered_pair(C!13, B!12), the_InternalRel(A!11))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[10])).
% 0.79/1.00 tff(13,plain,
% 0.79/1.00 (in(ordered_pair(C!13, B!12), the_InternalRel(A!11)) <=> in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11))),
% 0.79/1.00 inference(symmetry,[status(thm)],[12])).
% 0.79/1.00 tff(14,plain,
% 0.79/1.00 (((antisymmetric_relstr(A!11) & rel_str(A!11)) & (element(B!12, the_carrier(A!11)) & (~((B!12 = C!13) | (~element(C!13, the_carrier(A!11))) | (~(related(A!11, B!12, C!13) & related(A!11, C!13, B!12))))))) <=> (antisymmetric_relstr(A!11) & rel_str(A!11) & element(B!12, the_carrier(A!11)) & (~((B!12 = C!13) | (~element(C!13, the_carrier(A!11))) | (~(related(A!11, B!12, C!13) & related(A!11, C!13, B!12))))))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(15,plain,
% 0.79/1.00 ((~((B!12 = C!13) | (~element(C!13, the_carrier(A!11))) | (~(related(A!11, B!12, C!13) & related(A!11, C!13, B!12))))) <=> (~((B!12 = C!13) | (~element(C!13, the_carrier(A!11))) | (~(related(A!11, B!12, C!13) & related(A!11, C!13, B!12)))))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(16,plain,
% 0.79/1.00 ((element(B!12, the_carrier(A!11)) & (~((B!12 = C!13) | (~element(C!13, the_carrier(A!11))) | (~(related(A!11, B!12, C!13) & related(A!11, C!13, B!12)))))) <=> (element(B!12, the_carrier(A!11)) & (~((B!12 = C!13) | (~element(C!13, the_carrier(A!11))) | (~(related(A!11, B!12, C!13) & related(A!11, C!13, B!12))))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[15])).
% 0.79/1.00 tff(17,plain,
% 0.79/1.00 (((antisymmetric_relstr(A!11) & rel_str(A!11)) & (element(B!12, the_carrier(A!11)) & (~((B!12 = C!13) | (~element(C!13, the_carrier(A!11))) | (~(related(A!11, B!12, C!13) & related(A!11, C!13, B!12))))))) <=> ((antisymmetric_relstr(A!11) & rel_str(A!11)) & (element(B!12, the_carrier(A!11)) & (~((B!12 = C!13) | (~element(C!13, the_carrier(A!11))) | (~(related(A!11, B!12, C!13) & related(A!11, C!13, B!12)))))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[16])).
% 0.79/1.00 tff(18,plain,
% 0.79/1.00 (((antisymmetric_relstr(A!11) & rel_str(A!11)) & (element(B!12, the_carrier(A!11)) & (~((B!12 = C!13) | (~element(C!13, the_carrier(A!11))) | (~(related(A!11, B!12, C!13) & related(A!11, C!13, B!12))))))) <=> (antisymmetric_relstr(A!11) & rel_str(A!11) & element(B!12, the_carrier(A!11)) & (~((B!12 = C!13) | (~element(C!13, the_carrier(A!11))) | (~(related(A!11, B!12, C!13) & related(A!11, C!13, B!12))))))),
% 0.79/1.00 inference(transitivity,[status(thm)],[17, 14])).
% 0.79/1.00 tff(19,plain,
% 0.79/1.00 ((~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~(related(A, B, C) & related(A, C, B))))))) <=> (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~(related(A, B, C) & related(A, C, B)))))))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(20,plain,
% 0.79/1.00 ((~![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ((related(A, B, C) & related(A, C, B)) => (B = C)))))) <=> (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~(related(A, B, C) & related(A, C, B)))))))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(21,axiom,(~![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ((related(A, B, C) & related(A, C, B)) => (B = C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t25_orders_2')).
% 0.79/1.00 tff(22,plain,
% 0.79/1.00 (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~(related(A, B, C) & related(A, C, B))))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.79/1.00 tff(23,plain,
% 0.79/1.00 (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~(related(A, B, C) & related(A, C, B))))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.79/1.00 tff(24,plain,
% 0.79/1.00 (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~(related(A, B, C) & related(A, C, B))))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.79/1.00 tff(25,plain,
% 0.79/1.00 (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~(related(A, B, C) & related(A, C, B))))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.79/1.00 tff(26,plain,
% 0.79/1.00 (antisymmetric_relstr(A!11) & rel_str(A!11) & element(B!12, the_carrier(A!11)) & (~((B!12 = C!13) | (~element(C!13, the_carrier(A!11))) | (~(related(A!11, B!12, C!13) & related(A!11, C!13, B!12)))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.79/1.00 tff(27,plain,
% 0.79/1.00 (rel_str(A!11)),
% 0.79/1.00 inference(and_elim,[status(thm)],[26])).
% 0.79/1.00 tff(28,plain,
% 0.79/1.00 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(29,plain,
% 0.79/1.00 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[28])).
% 0.79/1.00 tff(30,plain,
% 0.79/1.00 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(31,plain,
% 0.79/1.00 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[30])).
% 0.79/1.00 tff(32,plain,
% 0.79/1.00 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.79/1.00 inference(transitivity,[status(thm)],[31, 29])).
% 0.79/1.00 tff(33,plain,
% 0.79/1.00 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(34,plain,
% 0.79/1.00 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))) <=> ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))), (![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> (element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), ((rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> (rel_str(A) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))), rewrite((rel_str(A) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), ((rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(35,plain,
% 0.79/1.00 (![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[34])).
% 0.79/1.00 tff(36,axiom,(![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_orders_2')).
% 0.79/1.00 tff(37,plain,
% 0.79/1.00 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.79/1.00 tff(38,plain,
% 0.79/1.00 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.79/1.00 tff(39,plain,(
% 0.79/1.00 ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.79/1.00 inference(skolemize,[status(sab)],[38])).
% 0.79/1.00 tff(40,plain,
% 0.79/1.00 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.79/1.00 tff(41,plain,
% 0.79/1.00 (((~![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!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!11))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | (~rel_str(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!11))))))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(42,plain,
% 0.79/1.00 ((~![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!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!11))))))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(43,plain,
% 0.79/1.00 ((~![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!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!11)))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.79/1.00 tff(44,plain,
% 0.79/1.00 (![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!11)))))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[43, 40, 27])).
% 0.79/1.00 tff(45,plain,
% 0.79/1.00 (~((B!12 = C!13) | (~element(C!13, the_carrier(A!11))) | (~(related(A!11, B!12, C!13) & related(A!11, C!13, B!12))))),
% 0.79/1.00 inference(and_elim,[status(thm)],[26])).
% 0.79/1.00 tff(46,plain,
% 0.79/1.00 (element(C!13, the_carrier(A!11))),
% 0.79/1.00 inference(or_elim,[status(thm)],[45])).
% 0.79/1.00 tff(47,plain,
% 0.79/1.00 (((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!11)))))) | ((~element(C!13, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, C!13, C) <=> in(ordered_pair(C!13, C), the_InternalRel(A!11)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!11)))))) | (~element(C!13, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, C!13, C) <=> in(ordered_pair(C!13, C), the_InternalRel(A!11)))))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(48,plain,
% 0.79/1.00 ((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!11)))))) | ((~element(C!13, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, C!13, C) <=> in(ordered_pair(C!13, C), the_InternalRel(A!11)))))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(49,plain,
% 0.79/1.00 ((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!11)))))) | (~element(C!13, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, C!13, C) <=> in(ordered_pair(C!13, C), the_InternalRel(A!11))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.79/1.00 tff(50,plain,
% 0.79/1.00 (![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, C!13, C) <=> in(ordered_pair(C!13, C), the_InternalRel(A!11))))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[49, 46, 44])).
% 0.79/1.00 tff(51,plain,
% 0.79/1.00 (element(B!12, the_carrier(A!11))),
% 0.79/1.00 inference(and_elim,[status(thm)],[26])).
% 0.79/1.00 tff(52,plain,
% 0.79/1.00 (((~![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, C!13, C) <=> in(ordered_pair(C!13, C), the_InternalRel(A!11))))) | ((~element(B!12, the_carrier(A!11))) | (related(A!11, C!13, B!12) <=> in(ordered_pair(C!13, B!12), the_InternalRel(A!11))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, C!13, C) <=> in(ordered_pair(C!13, C), the_InternalRel(A!11))))) | (~element(B!12, the_carrier(A!11))) | (related(A!11, C!13, B!12) <=> in(ordered_pair(C!13, B!12), the_InternalRel(A!11))))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(53,plain,
% 0.79/1.00 ((~![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, C!13, C) <=> in(ordered_pair(C!13, C), the_InternalRel(A!11))))) | ((~element(B!12, the_carrier(A!11))) | (related(A!11, C!13, B!12) <=> in(ordered_pair(C!13, B!12), the_InternalRel(A!11))))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(54,plain,
% 0.79/1.00 ((~![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, C!13, C) <=> in(ordered_pair(C!13, C), the_InternalRel(A!11))))) | (~element(B!12, the_carrier(A!11))) | (related(A!11, C!13, B!12) <=> in(ordered_pair(C!13, B!12), the_InternalRel(A!11)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.79/1.00 tff(55,plain,
% 0.79/1.00 (related(A!11, C!13, B!12) <=> in(ordered_pair(C!13, B!12), the_InternalRel(A!11))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[54, 51, 50])).
% 0.79/1.00 tff(56,plain,
% 0.79/1.00 (related(A!11, B!12, C!13) & related(A!11, C!13, B!12)),
% 0.79/1.00 inference(or_elim,[status(thm)],[45])).
% 0.79/1.00 tff(57,plain,
% 0.79/1.00 (related(A!11, C!13, B!12)),
% 0.79/1.00 inference(and_elim,[status(thm)],[56])).
% 0.79/1.00 tff(58,plain,
% 0.79/1.00 ((~(related(A!11, C!13, B!12) <=> in(ordered_pair(C!13, B!12), the_InternalRel(A!11)))) | (~related(A!11, C!13, B!12)) | in(ordered_pair(C!13, B!12), the_InternalRel(A!11))),
% 0.79/1.00 inference(tautology,[status(thm)],[])).
% 0.79/1.00 tff(59,plain,
% 0.79/1.00 ((~(related(A!11, C!13, B!12) <=> in(ordered_pair(C!13, B!12), the_InternalRel(A!11)))) | in(ordered_pair(C!13, B!12), the_InternalRel(A!11))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.79/1.00 tff(60,plain,
% 0.79/1.00 (in(ordered_pair(C!13, B!12), the_InternalRel(A!11))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[59, 55])).
% 0.79/1.00 tff(61,plain,
% 0.79/1.00 (in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[60, 13])).
% 0.79/1.00 tff(62,assumption,(~in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11))), introduced(assumption)).
% 0.79/1.00 tff(63,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.79/1.00 tff(64,plain,(in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11))), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(65,assumption,(~element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))), introduced(assumption)).
% 0.79/1.00 tff(66,plain,
% 0.79/1.00 (^[A: $i] : refl(((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(67,plain,
% 0.79/1.00 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[66])).
% 0.79/1.00 tff(68,plain,
% 0.79/1.00 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(69,plain,
% 0.79/1.00 (^[A: $i] : rewrite((rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(70,plain,
% 0.79/1.00 (![A: $i] : (rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[69])).
% 0.79/1.00 tff(71,axiom,(![A: $i] : (rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u1_orders_2')).
% 0.79/1.00 tff(72,plain,
% 0.79/1.00 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.79/1.00 tff(73,plain,
% 0.79/1.00 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.79/1.00 tff(74,plain,(
% 0.79/1.00 ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.79/1.00 inference(skolemize,[status(sab)],[73])).
% 0.79/1.00 tff(75,plain,
% 0.79/1.00 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.79/1.00 tff(76,plain,
% 0.79/1.00 (((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | ((~rel_str(A!11)) | relation_of2_as_subset(the_InternalRel(A!11), the_carrier(A!11), the_carrier(A!11)))) <=> ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | (~rel_str(A!11)) | relation_of2_as_subset(the_InternalRel(A!11), the_carrier(A!11), the_carrier(A!11)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(77,plain,
% 0.79/1.00 ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | ((~rel_str(A!11)) | relation_of2_as_subset(the_InternalRel(A!11), the_carrier(A!11), the_carrier(A!11)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(78,plain,
% 0.79/1.00 ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | (~rel_str(A!11)) | relation_of2_as_subset(the_InternalRel(A!11), the_carrier(A!11), the_carrier(A!11))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.79/1.00 tff(79,plain,
% 0.79/1.00 (relation_of2_as_subset(the_InternalRel(A!11), the_carrier(A!11), the_carrier(A!11))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[78, 75, 27])).
% 0.79/1.00 tff(80,plain,
% 0.79/1.00 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(81,plain,
% 0.79/1.00 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[80])).
% 0.79/1.00 tff(82,plain,
% 0.79/1.00 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(83,plain,
% 0.79/1.00 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(84,plain,
% 0.79/1.00 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[83])).
% 0.79/1.00 tff(85,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 0.79/1.00 tff(86,plain,
% 0.79/1.00 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.79/1.00 tff(87,plain,
% 0.79/1.00 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.79/1.00 tff(88,plain,(
% 0.79/1.00 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.79/1.00 inference(skolemize,[status(sab)],[87])).
% 0.79/1.00 tff(89,plain,
% 0.79/1.00 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.79/1.00 tff(90,plain,
% 0.79/1.00 (((~![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!11), the_carrier(A!11), the_carrier(A!11))) | element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))) <=> ((~![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!11), the_carrier(A!11), the_carrier(A!11))) | element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(91,plain,
% 0.79/1.00 ((~![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!11), the_carrier(A!11), the_carrier(A!11))) | element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(92,plain,
% 0.79/1.00 ((~![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!11), the_carrier(A!11), the_carrier(A!11))) | element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.79/1.00 tff(93,plain,
% 0.79/1.00 (element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[92, 89, 79])).
% 0.79/1.00 tff(94,plain,
% 0.79/1.00 (^[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)))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(95,plain,
% 0.79/1.00 (![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))))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[94])).
% 0.79/1.00 tff(96,plain,
% 0.79/1.00 (^[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))))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(97,plain,
% 0.79/1.00 (![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))))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[96])).
% 0.79/1.00 tff(98,plain,
% 0.79/1.00 (![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))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(99,plain,
% 0.79/1.00 (^[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)))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(100,plain,
% 0.79/1.00 (![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))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[99])).
% 0.79/1.00 tff(101,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')).
% 0.79/1.00 tff(102,plain,
% 0.79/1.00 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.79/1.00 tff(103,plain,
% 0.79/1.00 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.79/1.00 tff(104,plain,(
% 0.79/1.00 ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.79/1.00 inference(skolemize,[status(sab)],[103])).
% 0.79/1.00 tff(105,plain,
% 0.79/1.00 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.79/1.00 tff(106,plain,
% 0.79/1.00 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[105, 95])).
% 0.79/1.00 tff(107,plain,
% 0.79/1.00 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) | element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) | element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11))))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(108,plain,
% 0.79/1.00 ((element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11))) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))) <=> ((~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) | element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11))))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(109,plain,
% 0.79/1.00 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11))) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) | element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11)))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[108])).
% 0.79/1.00 tff(110,plain,
% 0.79/1.00 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11))) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) | element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11))))),
% 0.79/1.01 inference(transitivity,[status(thm)],[109, 107])).
% 0.79/1.01 tff(111,plain,
% 0.79/1.01 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11))) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(112,plain,
% 0.79/1.01 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) | element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), the_InternalRel(A!11)))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.79/1.01 tff(113,plain,
% 0.79/1.01 ($false),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[112, 106, 93, 65, 64])).
% 0.79/1.01 tff(114,plain,(element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))), inference(lemma,lemma(discharge,[]))).
% 0.79/1.01 tff(115,plain,
% 0.79/1.01 (^[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)))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(116,plain,
% 0.79/1.01 (![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))))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[115])).
% 0.79/1.01 tff(117,plain,
% 0.79/1.01 (^[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))))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(118,plain,
% 0.79/1.01 (![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))))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[117])).
% 0.79/1.01 tff(119,plain,
% 0.79/1.01 (![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)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(120,plain,
% 0.79/1.01 (^[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))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(121,plain,
% 0.79/1.01 (![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)))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[120])).
% 0.79/1.01 tff(122,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')).
% 0.79/1.01 tff(123,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.79/1.01 tff(124,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.79/1.01 tff(125,plain,(
% 0.79/1.01 ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.79/1.01 inference(skolemize,[status(sab)],[124])).
% 0.79/1.01 tff(126,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.79/1.01 tff(127,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.79/1.01 tff(128,plain,
% 0.79/1.01 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) | (~empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) | (~empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(129,plain,
% 0.79/1.01 (((~empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))) <=> ((~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) | (~empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(130,plain,
% 0.79/1.01 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) | (~empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11)))))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[129])).
% 0.79/1.01 tff(131,plain,
% 0.79/1.01 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) | (~empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))))),
% 0.79/1.01 inference(transitivity,[status(thm)],[130, 128])).
% 0.79/1.01 tff(132,plain,
% 0.79/1.01 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(133,plain,
% 0.79/1.01 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) | (~empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11)))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.79/1.01 tff(134,plain,
% 0.79/1.01 (~empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[133, 127, 93, 60])).
% 0.79/1.01 tff(135,plain,
% 0.79/1.01 (^[A: $i, B: $i] : refl((in(A, B) | empty(B) | (~element(A, B))) <=> (in(A, B) | empty(B) | (~element(A, B))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(136,plain,
% 0.79/1.01 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[135])).
% 0.79/1.01 tff(137,plain,
% 0.79/1.01 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(138,plain,
% 0.79/1.01 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (in(A, B) | empty(B) | (~element(A, B))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(139,plain,
% 0.79/1.01 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[138])).
% 0.79/1.01 tff(140,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 0.79/1.01 tff(141,plain,
% 0.79/1.01 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.79/1.01 tff(142,plain,
% 0.79/1.01 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.79/1.01 tff(143,plain,(
% 0.79/1.01 ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.79/1.01 inference(skolemize,[status(sab)],[142])).
% 0.79/1.01 tff(144,plain,
% 0.79/1.01 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.79/1.01 tff(145,plain,
% 0.79/1.01 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(146,plain,
% 0.79/1.01 ((in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) <=> (empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(147,plain,
% 0.79/1.01 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))))))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[146])).
% 0.79/1.01 tff(148,plain,
% 0.79/1.01 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))),
% 0.79/1.01 inference(transitivity,[status(thm)],[147, 145])).
% 0.79/1.01 tff(149,plain,
% 0.79/1.01 ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(150,plain,
% 0.79/1.01 ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | empty(cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.79/1.01 tff(151,plain,
% 0.79/1.01 (in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))) | (~element(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11))))),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[150, 144, 134])).
% 0.79/1.01 tff(152,plain,
% 0.79/1.01 (in(unordered_pair(unordered_pair(C!13, B!12), singleton(C!13)), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[151, 114])).
% 0.79/1.01 tff(153,plain,
% 0.79/1.01 (in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[152, 11])).
% 0.79/1.01 tff(154,plain,
% 0.79/1.01 (^[A: $i, B: $i, C: $i, D: $i] : refl((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(155,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[154])).
% 0.79/1.01 tff(156,plain,
% 0.79/1.01 (^[A: $i, B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((in(A, C) & in(B, D)) <=> (~((~in(A, C)) | (~in(B, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))), rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))), rewrite((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(157,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[156])).
% 0.79/1.01 tff(158,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(159,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t106_zfmisc_1')).
% 0.79/1.01 tff(160,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.79/1.01 tff(161,plain,(
% 0.79/1.01 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.79/1.01 inference(skolemize,[status(sab)],[160])).
% 0.79/1.01 tff(162,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.79/1.01 tff(163,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.79/1.01 tff(164,plain,
% 0.79/1.01 (((~![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!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))) <=> ((~![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!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11))))))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(165,plain,
% 0.79/1.01 ((~(((~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) <=> (~(((~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(166,plain,
% 0.79/1.01 ((((~in(C!13, the_carrier(A!11))) | (~in(B!12, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))) <=> (((~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11))))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(167,plain,
% 0.79/1.01 ((~(((~in(C!13, the_carrier(A!11))) | (~in(B!12, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) <=> (~(((~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[166])).
% 0.79/1.01 tff(168,plain,
% 0.79/1.01 ((~(((~in(C!13, the_carrier(A!11))) | (~in(B!12, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11))))) <=> (~(((~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))),
% 0.79/1.01 inference(transitivity,[status(thm)],[167, 165])).
% 0.79/1.01 tff(169,plain,
% 0.79/1.01 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(C!13, the_carrier(A!11))) | (~in(B!12, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))) <=> ((~![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!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11))))))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[168])).
% 0.79/1.01 tff(170,plain,
% 0.79/1.01 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(C!13, the_carrier(A!11))) | (~in(B!12, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))) <=> ((~![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!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11))))))),
% 0.79/1.01 inference(transitivity,[status(thm)],[169, 164])).
% 0.79/1.01 tff(171,plain,
% 0.79/1.01 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(C!13, the_carrier(A!11))) | (~in(B!12, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(172,plain,
% 0.79/1.01 ((~![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!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.79/1.01 tff(173,plain,
% 0.79/1.01 (~(((~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11))))),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[172, 163])).
% 0.79/1.01 tff(174,plain,
% 0.79/1.01 ((((~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))) <=> in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11)))) | (~((~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11))))) | (~in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11))))),
% 0.79/1.01 inference(tautology,[status(thm)],[])).
% 0.79/1.01 tff(175,plain,
% 0.79/1.01 ((~((~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11))))) | (~in(ordered_pair(C!13, B!12), cartesian_product2(the_carrier(A!11), the_carrier(A!11))))),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.79/1.01 tff(176,plain,
% 0.79/1.01 (~((~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11))))),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[175, 153])).
% 0.79/1.01 tff(177,plain,
% 0.79/1.01 (((~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))) | in(B!12, the_carrier(A!11))),
% 0.79/1.01 inference(tautology,[status(thm)],[])).
% 0.79/1.01 tff(178,plain,
% 0.79/1.01 (in(B!12, the_carrier(A!11))),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.79/1.01 tff(179,plain,
% 0.79/1.01 (((~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))) | in(C!13, the_carrier(A!11))),
% 0.79/1.01 inference(tautology,[status(thm)],[])).
% 0.79/1.01 tff(180,plain,
% 0.79/1.01 (in(C!13, the_carrier(A!11))),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[179, 176])).
% 0.79/1.01 tff(181,plain,
% 0.79/1.01 ((C!13 = B!12) <=> (B!12 = C!13)),
% 0.79/1.01 inference(commutativity,[status(thm)],[])).
% 0.79/1.01 tff(182,plain,
% 0.79/1.01 ((B!12 = C!13) <=> (C!13 = B!12)),
% 0.79/1.01 inference(symmetry,[status(thm)],[181])).
% 0.79/1.01 tff(183,plain,
% 0.79/1.01 ((~(B!12 = C!13)) <=> (~(C!13 = B!12))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[182])).
% 0.79/1.01 tff(184,plain,
% 0.79/1.01 (~(B!12 = C!13)),
% 0.79/1.01 inference(or_elim,[status(thm)],[45])).
% 0.79/1.01 tff(185,plain,
% 0.79/1.01 (~(C!13 = B!12)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.79/1.01 tff(186,plain,
% 0.79/1.01 (^[A: $i, B: $i, C: $i] : refl((relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(187,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[186])).
% 0.79/1.01 tff(188,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(189,plain,
% 0.79/1.01 (^[A: $i, B: $i, C: $i] : rewrite((element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(190,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[189])).
% 0.79/1.01 tff(191,axiom,(![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_relset_1')).
% 0.79/1.01 tff(192,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.79/1.01 tff(193,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.79/1.01 tff(194,plain,(
% 0.79/1.01 ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.79/1.01 inference(skolemize,[status(sab)],[193])).
% 0.79/1.01 tff(195,plain,
% 0.79/1.01 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.79/1.01 tff(196,plain,
% 0.79/1.01 (((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(the_InternalRel(A!11)) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))))) <=> ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(the_InternalRel(A!11)) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(197,plain,
% 0.79/1.01 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(the_InternalRel(A!11)) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11))))))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(198,plain,
% 0.79/1.01 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(the_InternalRel(A!11)) | (~element(the_InternalRel(A!11), powerset(cartesian_product2(the_carrier(A!11), the_carrier(A!11)))))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.79/1.01 tff(199,plain,
% 0.79/1.01 (relation(the_InternalRel(A!11))),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[198, 195, 93])).
% 0.79/1.01 tff(200,plain,
% 0.79/1.01 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(201,plain,
% 0.79/1.01 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[200])).
% 0.79/1.01 tff(202,plain,
% 0.79/1.01 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(203,plain,
% 0.79/1.01 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[202])).
% 0.79/1.01 tff(204,plain,
% 0.79/1.01 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.79/1.01 inference(transitivity,[status(thm)],[203, 201])).
% 0.79/1.01 tff(205,plain,
% 0.79/1.01 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))) & (is_antisymmetric_in(A, B) | (~((~(in(tptp_fun_C_1(B, A), B) & in(tptp_fun_D_0(B, A), B) & in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) & in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(206,plain,
% 0.79/1.01 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))) & (is_antisymmetric_in(A, B) | (~((~(in(tptp_fun_C_1(B, A), B) & in(tptp_fun_D_0(B, A), B) & in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) & in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[205])).
% 0.79/1.01 tff(207,plain,
% 0.79/1.01 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(208,plain,
% 0.79/1.01 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D))) <=> (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))), (![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D))) <=> ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))), ((relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D)))) <=> (relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D)))))), rewrite((relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D)))) <=> ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))), ((relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D)))) <=> ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(209,plain,
% 0.79/1.01 (![A: $i] : (relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[208])).
% 0.79/1.01 tff(210,axiom,(![A: $i] : (relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_relat_2')).
% 0.79/1.01 tff(211,plain,
% 0.79/1.01 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.79/1.01 tff(212,plain,
% 0.79/1.01 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.79/1.01 tff(213,plain,(
% 0.79/1.01 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))) & (is_antisymmetric_in(A, B) | (~((~(in(tptp_fun_C_1(B, A), B) & in(tptp_fun_D_0(B, A), B) & in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) & in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))))))),
% 0.79/1.01 inference(skolemize,[status(sab)],[212])).
% 0.79/1.01 tff(214,plain,
% 0.79/1.01 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[213, 206])).
% 0.79/1.01 tff(215,plain,
% 0.79/1.01 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[214, 204])).
% 0.79/1.01 tff(216,plain,
% 0.79/1.01 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | ((~relation(the_InternalRel(A!11))) | ![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | (~relation(the_InternalRel(A!11))) | ![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11))))))))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(217,plain,
% 0.85/1.02 (((~relation(the_InternalRel(A!11))) | ![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11))) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11)))))))))) <=> ((~relation(the_InternalRel(A!11))) | ![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11))))))))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(218,plain,
% 0.85/1.02 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | ((~relation(the_InternalRel(A!11))) | ![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11))) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | ((~relation(the_InternalRel(A!11))) | ![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11)))))))))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[217])).
% 0.85/1.02 tff(219,plain,
% 0.85/1.02 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | ((~relation(the_InternalRel(A!11))) | ![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11))) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | (~relation(the_InternalRel(A!11))) | ![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11))))))))))),
% 0.85/1.02 inference(transitivity,[status(thm)],[218, 216])).
% 0.85/1.02 tff(220,plain,
% 0.85/1.02 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | ((~relation(the_InternalRel(A!11))) | ![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11))) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))))))))))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(221,plain,
% 0.85/1.02 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | (~relation(the_InternalRel(A!11))) | ![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11)))))))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.85/1.02 tff(222,plain,
% 0.85/1.02 (![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11)))))))))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[221, 215, 199])).
% 0.85/1.02 tff(223,plain,
% 0.85/1.02 (((~![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11)))))))))) | (~((~((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)) | (~((tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)) = tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))) | (~in(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(ordered_pair(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11)))))))))) <=> ((~![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11)))))))))) | (~((~((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)) | (~((tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)) = tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))) | (~in(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(ordered_pair(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))))))))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(224,plain,
% 0.85/1.02 ((~((~((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)) | (~((~in(ordered_pair(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)) = tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))))))))) <=> (~((~((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)) | (~((tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)) = tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))) | (~in(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(ordered_pair(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11)))))))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(225,plain,
% 0.85/1.02 (((~![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11)))))))))) | (~((~((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)) | (~((~in(ordered_pair(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)) = tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)))))))))) <=> ((~![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11)))))))))) | (~((~((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)) | (~((tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)) = tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))) | (~in(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(ordered_pair(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))))))))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[224])).
% 0.85/1.02 tff(226,plain,
% 0.85/1.02 (((~![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11)))))))))) | (~((~((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)) | (~((~in(ordered_pair(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)) = tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)))))))))) <=> ((~![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11)))))))))) | (~((~((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)) | (~((tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)) = tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))) | (~in(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(ordered_pair(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))))))))))),
% 0.85/1.02 inference(transitivity,[status(thm)],[225, 223])).
% 0.85/1.02 tff(227,plain,
% 0.85/1.02 ((~![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11)))))))))) | (~((~((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)) | (~((~in(ordered_pair(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)) = tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)))))))))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(228,plain,
% 0.85/1.02 ((~![B: $i] : (~((~((~is_antisymmetric_in(the_InternalRel(A!11), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), B) | (~((~in(ordered_pair(tptp_fun_D_0(B, the_InternalRel(A!11)), tptp_fun_C_1(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_C_1(B, the_InternalRel(A!11)), tptp_fun_D_0(B, the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(tptp_fun_D_0(B, the_InternalRel(A!11)), B)) | (~in(tptp_fun_C_1(B, the_InternalRel(A!11)), B)) | (tptp_fun_C_1(B, the_InternalRel(A!11)) = tptp_fun_D_0(B, the_InternalRel(A!11)))))))))) | (~((~((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)) | (~((tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)) = tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))) | (~in(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(ordered_pair(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11)))))))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.85/1.02 tff(229,plain,
% 0.85/1.02 (~((~((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)) | (~((tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)) = tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))) | (~in(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(ordered_pair(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))))))))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[228, 222])).
% 0.85/1.02 tff(230,plain,
% 0.85/1.02 (((~((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11)))))) | (~(is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)) | (~((tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)) = tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))) | (~in(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), the_carrier(A!11))) | (~in(ordered_pair(tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11))) | (~in(ordered_pair(tptp_fun_D_0(the_carrier(A!11), the_InternalRel(A!11)), tptp_fun_C_1(the_carrier(A!11), the_InternalRel(A!11))), the_InternalRel(A!11)))))))) | ((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11)))))),
% 0.85/1.02 inference(tautology,[status(thm)],[])).
% 0.85/1.02 tff(231,plain,
% 0.85/1.02 ((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.85/1.02 tff(232,plain,
% 0.85/1.02 (^[A: $i] : refl(((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A)))) <=> ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A)))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(233,plain,
% 0.85/1.02 (![A: $i] : ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A)))) <=> ![A: $i] : ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A))))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[232])).
% 0.85/1.02 tff(234,plain,
% 0.85/1.02 (![A: $i] : ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A)))) <=> ![A: $i] : ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(235,plain,
% 0.85/1.02 (^[A: $i] : rewrite((rel_str(A) => (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A)))) <=> ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A)))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(236,plain,
% 0.85/1.02 (![A: $i] : (rel_str(A) => (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A)))) <=> ![A: $i] : ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A))))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[235])).
% 0.85/1.02 tff(237,axiom,(![A: $i] : (rel_str(A) => (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_orders_2')).
% 0.85/1.02 tff(238,plain,
% 0.85/1.02 (![A: $i] : ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.85/1.02 tff(239,plain,
% 0.85/1.02 (![A: $i] : ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[238, 234])).
% 0.85/1.02 tff(240,plain,(
% 0.85/1.02 ![A: $i] : ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A))))),
% 0.85/1.02 inference(skolemize,[status(sab)],[239])).
% 0.85/1.02 tff(241,plain,
% 0.85/1.02 (![A: $i] : ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[240, 233])).
% 0.85/1.02 tff(242,plain,
% 0.85/1.02 (((~![A: $i] : ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A))))) | ((~rel_str(A!11)) | (antisymmetric_relstr(A!11) <=> is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))))) <=> ((~![A: $i] : ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A))))) | (~rel_str(A!11)) | (antisymmetric_relstr(A!11) <=> is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(243,plain,
% 0.85/1.02 ((~![A: $i] : ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A))))) | ((~rel_str(A!11)) | (antisymmetric_relstr(A!11) <=> is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(244,plain,
% 0.85/1.02 ((~![A: $i] : ((~rel_str(A)) | (antisymmetric_relstr(A) <=> is_antisymmetric_in(the_InternalRel(A), the_carrier(A))))) | (~rel_str(A!11)) | (antisymmetric_relstr(A!11) <=> is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.85/1.02 tff(245,plain,
% 0.85/1.02 (antisymmetric_relstr(A!11) <=> is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[244, 241, 27])).
% 0.85/1.02 tff(246,plain,
% 0.85/1.02 (antisymmetric_relstr(A!11)),
% 0.85/1.02 inference(and_elim,[status(thm)],[26])).
% 0.85/1.02 tff(247,plain,
% 0.85/1.02 ((~(antisymmetric_relstr(A!11) <=> is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)))) | (~antisymmetric_relstr(A!11)) | is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))),
% 0.85/1.02 inference(tautology,[status(thm)],[])).
% 0.85/1.02 tff(248,plain,
% 0.85/1.02 ((~(antisymmetric_relstr(A!11) <=> is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11)))) | is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[247, 246])).
% 0.85/1.02 tff(249,plain,
% 0.85/1.02 (is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[248, 245])).
% 0.85/1.02 tff(250,plain,
% 0.85/1.02 ((~((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11)))))) | (~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))))),
% 0.85/1.02 inference(tautology,[status(thm)],[])).
% 0.85/1.02 tff(251,plain,
% 0.85/1.02 ((~((~is_antisymmetric_in(the_InternalRel(A!11), the_carrier(A!11))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11)))))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[250, 249])).
% 0.85/1.02 tff(252,plain,
% 0.85/1.02 (![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[251, 231])).
% 0.85/1.02 tff(253,plain,
% 0.85/1.02 (((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!11)))))) | ((~element(B!12, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B!12, C) <=> in(ordered_pair(B!12, C), the_InternalRel(A!11)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!11)))))) | (~element(B!12, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B!12, C) <=> in(ordered_pair(B!12, C), the_InternalRel(A!11)))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(254,plain,
% 0.85/1.02 ((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!11)))))) | ((~element(B!12, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B!12, C) <=> in(ordered_pair(B!12, C), the_InternalRel(A!11)))))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(255,plain,
% 0.85/1.02 ((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!11)))))) | (~element(B!12, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B!12, C) <=> in(ordered_pair(B!12, C), the_InternalRel(A!11))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.85/1.03 tff(256,plain,
% 0.85/1.03 (![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B!12, C) <=> in(ordered_pair(B!12, C), the_InternalRel(A!11))))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[255, 51, 44])).
% 0.85/1.03 tff(257,plain,
% 0.85/1.03 (((~![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B!12, C) <=> in(ordered_pair(B!12, C), the_InternalRel(A!11))))) | ((~element(C!13, the_carrier(A!11))) | (related(A!11, B!12, C!13) <=> in(ordered_pair(B!12, C!13), the_InternalRel(A!11))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B!12, C) <=> in(ordered_pair(B!12, C), the_InternalRel(A!11))))) | (~element(C!13, the_carrier(A!11))) | (related(A!11, B!12, C!13) <=> in(ordered_pair(B!12, C!13), the_InternalRel(A!11))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(258,plain,
% 0.85/1.03 ((~![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B!12, C) <=> in(ordered_pair(B!12, C), the_InternalRel(A!11))))) | ((~element(C!13, the_carrier(A!11))) | (related(A!11, B!12, C!13) <=> in(ordered_pair(B!12, C!13), the_InternalRel(A!11))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(259,plain,
% 0.85/1.03 ((~![C: $i] : ((~element(C, the_carrier(A!11))) | (related(A!11, B!12, C) <=> in(ordered_pair(B!12, C), the_InternalRel(A!11))))) | (~element(C!13, the_carrier(A!11))) | (related(A!11, B!12, C!13) <=> in(ordered_pair(B!12, C!13), the_InternalRel(A!11)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.85/1.03 tff(260,plain,
% 0.85/1.03 (related(A!11, B!12, C!13) <=> in(ordered_pair(B!12, C!13), the_InternalRel(A!11))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[259, 46, 256])).
% 0.85/1.03 tff(261,plain,
% 0.85/1.03 (related(A!11, B!12, C!13)),
% 0.85/1.03 inference(and_elim,[status(thm)],[56])).
% 0.85/1.03 tff(262,plain,
% 0.85/1.03 ((~(related(A!11, B!12, C!13) <=> in(ordered_pair(B!12, C!13), the_InternalRel(A!11)))) | (~related(A!11, B!12, C!13)) | in(ordered_pair(B!12, C!13), the_InternalRel(A!11))),
% 0.85/1.03 inference(tautology,[status(thm)],[])).
% 0.85/1.03 tff(263,plain,
% 0.85/1.03 ((~(related(A!11, B!12, C!13) <=> in(ordered_pair(B!12, C!13), the_InternalRel(A!11)))) | in(ordered_pair(B!12, C!13), the_InternalRel(A!11))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[262, 261])).
% 0.85/1.03 tff(264,plain,
% 0.85/1.03 (in(ordered_pair(B!12, C!13), the_InternalRel(A!11))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[263, 260])).
% 0.85/1.03 tff(265,plain,
% 0.85/1.03 (((~![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))))) | ((~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))) | (~in(ordered_pair(B!12, C!13), the_InternalRel(A!11))) | (~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11))) | (C!13 = B!12))) <=> ((~![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))))) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))) | (~in(ordered_pair(B!12, C!13), the_InternalRel(A!11))) | (~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11))) | (C!13 = B!12))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(266,plain,
% 0.85/1.03 (((C!13 = B!12) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))) | (~in(ordered_pair(B!12, C!13), the_InternalRel(A!11))) | (~in(C!13, the_carrier(A!11))) | (~in(B!12, the_carrier(A!11)))) <=> ((~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))) | (~in(ordered_pair(B!12, C!13), the_InternalRel(A!11))) | (~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11))) | (C!13 = B!12))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(267,plain,
% 0.85/1.03 (((~![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))))) | ((C!13 = B!12) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))) | (~in(ordered_pair(B!12, C!13), the_InternalRel(A!11))) | (~in(C!13, the_carrier(A!11))) | (~in(B!12, the_carrier(A!11))))) <=> ((~![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))))) | ((~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))) | (~in(ordered_pair(B!12, C!13), the_InternalRel(A!11))) | (~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11))) | (C!13 = B!12)))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[266])).
% 0.85/1.03 tff(268,plain,
% 0.85/1.03 (((~![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))))) | ((C!13 = B!12) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))) | (~in(ordered_pair(B!12, C!13), the_InternalRel(A!11))) | (~in(C!13, the_carrier(A!11))) | (~in(B!12, the_carrier(A!11))))) <=> ((~![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))))) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))) | (~in(ordered_pair(B!12, C!13), the_InternalRel(A!11))) | (~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11))) | (C!13 = B!12))),
% 0.85/1.03 inference(transitivity,[status(thm)],[267, 265])).
% 0.85/1.03 tff(269,plain,
% 0.85/1.03 ((~![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))))) | ((C!13 = B!12) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))) | (~in(ordered_pair(B!12, C!13), the_InternalRel(A!11))) | (~in(C!13, the_carrier(A!11))) | (~in(B!12, the_carrier(A!11))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(270,plain,
% 0.85/1.03 ((~![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), the_InternalRel(A!11))) | (~in(ordered_pair(D, C), the_InternalRel(A!11))) | (~in(C, the_carrier(A!11))) | (~in(D, the_carrier(A!11))))) | (~in(ordered_pair(C!13, B!12), the_InternalRel(A!11))) | (~in(ordered_pair(B!12, C!13), the_InternalRel(A!11))) | (~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11))) | (C!13 = B!12)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.85/1.03 tff(271,plain,
% 0.85/1.03 ((~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11))) | (C!13 = B!12)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[270, 60, 264, 252])).
% 0.85/1.03 tff(272,plain,
% 0.85/1.03 ((~in(B!12, the_carrier(A!11))) | (~in(C!13, the_carrier(A!11)))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[271, 185])).
% 0.85/1.03 tff(273,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[272, 180, 178])).
% 0.85/1.03 % SZS output end Proof
% 0.85/1.03 % E exiting
%------------------------------------------------------------------------------