%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU307+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:27:33 AM UTC 2025
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU307+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 06:40:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(tptp_fun_B_6_type, type, (
% 0.11/0.38 tptp_fun_B_6: $i)).
% 0.11/0.38 tff(subset_intersection2_type, type, (
% 0.11/0.38 subset_intersection2: ( $i * $i * $i ) > $i)).
% 0.11/0.38 tff(cast_as_carrier_subset_type, type, (
% 0.11/0.38 cast_as_carrier_subset: $i > $i)).
% 0.11/0.38 tff(tptp_fun_A_5_type, type, (
% 0.11/0.38 tptp_fun_A_5: $i)).
% 0.11/0.38 tff(the_carrier_type, type, (
% 0.11/0.38 the_carrier: $i > $i)).
% 0.11/0.38 tff(set_intersection2_type, type, (
% 0.11/0.38 set_intersection2: ( $i * $i ) > $i)).
% 0.11/0.38 tff(subset_type, type, (
% 0.11/0.38 subset: ( $i * $i ) > $o)).
% 0.11/0.38 tff(element_type, type, (
% 0.11/0.38 element: ( $i * $i ) > $o)).
% 0.11/0.38 tff(powerset_type, type, (
% 0.11/0.38 powerset: $i > $i)).
% 0.11/0.38 tff(one_sorted_str_type, type, (
% 0.11/0.38 one_sorted_str: $i > $o)).
% 0.11/0.38 tff(1,plain,
% 0.11/0.38 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(4,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.38 tff(6,plain,(
% 0.11/0.38 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.11/0.38 inference(skolemize,[status(sab)],[5])).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(B!6, powerset(the_carrier(A!5))) <=> subset(B!6, the_carrier(A!5)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (element(B!6, powerset(the_carrier(A!5))) <=> subset(B!6, the_carrier(A!5))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))) <=> (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 ((~![A: $i] : (one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))) <=> (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(12,axiom,(~![A: $i] : (one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t15_pre_topc')).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (~((~element(B!6, powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = B!6))),
% 0.11/0.38 inference(and_elim,[status(thm)],[16])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (element(B!6, powerset(the_carrier(A!5)))),
% 0.11/0.38 inference(or_elim,[status(thm)],[17])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 ((~(element(B!6, powerset(the_carrier(A!5))) <=> subset(B!6, the_carrier(A!5)))) | (~element(B!6, powerset(the_carrier(A!5)))) | subset(B!6, the_carrier(A!5))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 ((~(element(B!6, powerset(the_carrier(A!5))) <=> subset(B!6, the_carrier(A!5)))) | subset(B!6, the_carrier(A!5))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (subset(B!6, the_carrier(A!5))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[20, 9])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 (![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.11/0.38 tff(27,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t28_xboole_1')).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.11/0.38 tff(30,plain,(
% 0.11/0.38 ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.11/0.38 inference(skolemize,[status(sab)],[29])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(B!6, the_carrier(A!5))) | (set_intersection2(B!6, the_carrier(A!5)) = B!6))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(B!6, the_carrier(A!5))) | (set_intersection2(B!6, the_carrier(A!5)) = B!6))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(B!6, the_carrier(A!5))) | (set_intersection2(B!6, the_carrier(A!5)) = B!6))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(B!6, the_carrier(A!5))) | (set_intersection2(B!6, the_carrier(A!5)) = B!6)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 (set_intersection2(B!6, the_carrier(A!5)) = B!6),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (one_sorted_str(A!5)),
% 0.11/0.38 inference(and_elim,[status(thm)],[16])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 (^[A: $i] : refl(((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))) <=> ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))) <=> ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[37])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))) <=> ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (^[A: $i] : rewrite((one_sorted_str(A) => (cast_as_carrier_subset(A) = the_carrier(A))) <=> ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (![A: $i] : (one_sorted_str(A) => (cast_as_carrier_subset(A) = the_carrier(A))) <=> ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[40])).
% 0.11/0.38 tff(42,axiom,(![A: $i] : (one_sorted_str(A) => (cast_as_carrier_subset(A) = the_carrier(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_pre_topc')).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.11/0.38 tff(45,plain,(
% 0.11/0.38 ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[44])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!5)) | (cast_as_carrier_subset(A!5) = the_carrier(A!5)))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!5)) | (cast_as_carrier_subset(A!5) = the_carrier(A!5)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!5)) | (cast_as_carrier_subset(A!5) = the_carrier(A!5)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!5)) | (cast_as_carrier_subset(A!5) = the_carrier(A!5))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 (cast_as_carrier_subset(A!5) = the_carrier(A!5)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[49, 46, 36])).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 (the_carrier(A!5) = cast_as_carrier_subset(A!5)),
% 0.11/0.38 inference(symmetry,[status(thm)],[50])).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 (set_intersection2(B!6, the_carrier(A!5)) = set_intersection2(B!6, cast_as_carrier_subset(A!5))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[51])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 (set_intersection2(B!6, cast_as_carrier_subset(A!5)) = set_intersection2(B!6, the_carrier(A!5))),
% 0.11/0.38 inference(symmetry,[status(thm)],[52])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 (^[A: $i] : refl(((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[54])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (^[A: $i] : rewrite((one_sorted_str(A) => element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 (![A: $i] : (one_sorted_str(A) => element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[57])).
% 0.11/0.38 tff(59,axiom,(![A: $i] : (one_sorted_str(A) => element(cast_as_carrier_subset(A), powerset(the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_pre_topc')).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.11/0.38 tff(62,plain,(
% 0.11/0.38 ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[61])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 (((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!5)) | element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!5)) | element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(65,plain,
% 0.11/0.38 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!5)) | element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!5)) | element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 (element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[66, 63, 36])).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 (^[A: $i, B: $i, C: $i] : refl(((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A)))) <=> ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A)))) <=> ![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[68])).
% 0.11/0.38 tff(70,plain,
% 0.11/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((element(B, powerset(A)) & element(C, powerset(A))) <=> (~((~element(B, powerset(A))) | (~element(C, powerset(A)))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> (~(~((~element(B, powerset(A))) | (~element(C, powerset(A)))))))), rewrite((~(~((~element(B, powerset(A))) | (~element(C, powerset(A)))))) <=> ((~element(B, powerset(A))) | (~element(C, powerset(A))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> ((~element(B, powerset(A))) | (~element(C, powerset(A)))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> (((~element(B, powerset(A))) | (~element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))))), rewrite((((~element(B, powerset(A))) | (~element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(71,plain,
% 0.11/0.39 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[70])).
% 0.11/0.39 tff(72,plain,
% 0.11/0.39 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(73,plain,
% 0.11/0.39 (^[A: $i, B: $i, C: $i] : rewrite(((element(B, powerset(A)) & element(C, powerset(A))) => (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(74,plain,
% 0.11/0.39 (![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.11/0.39 tff(75,axiom,(![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => (subset_intersection2(A, B, C) = set_intersection2(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k5_subset_1')).
% 0.11/0.39 tff(76,plain,
% 0.11/0.39 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.11/0.39 tff(77,plain,
% 0.11/0.39 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.11/0.39 tff(78,plain,(
% 0.11/0.39 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[77])).
% 0.11/0.39 tff(79,plain,
% 0.11/0.39 (![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.11/0.39 tff(80,plain,
% 0.11/0.39 (![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[79, 69])).
% 0.11/0.39 tff(81,plain,
% 0.11/0.39 (((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = set_intersection2(B!6, cast_as_carrier_subset(A!5))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = set_intersection2(B!6, cast_as_carrier_subset(A!5))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(82,plain,
% 0.11/0.39 (((subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = set_intersection2(B!6, cast_as_carrier_subset(A!5))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5))))) <=> ((~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = set_intersection2(B!6, cast_as_carrier_subset(A!5))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(83,plain,
% 0.11/0.39 (((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = set_intersection2(B!6, cast_as_carrier_subset(A!5))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = set_intersection2(B!6, cast_as_carrier_subset(A!5)))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[82])).
% 0.11/0.39 tff(84,plain,
% 0.11/0.39 (((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = set_intersection2(B!6, cast_as_carrier_subset(A!5))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = set_intersection2(B!6, cast_as_carrier_subset(A!5))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[83, 81])).
% 0.11/0.39 tff(85,plain,
% 0.11/0.39 ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = set_intersection2(B!6, cast_as_carrier_subset(A!5))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(86,plain,
% 0.11/0.39 ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = set_intersection2(B!6, cast_as_carrier_subset(A!5)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.11/0.39 tff(87,plain,
% 0.11/0.39 ((~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = set_intersection2(B!6, cast_as_carrier_subset(A!5)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[86, 80, 18])).
% 0.11/0.39 tff(88,plain,
% 0.11/0.39 (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = set_intersection2(B!6, cast_as_carrier_subset(A!5))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[87, 67])).
% 0.11/0.39 tff(89,plain,
% 0.11/0.39 (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = B!6),
% 0.11/0.39 inference(transitivity,[status(thm)],[88, 53, 35])).
% 0.11/0.39 tff(90,plain,
% 0.11/0.39 (~(subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = B!6)),
% 0.11/0.39 inference(or_elim,[status(thm)],[17])).
% 0.11/0.39 tff(91,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.11/0.39 % SZS output end Proof
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------