%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU307+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 1.14s 1.31s
% Output : Proof 1.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU307+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:43:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.14/1.31 % SZS status Theorem
% 1.14/1.31 % SZS output start Proof
% 1.14/1.31 tff(tptp_fun_B_205_type, type, (
% 1.14/1.31 tptp_fun_B_205: $i)).
% 1.14/1.31 tff(subset_intersection2_type, type, (
% 1.14/1.31 subset_intersection2: ( $i * $i * $i ) > $i)).
% 1.14/1.31 tff(cast_as_carrier_subset_type, type, (
% 1.14/1.31 cast_as_carrier_subset: $i > $i)).
% 1.14/1.31 tff(tptp_fun_A_204_type, type, (
% 1.14/1.31 tptp_fun_A_204: $i)).
% 1.14/1.31 tff(the_carrier_type, type, (
% 1.14/1.31 the_carrier: $i > $i)).
% 1.14/1.31 tff(set_intersection2_type, type, (
% 1.14/1.31 set_intersection2: ( $i * $i ) > $i)).
% 1.14/1.31 tff(subset_type, type, (
% 1.14/1.31 subset: ( $i * $i ) > $o)).
% 1.14/1.31 tff(element_type, type, (
% 1.14/1.31 element: ( $i * $i ) > $o)).
% 1.14/1.31 tff(powerset_type, type, (
% 1.14/1.31 powerset: $i > $i)).
% 1.14/1.31 tff(one_sorted_str_type, type, (
% 1.14/1.31 one_sorted_str: $i > $o)).
% 1.14/1.31 tff(1,plain,
% 1.14/1.31 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 1.14/1.31 inference(bind,[status(th)],[])).
% 1.14/1.31 tff(2,plain,
% 1.14/1.31 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.14/1.31 inference(quant_intro,[status(thm)],[1])).
% 1.14/1.31 tff(3,plain,
% 1.14/1.31 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(4,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 1.14/1.31 tff(5,plain,
% 1.14/1.31 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.14/1.31 tff(6,plain,(
% 1.14/1.31 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.14/1.31 inference(skolemize,[status(sab)],[5])).
% 1.14/1.31 tff(7,plain,
% 1.14/1.31 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.14/1.31 tff(8,plain,
% 1.14/1.31 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(B!205, powerset(the_carrier(A!204))) <=> subset(B!205, the_carrier(A!204)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(9,plain,
% 1.14/1.31 (element(B!205, powerset(the_carrier(A!204))) <=> subset(B!205, the_carrier(A!204))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.14/1.31 tff(10,plain,
% 1.14/1.31 ((~![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))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(11,plain,
% 1.14/1.31 ((~![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))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 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/sandbox2/benchmark/theBenchmark.p','t15_pre_topc')).
% 1.14/1.31 tff(13,plain,
% 1.14/1.31 (~![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)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[12, 11])).
% 1.14/1.31 tff(14,plain,
% 1.14/1.31 (~![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)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[13, 10])).
% 1.14/1.31 tff(15,plain,
% 1.14/1.31 (~![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)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[14, 10])).
% 1.14/1.31 tff(16,plain,
% 1.14/1.31 (~![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)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[15, 10])).
% 1.14/1.31 tff(17,plain,
% 1.14/1.31 (~((~element(B!205, powerset(the_carrier(A!204)))) | (subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = B!205))),
% 1.14/1.31 inference(and_elim,[status(thm)],[16])).
% 1.14/1.31 tff(18,plain,
% 1.14/1.31 (element(B!205, powerset(the_carrier(A!204)))),
% 1.14/1.31 inference(or_elim,[status(thm)],[17])).
% 1.14/1.31 tff(19,plain,
% 1.14/1.31 ((~(element(B!205, powerset(the_carrier(A!204))) <=> subset(B!205, the_carrier(A!204)))) | (~element(B!205, powerset(the_carrier(A!204)))) | subset(B!205, the_carrier(A!204))),
% 1.14/1.31 inference(tautology,[status(thm)],[])).
% 1.14/1.31 tff(20,plain,
% 1.14/1.31 ((~(element(B!205, powerset(the_carrier(A!204))) <=> subset(B!205, the_carrier(A!204)))) | subset(B!205, the_carrier(A!204))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[19, 18])).
% 1.14/1.31 tff(21,plain,
% 1.14/1.31 (subset(B!205, the_carrier(A!204))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[20, 9])).
% 1.14/1.31 tff(22,plain,
% 1.14/1.31 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 1.14/1.31 inference(bind,[status(th)],[])).
% 1.14/1.31 tff(23,plain,
% 1.14/1.31 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 1.14/1.31 inference(quant_intro,[status(thm)],[22])).
% 1.14/1.31 tff(24,plain,
% 1.14/1.31 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(25,plain,
% 1.14/1.31 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 1.14/1.31 inference(bind,[status(th)],[])).
% 1.14/1.31 tff(26,plain,
% 1.14/1.31 (![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 1.14/1.31 inference(quant_intro,[status(thm)],[25])).
% 1.14/1.31 tff(27,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_xboole_1')).
% 1.14/1.31 tff(28,plain,
% 1.14/1.31 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.14/1.31 tff(29,plain,
% 1.14/1.31 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.14/1.31 tff(30,plain,(
% 1.14/1.31 ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 1.14/1.31 inference(skolemize,[status(sab)],[29])).
% 1.14/1.31 tff(31,plain,
% 1.14/1.31 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.14/1.31 tff(32,plain,
% 1.14/1.31 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(B!205, the_carrier(A!204))) | (set_intersection2(B!205, the_carrier(A!204)) = B!205))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(B!205, the_carrier(A!204))) | (set_intersection2(B!205, the_carrier(A!204)) = B!205))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(33,plain,
% 1.14/1.31 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(B!205, the_carrier(A!204))) | (set_intersection2(B!205, the_carrier(A!204)) = B!205))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(34,plain,
% 1.14/1.31 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(B!205, the_carrier(A!204))) | (set_intersection2(B!205, the_carrier(A!204)) = B!205)),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[33, 32])).
% 1.14/1.31 tff(35,plain,
% 1.14/1.31 (set_intersection2(B!205, the_carrier(A!204)) = B!205),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 1.14/1.31 tff(36,plain,
% 1.14/1.31 (one_sorted_str(A!204)),
% 1.14/1.31 inference(and_elim,[status(thm)],[16])).
% 1.14/1.31 tff(37,plain,
% 1.14/1.31 (^[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))))),
% 1.14/1.31 inference(bind,[status(th)],[])).
% 1.14/1.31 tff(38,plain,
% 1.14/1.31 (![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)))),
% 1.14/1.31 inference(quant_intro,[status(thm)],[37])).
% 1.14/1.31 tff(39,plain,
% 1.14/1.31 (![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)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(40,plain,
% 1.14/1.31 (^[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))))),
% 1.14/1.31 inference(bind,[status(th)],[])).
% 1.14/1.31 tff(41,plain,
% 1.14/1.31 (![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)))),
% 1.14/1.31 inference(quant_intro,[status(thm)],[40])).
% 1.14/1.31 tff(42,axiom,(![A: $i] : (one_sorted_str(A) => (cast_as_carrier_subset(A) = the_carrier(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_pre_topc')).
% 1.14/1.31 tff(43,plain,
% 1.14/1.31 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.14/1.31 tff(44,plain,
% 1.14/1.31 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[43, 39])).
% 1.14/1.31 tff(45,plain,(
% 1.14/1.31 ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 1.14/1.31 inference(skolemize,[status(sab)],[44])).
% 1.14/1.31 tff(46,plain,
% 1.14/1.31 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[45, 38])).
% 1.14/1.31 tff(47,plain,
% 1.14/1.31 (((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!204)) | (cast_as_carrier_subset(A!204) = the_carrier(A!204)))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!204)) | (cast_as_carrier_subset(A!204) = the_carrier(A!204)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(48,plain,
% 1.14/1.31 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!204)) | (cast_as_carrier_subset(A!204) = the_carrier(A!204)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(49,plain,
% 1.14/1.31 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!204)) | (cast_as_carrier_subset(A!204) = the_carrier(A!204))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.14/1.31 tff(50,plain,
% 1.14/1.31 (cast_as_carrier_subset(A!204) = the_carrier(A!204)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[49, 46, 36])).
% 1.14/1.31 tff(51,plain,
% 1.14/1.31 (set_intersection2(B!205, cast_as_carrier_subset(A!204)) = set_intersection2(B!205, the_carrier(A!204))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[50])).
% 1.14/1.31 tff(52,plain,
% 1.14/1.31 (^[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)))))),
% 1.14/1.31 inference(bind,[status(th)],[])).
% 1.14/1.31 tff(53,plain,
% 1.14/1.31 (![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))))),
% 1.14/1.31 inference(quant_intro,[status(thm)],[52])).
% 1.14/1.31 tff(54,plain,
% 1.14/1.31 (![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))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(55,plain,
% 1.14/1.31 (^[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)))))),
% 1.14/1.31 inference(bind,[status(th)],[])).
% 1.14/1.31 tff(56,plain,
% 1.14/1.31 (![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))))),
% 1.14/1.31 inference(quant_intro,[status(thm)],[55])).
% 1.14/1.31 tff(57,axiom,(![A: $i] : (one_sorted_str(A) => element(cast_as_carrier_subset(A), powerset(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_pre_topc')).
% 1.14/1.31 tff(58,plain,
% 1.14/1.31 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.14/1.31 tff(59,plain,
% 1.14/1.31 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[58, 54])).
% 1.14/1.31 tff(60,plain,(
% 1.14/1.31 ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 1.14/1.31 inference(skolemize,[status(sab)],[59])).
% 1.14/1.31 tff(61,plain,
% 1.14/1.31 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[60, 53])).
% 1.14/1.31 tff(62,plain,
% 1.14/1.31 (((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!204)) | element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!204)) | element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(63,plain,
% 1.14/1.31 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!204)) | element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(64,plain,
% 1.14/1.31 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!204)) | element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.14/1.31 tff(65,plain,
% 1.14/1.31 (element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204)))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[64, 61, 36])).
% 1.14/1.31 tff(66,plain,
% 1.14/1.31 (^[A: $i, B: $i, C: $i] : refl(((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))) <=> ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))))),
% 1.14/1.31 inference(bind,[status(th)],[])).
% 1.14/1.31 tff(67,plain,
% 1.14/1.31 (![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))) <=> ![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 1.14/1.31 inference(quant_intro,[status(thm)],[66])).
% 1.14/1.31 tff(68,plain,
% 1.14/1.31 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((element(B, powerset(A)) & element(C, powerset(A))) <=> (~((~element(C, powerset(A))) | (~element(B, powerset(A)))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> (~(~((~element(C, powerset(A))) | (~element(B, powerset(A)))))))), rewrite((~(~((~element(C, powerset(A))) | (~element(B, powerset(A)))))) <=> ((~element(C, powerset(A))) | (~element(B, powerset(A))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> ((~element(C, powerset(A))) | (~element(B, powerset(A)))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> (((~element(C, powerset(A))) | (~element(B, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))))), rewrite((((~element(C, powerset(A))) | (~element(B, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, 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(C, powerset(A))) | (~element(B, powerset(A))))))),
% 1.14/1.31 inference(bind,[status(th)],[])).
% 1.14/1.31 tff(69,plain,
% 1.14/1.31 (![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(C, powerset(A))) | (~element(B, powerset(A))))),
% 1.14/1.31 inference(quant_intro,[status(thm)],[68])).
% 1.14/1.31 tff(70,plain,
% 1.14/1.31 (![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)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(71,plain,
% 1.14/1.31 (^[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))))),
% 1.14/1.31 inference(bind,[status(th)],[])).
% 1.14/1.31 tff(72,plain,
% 1.14/1.31 (![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)))),
% 1.14/1.31 inference(quant_intro,[status(thm)],[71])).
% 1.14/1.31 tff(73,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/sandbox2/benchmark/theBenchmark.p','redefinition_k5_subset_1')).
% 1.14/1.31 tff(74,plain,
% 1.14/1.31 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.14/1.31 tff(75,plain,
% 1.14/1.31 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[74, 70])).
% 1.14/1.31 tff(76,plain,(
% 1.14/1.31 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 1.14/1.31 inference(skolemize,[status(sab)],[75])).
% 1.14/1.31 tff(77,plain,
% 1.14/1.31 (![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[76, 69])).
% 1.14/1.31 tff(78,plain,
% 1.14/1.31 (![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[77, 67])).
% 1.14/1.31 tff(79,plain,
% 1.14/1.31 (((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(B!205, powerset(the_carrier(A!204)))) | (subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = set_intersection2(B!205, cast_as_carrier_subset(A!204))) | (~element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(B!205, powerset(the_carrier(A!204)))) | (subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = set_intersection2(B!205, cast_as_carrier_subset(A!204))) | (~element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204)))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(80,plain,
% 1.14/1.31 (((subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = set_intersection2(B!205, cast_as_carrier_subset(A!204))) | (~element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204)))) | (~element(B!205, powerset(the_carrier(A!204))))) <=> ((~element(B!205, powerset(the_carrier(A!204)))) | (subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = set_intersection2(B!205, cast_as_carrier_subset(A!204))) | (~element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204)))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(81,plain,
% 1.14/1.33 (((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = set_intersection2(B!205, cast_as_carrier_subset(A!204))) | (~element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204)))) | (~element(B!205, powerset(the_carrier(A!204)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(B!205, powerset(the_carrier(A!204)))) | (subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = set_intersection2(B!205, cast_as_carrier_subset(A!204))) | (~element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[80])).
% 1.14/1.33 tff(82,plain,
% 1.14/1.33 (((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = set_intersection2(B!205, cast_as_carrier_subset(A!204))) | (~element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204)))) | (~element(B!205, powerset(the_carrier(A!204)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(B!205, powerset(the_carrier(A!204)))) | (subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = set_intersection2(B!205, cast_as_carrier_subset(A!204))) | (~element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204)))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[81, 79])).
% 1.14/1.33 tff(83,plain,
% 1.14/1.33 ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = set_intersection2(B!205, cast_as_carrier_subset(A!204))) | (~element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204)))) | (~element(B!205, powerset(the_carrier(A!204)))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(84,plain,
% 1.14/1.33 ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(B!205, powerset(the_carrier(A!204)))) | (subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = set_intersection2(B!205, cast_as_carrier_subset(A!204))) | (~element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.14/1.33 tff(85,plain,
% 1.14/1.33 ((subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = set_intersection2(B!205, cast_as_carrier_subset(A!204))) | (~element(cast_as_carrier_subset(A!204), powerset(the_carrier(A!204))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[84, 78, 18])).
% 1.14/1.33 tff(86,plain,
% 1.14/1.33 (subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = set_intersection2(B!205, cast_as_carrier_subset(A!204))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[85, 65])).
% 1.14/1.33 tff(87,plain,
% 1.14/1.33 (subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = B!205),
% 1.14/1.33 inference(transitivity,[status(thm)],[86, 51, 35])).
% 1.14/1.33 tff(88,plain,
% 1.14/1.33 (~(subset_intersection2(the_carrier(A!204), B!205, cast_as_carrier_subset(A!204)) = B!205)),
% 1.14/1.33 inference(or_elim,[status(thm)],[17])).
% 1.14/1.33 tff(89,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[88, 87])).
% 1.14/1.33 % SZS output end Proof
% 1.14/1.33 % E exiting
%------------------------------------------------------------------------------