%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU309+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 05:27:34 AM UTC 2025
% Result : Theorem 1.31s 1.49s
% Output : Proof 1.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU309+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 06:42:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.31/1.49 % SZS status Theorem
% 1.31/1.49 % SZS output start Proof
% 1.31/1.49 tff(tptp_fun_B_207_type, type, (
% 1.31/1.49 tptp_fun_B_207: $i)).
% 1.31/1.49 tff(subset_difference_type, type, (
% 1.31/1.49 subset_difference: ( $i * $i * $i ) > $i)).
% 1.31/1.49 tff(cast_as_carrier_subset_type, type, (
% 1.31/1.49 cast_as_carrier_subset: $i > $i)).
% 1.31/1.49 tff(tptp_fun_A_206_type, type, (
% 1.31/1.49 tptp_fun_A_206: $i)).
% 1.31/1.49 tff(the_carrier_type, type, (
% 1.31/1.49 the_carrier: $i > $i)).
% 1.31/1.49 tff(subset_complement_type, type, (
% 1.31/1.49 subset_complement: ( $i * $i ) > $i)).
% 1.31/1.49 tff(element_type, type, (
% 1.31/1.49 element: ( $i * $i ) > $o)).
% 1.31/1.49 tff(powerset_type, type, (
% 1.31/1.49 powerset: $i > $i)).
% 1.31/1.49 tff(one_sorted_str_type, type, (
% 1.31/1.49 one_sorted_str: $i > $o)).
% 1.31/1.49 tff(set_difference_type, type, (
% 1.31/1.49 set_difference: ( $i * $i ) > $i)).
% 1.31/1.49 tff(subset_type, type, (
% 1.31/1.49 subset: ( $i * $i ) > $o)).
% 1.31/1.49 tff(1,plain,
% 1.31/1.49 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))) <=> (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(2,plain,
% 1.31/1.49 ((~![A: $i] : (one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))) <=> (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3,axiom,(~![A: $i] : (one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t22_pre_topc')).
% 1.31/1.49 tff(4,plain,
% 1.31/1.49 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[3, 2])).
% 1.31/1.49 tff(5,plain,
% 1.31/1.49 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[4, 1])).
% 1.31/1.49 tff(6,plain,
% 1.31/1.49 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[5, 1])).
% 1.31/1.49 tff(7,plain,
% 1.31/1.49 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[6, 1])).
% 1.31/1.49 tff(8,plain,
% 1.31/1.49 (~((~element(B!207, powerset(the_carrier(A!206)))) | (subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207)) = B!207))),
% 1.31/1.49 inference(and_elim,[status(thm)],[7])).
% 1.31/1.49 tff(9,plain,
% 1.31/1.49 (element(B!207, powerset(the_carrier(A!206)))),
% 1.31/1.49 inference(or_elim,[status(thm)],[8])).
% 1.31/1.49 tff(10,plain,
% 1.31/1.49 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(11,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[10])).
% 1.31/1.49 tff(12,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(13,plain,
% 1.31/1.49 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B)) <=> ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(14,plain,
% 1.31/1.49 (![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[13])).
% 1.31/1.49 tff(15,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','involutiveness_k3_subset_1')).
% 1.31/1.49 tff(16,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[15, 14])).
% 1.31/1.49 tff(17,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[16, 12])).
% 1.31/1.49 tff(18,plain,(
% 1.31/1.49 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 1.31/1.49 inference(skolemize,[status(sab)],[17])).
% 1.31/1.49 tff(19,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[18, 11])).
% 1.31/1.49 tff(20,plain,
% 1.31/1.49 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(B!207, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), subset_complement(the_carrier(A!206), B!207)) = B!207))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(B!207, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), subset_complement(the_carrier(A!206), B!207)) = B!207))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(21,plain,
% 1.31/1.49 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(B!207, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), subset_complement(the_carrier(A!206), B!207)) = B!207))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(22,plain,
% 1.31/1.49 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(B!207, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), subset_complement(the_carrier(A!206), B!207)) = B!207)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[21, 20])).
% 1.31/1.49 tff(23,plain,
% 1.31/1.49 (subset_complement(the_carrier(A!206), subset_complement(the_carrier(A!206), B!207)) = B!207),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 1.31/1.49 tff(24,plain,
% 1.31/1.49 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(25,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[24])).
% 1.31/1.49 tff(26,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(27,plain,
% 1.31/1.49 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B))) <=> ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(28,plain,
% 1.31/1.49 (![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[27])).
% 1.31/1.49 tff(29,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d5_subset_1')).
% 1.31/1.49 tff(30,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.31/1.49 tff(31,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.31/1.49 tff(32,plain,(
% 1.31/1.49 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.31/1.49 inference(skolemize,[status(sab)],[31])).
% 1.31/1.49 tff(33,plain,
% 1.31/1.49 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[32, 25])).
% 1.31/1.49 tff(34,plain,
% 1.31/1.49 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!207, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), B!207) = set_difference(the_carrier(A!206), B!207)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!207, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), B!207) = set_difference(the_carrier(A!206), B!207)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(35,plain,
% 1.31/1.49 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!207, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), B!207) = set_difference(the_carrier(A!206), B!207)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(36,plain,
% 1.31/1.49 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!207, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), B!207) = set_difference(the_carrier(A!206), B!207))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.31/1.49 tff(37,plain,
% 1.31/1.49 (subset_complement(the_carrier(A!206), B!207) = set_difference(the_carrier(A!206), B!207)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[36, 33, 9])).
% 1.31/1.49 tff(38,plain,
% 1.31/1.49 (set_difference(the_carrier(A!206), B!207) = subset_complement(the_carrier(A!206), B!207)),
% 1.31/1.49 inference(symmetry,[status(thm)],[37])).
% 1.31/1.49 tff(39,plain,
% 1.31/1.49 (subset_complement(the_carrier(A!206), set_difference(the_carrier(A!206), B!207)) = subset_complement(the_carrier(A!206), subset_complement(the_carrier(A!206), B!207))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[38])).
% 1.31/1.49 tff(40,plain,
% 1.31/1.49 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(41,plain,
% 1.31/1.49 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[40])).
% 1.31/1.49 tff(42,plain,
% 1.31/1.49 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(43,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 1.31/1.49 tff(44,plain,
% 1.31/1.49 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.31/1.49 tff(45,plain,(
% 1.31/1.49 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.31/1.49 inference(skolemize,[status(sab)],[44])).
% 1.31/1.49 tff(46,plain,
% 1.31/1.49 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[45, 41])).
% 1.31/1.49 tff(47,plain,
% 1.31/1.49 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(set_difference(the_carrier(A!206), B!207), powerset(the_carrier(A!206))) <=> subset(set_difference(the_carrier(A!206), B!207), the_carrier(A!206)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(48,plain,
% 1.31/1.49 (element(set_difference(the_carrier(A!206), B!207), powerset(the_carrier(A!206))) <=> subset(set_difference(the_carrier(A!206), B!207), the_carrier(A!206))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[47, 46])).
% 1.31/1.49 tff(49,plain,
% 1.31/1.49 (^[A: $i, B: $i] : refl(subset(set_difference(A, B), A) <=> subset(set_difference(A, B), A))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(50,plain,
% 1.31/1.49 (![A: $i, B: $i] : subset(set_difference(A, B), A) <=> ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 1.31/1.49 inference(quant_intro,[status(thm)],[49])).
% 1.31/1.49 tff(51,plain,
% 1.31/1.49 (![A: $i, B: $i] : subset(set_difference(A, B), A) <=> ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(52,axiom,(![A: $i, B: $i] : subset(set_difference(A, B), A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t36_xboole_1')).
% 1.31/1.49 tff(53,plain,
% 1.31/1.49 (![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.31/1.49 tff(54,plain,(
% 1.31/1.49 ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 1.31/1.49 inference(skolemize,[status(sab)],[53])).
% 1.31/1.49 tff(55,plain,
% 1.31/1.49 (![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[54, 50])).
% 1.31/1.49 tff(56,plain,
% 1.31/1.49 ((~![A: $i, B: $i] : subset(set_difference(A, B), A)) | subset(set_difference(the_carrier(A!206), B!207), the_carrier(A!206))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(57,plain,
% 1.31/1.49 (subset(set_difference(the_carrier(A!206), B!207), the_carrier(A!206))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[56, 55])).
% 1.31/1.49 tff(58,plain,
% 1.31/1.49 ((~(element(set_difference(the_carrier(A!206), B!207), powerset(the_carrier(A!206))) <=> subset(set_difference(the_carrier(A!206), B!207), the_carrier(A!206)))) | element(set_difference(the_carrier(A!206), B!207), powerset(the_carrier(A!206))) | (~subset(set_difference(the_carrier(A!206), B!207), the_carrier(A!206)))),
% 1.31/1.49 inference(tautology,[status(thm)],[])).
% 1.31/1.49 tff(59,plain,
% 1.31/1.49 (element(set_difference(the_carrier(A!206), B!207), powerset(the_carrier(A!206)))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[58, 57, 48])).
% 1.31/1.49 tff(60,plain,
% 1.31/1.49 (one_sorted_str(A!206)),
% 1.31/1.49 inference(and_elim,[status(thm)],[7])).
% 1.31/1.49 tff(61,plain,
% 1.31/1.49 (^[A: $i] : refl(((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(62,plain,
% 1.31/1.49 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[61])).
% 1.31/1.49 tff(63,plain,
% 1.31/1.49 (^[A: $i] : rewrite(((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(64,plain,
% 1.31/1.49 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[63])).
% 1.31/1.49 tff(65,plain,
% 1.31/1.49 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 1.31/1.49 inference(transitivity,[status(thm)],[64, 62])).
% 1.31/1.49 tff(66,plain,
% 1.31/1.49 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(67,plain,
% 1.31/1.49 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))) <=> ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))), ((one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> (one_sorted_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))))), rewrite((one_sorted_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))), ((one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(68,plain,
% 1.31/1.49 (![A: $i] : (one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[67])).
% 1.31/1.49 tff(69,axiom,(![A: $i] : (one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t17_pre_topc')).
% 1.31/1.49 tff(70,plain,
% 1.31/1.49 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[69, 68])).
% 1.31/1.49 tff(71,plain,
% 1.31/1.49 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[70, 66])).
% 1.31/1.50 tff(72,plain,(
% 1.31/1.50 ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 1.31/1.50 inference(skolemize,[status(sab)],[71])).
% 1.31/1.50 tff(73,plain,
% 1.31/1.50 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[72, 65])).
% 1.31/1.50 tff(74,plain,
% 1.31/1.50 (((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))) | ((~one_sorted_str(A!206)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), B) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))) | (~one_sorted_str(A!206)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), B) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B))))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(75,plain,
% 1.31/1.50 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))) | ((~one_sorted_str(A!206)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), B) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B))))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(76,plain,
% 1.31/1.50 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))) | (~one_sorted_str(A!206)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), B) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.31/1.50 tff(77,plain,
% 1.31/1.50 (![B: $i] : ((~element(B, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), B) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B)))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[76, 73, 60])).
% 1.31/1.50 tff(78,plain,
% 1.31/1.50 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), B) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B)))) | ((~element(set_difference(the_carrier(A!206), B!207), powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), set_difference(the_carrier(A!206), B!207)) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), set_difference(the_carrier(A!206), B!207))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), B) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B)))) | (~element(set_difference(the_carrier(A!206), B!207), powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), set_difference(the_carrier(A!206), B!207)) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), set_difference(the_carrier(A!206), B!207))))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(79,plain,
% 1.31/1.50 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), B) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B)))) | ((~element(set_difference(the_carrier(A!206), B!207), powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), set_difference(the_carrier(A!206), B!207)) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), set_difference(the_carrier(A!206), B!207))))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(80,plain,
% 1.31/1.50 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), B) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B)))) | (~element(set_difference(the_carrier(A!206), B!207), powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), set_difference(the_carrier(A!206), B!207)) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), set_difference(the_carrier(A!206), B!207)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.31/1.50 tff(81,plain,
% 1.31/1.50 ((~element(set_difference(the_carrier(A!206), B!207), powerset(the_carrier(A!206)))) | (subset_complement(the_carrier(A!206), set_difference(the_carrier(A!206), B!207)) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), set_difference(the_carrier(A!206), B!207)))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[80, 77])).
% 1.31/1.50 tff(82,plain,
% 1.31/1.50 (subset_complement(the_carrier(A!206), set_difference(the_carrier(A!206), B!207)) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), set_difference(the_carrier(A!206), B!207))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[81, 59])).
% 1.31/1.50 tff(83,plain,
% 1.31/1.50 (subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), set_difference(the_carrier(A!206), B!207)) = subset_complement(the_carrier(A!206), set_difference(the_carrier(A!206), B!207))),
% 1.31/1.50 inference(symmetry,[status(thm)],[82])).
% 1.31/1.50 tff(84,plain,
% 1.31/1.50 (^[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))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(85,plain,
% 1.31/1.50 (![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)))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[84])).
% 1.31/1.50 tff(86,plain,
% 1.31/1.50 (![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)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(87,plain,
% 1.31/1.50 (^[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))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(88,plain,
% 1.31/1.50 (![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)))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[87])).
% 1.31/1.50 tff(89,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')).
% 1.31/1.50 tff(90,plain,
% 1.31/1.50 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[89, 88])).
% 1.31/1.50 tff(91,plain,
% 1.31/1.50 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[90, 86])).
% 1.31/1.50 tff(92,plain,(
% 1.31/1.50 ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 1.31/1.50 inference(skolemize,[status(sab)],[91])).
% 1.31/1.50 tff(93,plain,
% 1.31/1.50 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[92, 85])).
% 1.31/1.50 tff(94,plain,
% 1.31/1.50 (((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!206)) | (cast_as_carrier_subset(A!206) = the_carrier(A!206)))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!206)) | (cast_as_carrier_subset(A!206) = the_carrier(A!206)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(95,plain,
% 1.31/1.50 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!206)) | (cast_as_carrier_subset(A!206) = the_carrier(A!206)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(96,plain,
% 1.31/1.50 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!206)) | (cast_as_carrier_subset(A!206) = the_carrier(A!206))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.31/1.50 tff(97,plain,
% 1.31/1.50 (cast_as_carrier_subset(A!206) = the_carrier(A!206)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[96, 93, 60])).
% 1.31/1.50 tff(98,plain,
% 1.31/1.50 (set_difference(cast_as_carrier_subset(A!206), B!207) = set_difference(the_carrier(A!206), B!207)),
% 1.31/1.50 inference(monotonicity,[status(thm)],[97])).
% 1.31/1.50 tff(99,plain,
% 1.31/1.50 (^[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)))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(100,plain,
% 1.31/1.50 (![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))))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[99])).
% 1.31/1.50 tff(101,plain,
% 1.31/1.50 (![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))))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(102,plain,
% 1.31/1.50 (^[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)))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(103,plain,
% 1.31/1.50 (![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))))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[102])).
% 1.31/1.50 tff(104,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')).
% 1.31/1.50 tff(105,plain,
% 1.31/1.50 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.31/1.50 tff(106,plain,
% 1.31/1.50 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[105, 101])).
% 1.31/1.50 tff(107,plain,(
% 1.31/1.50 ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 1.31/1.50 inference(skolemize,[status(sab)],[106])).
% 1.31/1.50 tff(108,plain,
% 1.31/1.50 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[107, 100])).
% 1.31/1.50 tff(109,plain,
% 1.31/1.50 (((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!206)) | element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!206)) | element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206))))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(110,plain,
% 1.31/1.50 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!206)) | element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206))))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(111,plain,
% 1.31/1.50 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!206)) | element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.31/1.50 tff(112,plain,
% 1.31/1.50 (element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206)))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[111, 108, 60])).
% 1.31/1.50 tff(113,plain,
% 1.31/1.50 (^[A: $i, B: $i, C: $i] : refl(((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))) <=> ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(114,plain,
% 1.31/1.50 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))) <=> ![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[113])).
% 1.31/1.50 tff(115,plain,
% 1.31/1.50 (^[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_difference(A, B, C) = set_difference(B, C))) <=> (((~element(C, powerset(A))) | (~element(B, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))))), rewrite((((~element(C, powerset(A))) | (~element(B, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))) <=> ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))) <=> ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(116,plain,
% 1.31/1.50 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[115])).
% 1.31/1.50 tff(117,plain,
% 1.31/1.50 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(118,plain,
% 1.31/1.50 (^[A: $i, B: $i, C: $i] : rewrite(((element(B, powerset(A)) & element(C, powerset(A))) => (subset_difference(A, B, C) = set_difference(B, C))) <=> ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(119,plain,
% 1.31/1.50 (![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => (subset_difference(A, B, C) = set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[118])).
% 1.31/1.50 tff(120,axiom,(![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => (subset_difference(A, B, C) = set_difference(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k6_subset_1')).
% 1.31/1.50 tff(121,plain,
% 1.31/1.50 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.31/1.50 tff(122,plain,
% 1.31/1.50 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[121, 117])).
% 1.31/1.50 tff(123,plain,(
% 1.31/1.50 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 1.31/1.50 inference(skolemize,[status(sab)],[122])).
% 1.31/1.50 tff(124,plain,
% 1.31/1.50 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[123, 116])).
% 1.31/1.50 tff(125,plain,
% 1.31/1.50 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[124, 114])).
% 1.31/1.50 tff(126,plain,
% 1.31/1.50 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(B!207, powerset(the_carrier(A!206)))) | (~element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206)))) | (subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207) = set_difference(cast_as_carrier_subset(A!206), B!207)))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(B!207, powerset(the_carrier(A!206)))) | (~element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206)))) | (subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207) = set_difference(cast_as_carrier_subset(A!206), B!207)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(127,plain,
% 1.31/1.50 (((subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207) = set_difference(cast_as_carrier_subset(A!206), B!207)) | (~element(B!207, powerset(the_carrier(A!206)))) | (~element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206))))) <=> ((~element(B!207, powerset(the_carrier(A!206)))) | (~element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206)))) | (subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207) = set_difference(cast_as_carrier_subset(A!206), B!207)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(128,plain,
% 1.31/1.50 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207) = set_difference(cast_as_carrier_subset(A!206), B!207)) | (~element(B!207, powerset(the_carrier(A!206)))) | (~element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(B!207, powerset(the_carrier(A!206)))) | (~element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206)))) | (subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207) = set_difference(cast_as_carrier_subset(A!206), B!207))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[127])).
% 1.31/1.50 tff(129,plain,
% 1.31/1.50 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207) = set_difference(cast_as_carrier_subset(A!206), B!207)) | (~element(B!207, powerset(the_carrier(A!206)))) | (~element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(B!207, powerset(the_carrier(A!206)))) | (~element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206)))) | (subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207) = set_difference(cast_as_carrier_subset(A!206), B!207)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[128, 126])).
% 1.31/1.50 tff(130,plain,
% 1.31/1.50 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207) = set_difference(cast_as_carrier_subset(A!206), B!207)) | (~element(B!207, powerset(the_carrier(A!206)))) | (~element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206)))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(131,plain,
% 1.35/1.52 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(B!207, powerset(the_carrier(A!206)))) | (~element(cast_as_carrier_subset(A!206), powerset(the_carrier(A!206)))) | (subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207) = set_difference(cast_as_carrier_subset(A!206), B!207))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[130, 129])).
% 1.35/1.52 tff(132,plain,
% 1.35/1.52 (subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207) = set_difference(cast_as_carrier_subset(A!206), B!207)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[131, 125, 9, 112])).
% 1.35/1.52 tff(133,plain,
% 1.35/1.52 (subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207) = set_difference(the_carrier(A!206), B!207)),
% 1.35/1.52 inference(transitivity,[status(thm)],[132, 98])).
% 1.35/1.52 tff(134,plain,
% 1.35/1.52 (subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207)) = subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), set_difference(the_carrier(A!206), B!207))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[133])).
% 1.35/1.52 tff(135,plain,
% 1.35/1.52 (subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207)) = B!207),
% 1.35/1.52 inference(transitivity,[status(thm)],[134, 83, 39, 23])).
% 1.35/1.52 tff(136,plain,
% 1.35/1.52 (~(subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), subset_difference(the_carrier(A!206), cast_as_carrier_subset(A!206), B!207)) = B!207)),
% 1.35/1.52 inference(or_elim,[status(thm)],[8])).
% 1.35/1.52 tff(137,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[136, 135])).
% 1.35/1.52 % SZS output end Proof
% 1.35/1.53 % E exiting
%------------------------------------------------------------------------------