TSTP Solution File: SEU309+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU309+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 : Tue Sep 20 07:28:50 EDT 2022
% Result : Theorem 2.15s 1.65s
% Output : Proof 2.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU309+2 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 11:49:59 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 2.15/1.65 % SZS status Theorem
% 2.15/1.65 % SZS output start Proof
% 2.15/1.65 tff(tptp_fun_B_278_type, type, (
% 2.15/1.65 tptp_fun_B_278: $i)).
% 2.15/1.65 tff(subset_difference_type, type, (
% 2.15/1.65 subset_difference: ( $i * $i * $i ) > $i)).
% 2.15/1.65 tff(cast_as_carrier_subset_type, type, (
% 2.15/1.65 cast_as_carrier_subset: $i > $i)).
% 2.15/1.65 tff(tptp_fun_A_277_type, type, (
% 2.15/1.65 tptp_fun_A_277: $i)).
% 2.15/1.65 tff(the_carrier_type, type, (
% 2.15/1.65 the_carrier: $i > $i)).
% 2.15/1.65 tff(subset_complement_type, type, (
% 2.15/1.65 subset_complement: ( $i * $i ) > $i)).
% 2.15/1.65 tff(element_type, type, (
% 2.15/1.65 element: ( $i * $i ) > $o)).
% 2.15/1.65 tff(powerset_type, type, (
% 2.15/1.65 powerset: $i > $i)).
% 2.15/1.65 tff(one_sorted_str_type, type, (
% 2.15/1.65 one_sorted_str: $i > $o)).
% 2.15/1.65 tff(set_difference_type, type, (
% 2.15/1.65 set_difference: ( $i * $i ) > $i)).
% 2.15/1.65 tff(subset_type, type, (
% 2.15/1.65 subset: ( $i * $i ) > $o)).
% 2.15/1.65 tff(1,plain,
% 2.15/1.65 (((~(~one_sorted_str(A!277))) & (~((~element(B!278, powerset(the_carrier(A!277)))) | (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278)) = B!278)))) <=> (one_sorted_str(A!277) & (~((~element(B!278, powerset(the_carrier(A!277)))) | (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278)) = B!278))))),
% 2.15/1.65 inference(rewrite,[status(thm)],[])).
% 2.15/1.65 tff(2,plain,
% 2.15/1.65 ((~![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))))),
% 2.15/1.65 inference(rewrite,[status(thm)],[])).
% 2.15/1.65 tff(3,plain,
% 2.15/1.65 ((~![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))))),
% 2.15/1.65 inference(rewrite,[status(thm)],[])).
% 2.15/1.65 tff(4,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')).
% 2.15/1.65 tff(5,plain,
% 2.15/1.65 (~![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)))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[4, 3])).
% 2.15/1.65 tff(6,plain,
% 2.15/1.65 (~![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)))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[5, 2])).
% 2.15/1.65 tff(7,plain,
% 2.15/1.65 (~![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)))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[6, 2])).
% 2.15/1.65 tff(8,plain,
% 2.15/1.65 (~![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)))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[7, 2])).
% 2.15/1.65 tff(9,plain,
% 2.15/1.65 (~![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)))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[8, 2])).
% 2.15/1.65 tff(10,plain,
% 2.15/1.65 (~![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)))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[9, 2])).
% 2.15/1.65 tff(11,plain,
% 2.15/1.65 (~![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)))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[10, 2])).
% 2.15/1.65 tff(12,plain,
% 2.15/1.65 (one_sorted_str(A!277) & (~((~element(B!278, powerset(the_carrier(A!277)))) | (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278)) = B!278)))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[11, 1])).
% 2.15/1.65 tff(13,plain,
% 2.15/1.65 (~((~element(B!278, powerset(the_carrier(A!277)))) | (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278)) = B!278))),
% 2.15/1.65 inference(and_elim,[status(thm)],[12])).
% 2.15/1.65 tff(14,plain,
% 2.15/1.65 (element(B!278, powerset(the_carrier(A!277)))),
% 2.15/1.65 inference(or_elim,[status(thm)],[13])).
% 2.15/1.65 tff(15,plain,
% 2.15/1.65 (^[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)))),
% 2.15/1.65 inference(bind,[status(th)],[])).
% 2.15/1.65 tff(16,plain,
% 2.15/1.65 (![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))),
% 2.15/1.65 inference(quant_intro,[status(thm)],[15])).
% 2.15/1.65 tff(17,plain,
% 2.15/1.65 (![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))),
% 2.15/1.65 inference(rewrite,[status(thm)],[])).
% 2.15/1.65 tff(18,plain,
% 2.15/1.65 (^[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)))),
% 2.15/1.65 inference(bind,[status(th)],[])).
% 2.15/1.65 tff(19,plain,
% 2.15/1.65 (![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))),
% 2.15/1.65 inference(quant_intro,[status(thm)],[18])).
% 2.15/1.65 tff(20,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')).
% 2.15/1.65 tff(21,plain,
% 2.15/1.65 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[20, 19])).
% 2.15/1.65 tff(22,plain,
% 2.15/1.65 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[21, 17])).
% 2.15/1.65 tff(23,plain,(
% 2.15/1.65 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 2.15/1.65 inference(skolemize,[status(sab)],[22])).
% 2.15/1.65 tff(24,plain,
% 2.15/1.65 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[23, 16])).
% 2.15/1.65 tff(25,plain,
% 2.15/1.65 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(B!278, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), subset_complement(the_carrier(A!277), B!278)) = B!278))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(B!278, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), subset_complement(the_carrier(A!277), B!278)) = B!278))),
% 2.15/1.65 inference(rewrite,[status(thm)],[])).
% 2.15/1.65 tff(26,plain,
% 2.15/1.65 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(B!278, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), subset_complement(the_carrier(A!277), B!278)) = B!278))),
% 2.15/1.65 inference(quant_inst,[status(thm)],[])).
% 2.15/1.65 tff(27,plain,
% 2.15/1.65 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(B!278, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), subset_complement(the_carrier(A!277), B!278)) = B!278)),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[26, 25])).
% 2.15/1.65 tff(28,plain,
% 2.15/1.65 (subset_complement(the_carrier(A!277), subset_complement(the_carrier(A!277), B!278)) = B!278),
% 2.15/1.65 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 2.15/1.65 tff(29,plain,
% 2.15/1.65 (^[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))))),
% 2.15/1.65 inference(bind,[status(th)],[])).
% 2.15/1.65 tff(30,plain,
% 2.15/1.65 (![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)))),
% 2.15/1.65 inference(quant_intro,[status(thm)],[29])).
% 2.15/1.65 tff(31,plain,
% 2.15/1.65 (![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)))),
% 2.15/1.65 inference(rewrite,[status(thm)],[])).
% 2.15/1.65 tff(32,plain,
% 2.15/1.65 (^[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))))),
% 2.15/1.65 inference(bind,[status(th)],[])).
% 2.15/1.65 tff(33,plain,
% 2.15/1.65 (![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)))),
% 2.15/1.65 inference(quant_intro,[status(thm)],[32])).
% 2.15/1.65 tff(34,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')).
% 2.15/1.65 tff(35,plain,
% 2.15/1.65 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[34, 33])).
% 2.15/1.65 tff(36,plain,
% 2.15/1.65 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[35, 31])).
% 2.15/1.65 tff(37,plain,(
% 2.15/1.65 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 2.15/1.65 inference(skolemize,[status(sab)],[36])).
% 2.15/1.65 tff(38,plain,
% 2.15/1.65 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[37, 30])).
% 2.15/1.65 tff(39,plain,
% 2.15/1.65 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!278, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), B!278) = set_difference(the_carrier(A!277), B!278)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!278, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), B!278) = set_difference(the_carrier(A!277), B!278)))),
% 2.15/1.65 inference(rewrite,[status(thm)],[])).
% 2.15/1.65 tff(40,plain,
% 2.15/1.65 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!278, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), B!278) = set_difference(the_carrier(A!277), B!278)))),
% 2.15/1.65 inference(quant_inst,[status(thm)],[])).
% 2.15/1.65 tff(41,plain,
% 2.15/1.65 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!278, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), B!278) = set_difference(the_carrier(A!277), B!278))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[40, 39])).
% 2.15/1.65 tff(42,plain,
% 2.15/1.65 (subset_complement(the_carrier(A!277), B!278) = set_difference(the_carrier(A!277), B!278)),
% 2.15/1.65 inference(unit_resolution,[status(thm)],[41, 38, 14])).
% 2.15/1.65 tff(43,plain,
% 2.15/1.65 (set_difference(the_carrier(A!277), B!278) = subset_complement(the_carrier(A!277), B!278)),
% 2.15/1.65 inference(symmetry,[status(thm)],[42])).
% 2.15/1.65 tff(44,plain,
% 2.15/1.65 (subset_complement(the_carrier(A!277), set_difference(the_carrier(A!277), B!278)) = subset_complement(the_carrier(A!277), subset_complement(the_carrier(A!277), B!278))),
% 2.15/1.65 inference(monotonicity,[status(thm)],[43])).
% 2.15/1.65 tff(45,plain,
% 2.15/1.65 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 2.15/1.65 inference(bind,[status(th)],[])).
% 2.15/1.65 tff(46,plain,
% 2.15/1.65 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 2.15/1.65 inference(quant_intro,[status(thm)],[45])).
% 2.15/1.65 tff(47,plain,
% 2.15/1.65 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 2.15/1.65 inference(rewrite,[status(thm)],[])).
% 2.15/1.65 tff(48,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 2.15/1.65 tff(49,plain,
% 2.15/1.65 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[48, 47])).
% 2.15/1.65 tff(50,plain,(
% 2.15/1.65 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 2.15/1.65 inference(skolemize,[status(sab)],[49])).
% 2.15/1.65 tff(51,plain,
% 2.15/1.65 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[50, 46])).
% 2.15/1.65 tff(52,plain,
% 2.15/1.65 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(set_difference(the_carrier(A!277), B!278), powerset(the_carrier(A!277))) <=> subset(set_difference(the_carrier(A!277), B!278), the_carrier(A!277)))),
% 2.15/1.65 inference(quant_inst,[status(thm)],[])).
% 2.15/1.65 tff(53,plain,
% 2.15/1.65 (element(set_difference(the_carrier(A!277), B!278), powerset(the_carrier(A!277))) <=> subset(set_difference(the_carrier(A!277), B!278), the_carrier(A!277))),
% 2.15/1.65 inference(unit_resolution,[status(thm)],[52, 51])).
% 2.15/1.65 tff(54,plain,
% 2.15/1.65 (^[A: $i, B: $i] : refl(subset(set_difference(A, B), A) <=> subset(set_difference(A, B), A))),
% 2.15/1.65 inference(bind,[status(th)],[])).
% 2.15/1.65 tff(55,plain,
% 2.15/1.65 (![A: $i, B: $i] : subset(set_difference(A, B), A) <=> ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 2.15/1.65 inference(quant_intro,[status(thm)],[54])).
% 2.15/1.65 tff(56,plain,
% 2.15/1.65 (![A: $i, B: $i] : subset(set_difference(A, B), A) <=> ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 2.15/1.65 inference(rewrite,[status(thm)],[])).
% 2.15/1.65 tff(57,axiom,(![A: $i, B: $i] : subset(set_difference(A, B), A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t36_xboole_1')).
% 2.15/1.65 tff(58,plain,
% 2.15/1.65 (![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[57, 56])).
% 2.15/1.65 tff(59,plain,(
% 2.15/1.65 ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 2.15/1.65 inference(skolemize,[status(sab)],[58])).
% 2.15/1.65 tff(60,plain,
% 2.15/1.65 (![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[59, 55])).
% 2.15/1.65 tff(61,plain,
% 2.15/1.65 ((~![A: $i, B: $i] : subset(set_difference(A, B), A)) | subset(set_difference(the_carrier(A!277), B!278), the_carrier(A!277))),
% 2.15/1.65 inference(quant_inst,[status(thm)],[])).
% 2.15/1.65 tff(62,plain,
% 2.15/1.65 (subset(set_difference(the_carrier(A!277), B!278), the_carrier(A!277))),
% 2.15/1.65 inference(unit_resolution,[status(thm)],[61, 60])).
% 2.15/1.65 tff(63,plain,
% 2.15/1.65 ((~(element(set_difference(the_carrier(A!277), B!278), powerset(the_carrier(A!277))) <=> subset(set_difference(the_carrier(A!277), B!278), the_carrier(A!277)))) | element(set_difference(the_carrier(A!277), B!278), powerset(the_carrier(A!277))) | (~subset(set_difference(the_carrier(A!277), B!278), the_carrier(A!277)))),
% 2.15/1.65 inference(tautology,[status(thm)],[])).
% 2.15/1.65 tff(64,plain,
% 2.15/1.65 (element(set_difference(the_carrier(A!277), B!278), powerset(the_carrier(A!277)))),
% 2.15/1.65 inference(unit_resolution,[status(thm)],[63, 62, 53])).
% 2.15/1.65 tff(65,plain,
% 2.15/1.65 (one_sorted_str(A!277)),
% 2.15/1.65 inference(and_elim,[status(thm)],[12])).
% 2.15/1.65 tff(66,plain,
% 2.15/1.65 (^[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)))))),
% 2.15/1.65 inference(bind,[status(th)],[])).
% 2.15/1.65 tff(67,plain,
% 2.15/1.65 (![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))))),
% 2.15/1.65 inference(quant_intro,[status(thm)],[66])).
% 2.15/1.65 tff(68,plain,
% 2.15/1.65 (^[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)))))),
% 2.15/1.65 inference(bind,[status(th)],[])).
% 2.15/1.65 tff(69,plain,
% 2.15/1.65 (![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))))),
% 2.15/1.65 inference(quant_intro,[status(thm)],[68])).
% 2.15/1.65 tff(70,plain,
% 2.15/1.65 (![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))))),
% 2.15/1.65 inference(transitivity,[status(thm)],[69, 67])).
% 2.15/1.65 tff(71,plain,
% 2.15/1.65 (![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))))),
% 2.15/1.65 inference(rewrite,[status(thm)],[])).
% 2.15/1.65 tff(72,plain,
% 2.15/1.65 (^[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))))))),
% 2.15/1.65 inference(bind,[status(th)],[])).
% 2.15/1.65 tff(73,plain,
% 2.15/1.65 (![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))))),
% 2.15/1.65 inference(quant_intro,[status(thm)],[72])).
% 2.15/1.65 tff(74,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')).
% 2.15/1.65 tff(75,plain,
% 2.15/1.65 (![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))))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[74, 73])).
% 2.15/1.65 tff(76,plain,
% 2.15/1.65 (![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))))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[75, 71])).
% 2.15/1.65 tff(77,plain,(
% 2.15/1.65 ![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))))),
% 2.15/1.65 inference(skolemize,[status(sab)],[76])).
% 2.15/1.65 tff(78,plain,
% 2.15/1.65 (![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))))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[77, 70])).
% 2.15/1.65 tff(79,plain,
% 2.15/1.65 (((~![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!277)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), B) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), 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!277)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), B) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B))))),
% 2.15/1.65 inference(rewrite,[status(thm)],[])).
% 2.15/1.65 tff(80,plain,
% 2.15/1.65 ((~![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!277)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), B) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B))))),
% 2.15/1.65 inference(quant_inst,[status(thm)],[])).
% 2.15/1.65 tff(81,plain,
% 2.15/1.65 ((~![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!277)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), B) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B)))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[80, 79])).
% 2.15/1.65 tff(82,plain,
% 2.15/1.65 (![B: $i] : ((~element(B, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), B) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B)))),
% 2.15/1.65 inference(unit_resolution,[status(thm)],[81, 78, 65])).
% 2.15/1.65 tff(83,plain,
% 2.15/1.65 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), B) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B)))) | ((~element(set_difference(the_carrier(A!277), B!278), powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), set_difference(the_carrier(A!277), B!278)) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), set_difference(the_carrier(A!277), B!278))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), B) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B)))) | (~element(set_difference(the_carrier(A!277), B!278), powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), set_difference(the_carrier(A!277), B!278)) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), set_difference(the_carrier(A!277), B!278))))),
% 2.15/1.65 inference(rewrite,[status(thm)],[])).
% 2.15/1.65 tff(84,plain,
% 2.15/1.65 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), B) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B)))) | ((~element(set_difference(the_carrier(A!277), B!278), powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), set_difference(the_carrier(A!277), B!278)) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), set_difference(the_carrier(A!277), B!278))))),
% 2.15/1.65 inference(quant_inst,[status(thm)],[])).
% 2.15/1.65 tff(85,plain,
% 2.15/1.65 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), B) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B)))) | (~element(set_difference(the_carrier(A!277), B!278), powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), set_difference(the_carrier(A!277), B!278)) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), set_difference(the_carrier(A!277), B!278)))),
% 2.15/1.65 inference(modus_ponens,[status(thm)],[84, 83])).
% 2.15/1.65 tff(86,plain,
% 2.15/1.65 ((~element(set_difference(the_carrier(A!277), B!278), powerset(the_carrier(A!277)))) | (subset_complement(the_carrier(A!277), set_difference(the_carrier(A!277), B!278)) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), set_difference(the_carrier(A!277), B!278)))),
% 2.15/1.65 inference(unit_resolution,[status(thm)],[85, 82])).
% 2.15/1.65 tff(87,plain,
% 2.15/1.65 (subset_complement(the_carrier(A!277), set_difference(the_carrier(A!277), B!278)) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), set_difference(the_carrier(A!277), B!278))),
% 2.15/1.65 inference(unit_resolution,[status(thm)],[86, 64])).
% 2.15/1.65 tff(88,plain,
% 2.15/1.65 (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), set_difference(the_carrier(A!277), B!278)) = subset_complement(the_carrier(A!277), set_difference(the_carrier(A!277), B!278))),
% 2.15/1.65 inference(symmetry,[status(thm)],[87])).
% 2.15/1.65 tff(89,plain,
% 2.15/1.65 (^[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))))),
% 2.15/1.65 inference(bind,[status(th)],[])).
% 2.15/1.65 tff(90,plain,
% 2.15/1.65 (![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)))),
% 2.15/1.65 inference(quant_intro,[status(thm)],[89])).
% 2.15/1.65 tff(91,plain,
% 2.15/1.65 (![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)))),
% 2.15/1.66 inference(rewrite,[status(thm)],[])).
% 2.15/1.66 tff(92,plain,
% 2.15/1.66 (^[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))))),
% 2.15/1.66 inference(bind,[status(th)],[])).
% 2.15/1.66 tff(93,plain,
% 2.15/1.66 (![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)))),
% 2.15/1.66 inference(quant_intro,[status(thm)],[92])).
% 2.15/1.66 tff(94,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')).
% 2.15/1.66 tff(95,plain,
% 2.15/1.66 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 2.15/1.66 inference(modus_ponens,[status(thm)],[94, 93])).
% 2.15/1.66 tff(96,plain,
% 2.15/1.66 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 2.15/1.66 inference(modus_ponens,[status(thm)],[95, 91])).
% 2.15/1.66 tff(97,plain,(
% 2.15/1.66 ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 2.15/1.66 inference(skolemize,[status(sab)],[96])).
% 2.15/1.66 tff(98,plain,
% 2.15/1.66 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 2.15/1.66 inference(modus_ponens,[status(thm)],[97, 90])).
% 2.15/1.66 tff(99,plain,
% 2.15/1.66 (((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!277)) | (cast_as_carrier_subset(A!277) = the_carrier(A!277)))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!277)) | (cast_as_carrier_subset(A!277) = the_carrier(A!277)))),
% 2.15/1.66 inference(rewrite,[status(thm)],[])).
% 2.15/1.66 tff(100,plain,
% 2.15/1.66 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!277)) | (cast_as_carrier_subset(A!277) = the_carrier(A!277)))),
% 2.15/1.66 inference(quant_inst,[status(thm)],[])).
% 2.15/1.66 tff(101,plain,
% 2.15/1.66 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!277)) | (cast_as_carrier_subset(A!277) = the_carrier(A!277))),
% 2.15/1.66 inference(modus_ponens,[status(thm)],[100, 99])).
% 2.15/1.66 tff(102,plain,
% 2.15/1.66 (cast_as_carrier_subset(A!277) = the_carrier(A!277)),
% 2.15/1.66 inference(unit_resolution,[status(thm)],[101, 98, 65])).
% 2.15/1.66 tff(103,plain,
% 2.15/1.66 (set_difference(cast_as_carrier_subset(A!277), B!278) = set_difference(the_carrier(A!277), B!278)),
% 2.15/1.66 inference(monotonicity,[status(thm)],[102])).
% 2.15/1.66 tff(104,plain,
% 2.15/1.66 (^[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)))))),
% 2.15/1.66 inference(bind,[status(th)],[])).
% 2.15/1.66 tff(105,plain,
% 2.15/1.66 (![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))))),
% 2.15/1.66 inference(quant_intro,[status(thm)],[104])).
% 2.15/1.66 tff(106,plain,
% 2.15/1.66 (![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))))),
% 2.15/1.66 inference(rewrite,[status(thm)],[])).
% 2.15/1.66 tff(107,plain,
% 2.15/1.66 (^[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)))))),
% 2.15/1.66 inference(bind,[status(th)],[])).
% 2.15/1.66 tff(108,plain,
% 2.15/1.66 (![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))))),
% 2.15/1.66 inference(quant_intro,[status(thm)],[107])).
% 2.15/1.66 tff(109,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')).
% 2.15/1.66 tff(110,plain,
% 2.15/1.66 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 2.15/1.66 inference(modus_ponens,[status(thm)],[109, 108])).
% 2.15/1.66 tff(111,plain,
% 2.15/1.66 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 2.15/1.66 inference(modus_ponens,[status(thm)],[110, 106])).
% 2.15/1.66 tff(112,plain,(
% 2.15/1.66 ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 2.15/1.66 inference(skolemize,[status(sab)],[111])).
% 2.15/1.66 tff(113,plain,
% 2.15/1.66 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 2.15/1.66 inference(modus_ponens,[status(thm)],[112, 105])).
% 2.15/1.66 tff(114,plain,
% 2.15/1.66 (((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!277)) | element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!277)) | element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277))))),
% 2.15/1.66 inference(rewrite,[status(thm)],[])).
% 2.15/1.66 tff(115,plain,
% 2.15/1.66 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!277)) | element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277))))),
% 2.15/1.66 inference(quant_inst,[status(thm)],[])).
% 2.15/1.66 tff(116,plain,
% 2.15/1.66 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!277)) | element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277)))),
% 2.15/1.66 inference(modus_ponens,[status(thm)],[115, 114])).
% 2.15/1.66 tff(117,plain,
% 2.15/1.66 (element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277)))),
% 2.15/1.66 inference(unit_resolution,[status(thm)],[116, 113, 65])).
% 2.15/1.66 tff(118,plain,
% 2.15/1.66 (^[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)))))),
% 2.15/1.66 inference(bind,[status(th)],[])).
% 2.15/1.66 tff(119,plain,
% 2.15/1.66 (![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))))),
% 2.15/1.66 inference(quant_intro,[status(thm)],[118])).
% 2.15/1.66 tff(120,plain,
% 2.15/1.66 (^[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))))))),
% 2.15/1.66 inference(bind,[status(th)],[])).
% 2.15/1.66 tff(121,plain,
% 2.15/1.66 (![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))))),
% 2.15/1.66 inference(quant_intro,[status(thm)],[120])).
% 2.15/1.66 tff(122,plain,
% 2.15/1.66 (![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)))),
% 2.15/1.66 inference(rewrite,[status(thm)],[])).
% 2.15/1.66 tff(123,plain,
% 2.15/1.66 (^[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))))),
% 2.15/1.66 inference(bind,[status(th)],[])).
% 2.15/1.66 tff(124,plain,
% 2.15/1.66 (![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)))),
% 2.15/1.66 inference(quant_intro,[status(thm)],[123])).
% 2.15/1.66 tff(125,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')).
% 2.15/1.66 tff(126,plain,
% 2.15/1.66 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 2.15/1.66 inference(modus_ponens,[status(thm)],[125, 124])).
% 2.15/1.66 tff(127,plain,
% 2.15/1.66 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 2.15/1.66 inference(modus_ponens,[status(thm)],[126, 122])).
% 2.15/1.66 tff(128,plain,(
% 2.15/1.66 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 2.15/1.66 inference(skolemize,[status(sab)],[127])).
% 2.15/1.66 tff(129,plain,
% 2.15/1.66 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 2.15/1.66 inference(modus_ponens,[status(thm)],[128, 121])).
% 2.15/1.66 tff(130,plain,
% 2.15/1.66 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 2.15/1.66 inference(modus_ponens,[status(thm)],[129, 119])).
% 2.15/1.66 tff(131,plain,
% 2.15/1.66 (((~![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!278, powerset(the_carrier(A!277)))) | (~element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277)))) | (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278) = set_difference(cast_as_carrier_subset(A!277), B!278)))) <=> ((~![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!278, powerset(the_carrier(A!277)))) | (~element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277)))) | (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278) = set_difference(cast_as_carrier_subset(A!277), B!278)))),
% 2.15/1.66 inference(rewrite,[status(thm)],[])).
% 2.15/1.66 tff(132,plain,
% 2.15/1.66 (((subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278) = set_difference(cast_as_carrier_subset(A!277), B!278)) | (~element(B!278, powerset(the_carrier(A!277)))) | (~element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277))))) <=> ((~element(B!278, powerset(the_carrier(A!277)))) | (~element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277)))) | (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278) = set_difference(cast_as_carrier_subset(A!277), B!278)))),
% 2.15/1.66 inference(rewrite,[status(thm)],[])).
% 2.15/1.66 tff(133,plain,
% 2.15/1.66 (((~![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!277), cast_as_carrier_subset(A!277), B!278) = set_difference(cast_as_carrier_subset(A!277), B!278)) | (~element(B!278, powerset(the_carrier(A!277)))) | (~element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277)))))) <=> ((~![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!278, powerset(the_carrier(A!277)))) | (~element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277)))) | (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278) = set_difference(cast_as_carrier_subset(A!277), B!278))))),
% 2.15/1.68 inference(monotonicity,[status(thm)],[132])).
% 2.15/1.68 tff(134,plain,
% 2.15/1.68 (((~![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!277), cast_as_carrier_subset(A!277), B!278) = set_difference(cast_as_carrier_subset(A!277), B!278)) | (~element(B!278, powerset(the_carrier(A!277)))) | (~element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277)))))) <=> ((~![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!278, powerset(the_carrier(A!277)))) | (~element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277)))) | (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278) = set_difference(cast_as_carrier_subset(A!277), B!278)))),
% 2.15/1.68 inference(transitivity,[status(thm)],[133, 131])).
% 2.15/1.68 tff(135,plain,
% 2.15/1.68 ((~![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!277), cast_as_carrier_subset(A!277), B!278) = set_difference(cast_as_carrier_subset(A!277), B!278)) | (~element(B!278, powerset(the_carrier(A!277)))) | (~element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277)))))),
% 2.15/1.68 inference(quant_inst,[status(thm)],[])).
% 2.15/1.68 tff(136,plain,
% 2.15/1.68 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(B!278, powerset(the_carrier(A!277)))) | (~element(cast_as_carrier_subset(A!277), powerset(the_carrier(A!277)))) | (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278) = set_difference(cast_as_carrier_subset(A!277), B!278))),
% 2.15/1.68 inference(modus_ponens,[status(thm)],[135, 134])).
% 2.15/1.68 tff(137,plain,
% 2.15/1.68 (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278) = set_difference(cast_as_carrier_subset(A!277), B!278)),
% 2.15/1.68 inference(unit_resolution,[status(thm)],[136, 130, 14, 117])).
% 2.15/1.68 tff(138,plain,
% 2.15/1.68 (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278) = set_difference(the_carrier(A!277), B!278)),
% 2.15/1.68 inference(transitivity,[status(thm)],[137, 103])).
% 2.15/1.68 tff(139,plain,
% 2.15/1.68 (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278)) = subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), set_difference(the_carrier(A!277), B!278))),
% 2.15/1.68 inference(monotonicity,[status(thm)],[138])).
% 2.15/1.68 tff(140,plain,
% 2.15/1.68 (subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278)) = B!278),
% 2.15/1.68 inference(transitivity,[status(thm)],[139, 88, 44, 28])).
% 2.15/1.68 tff(141,plain,
% 2.15/1.68 (~(subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), subset_difference(the_carrier(A!277), cast_as_carrier_subset(A!277), B!278)) = B!278)),
% 2.15/1.68 inference(or_elim,[status(thm)],[13])).
% 2.15/1.68 tff(142,plain,
% 2.15/1.68 ($false),
% 2.15/1.68 inference(unit_resolution,[status(thm)],[141, 140])).
% 2.15/1.68 % SZS output end Proof
%------------------------------------------------------------------------------