TSTP Solution File: SEU308+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU308+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 0.71s 0.74s
% Output : Proof 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : SEU308+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Sep 3 11:56:55 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.71/0.74 % SZS status Theorem
% 0.71/0.74 % SZS output start Proof
% 0.71/0.74 tff(subset_difference_type, type, (
% 0.71/0.74 subset_difference: ( $i * $i * $i ) > $i)).
% 0.71/0.74 tff(tptp_fun_B_277_type, type, (
% 0.71/0.74 tptp_fun_B_277: $i)).
% 0.71/0.74 tff(cast_as_carrier_subset_type, type, (
% 0.71/0.74 cast_as_carrier_subset: $i > $i)).
% 0.71/0.74 tff(tptp_fun_A_276_type, type, (
% 0.71/0.74 tptp_fun_A_276: $i)).
% 0.71/0.74 tff(the_carrier_type, type, (
% 0.71/0.74 the_carrier: $i > $i)).
% 0.71/0.74 tff(subset_complement_type, type, (
% 0.71/0.74 subset_complement: ( $i * $i ) > $i)).
% 0.71/0.74 tff(set_difference_type, type, (
% 0.71/0.74 set_difference: ( $i * $i ) > $i)).
% 0.71/0.74 tff(element_type, type, (
% 0.71/0.74 element: ( $i * $i ) > $o)).
% 0.71/0.74 tff(powerset_type, type, (
% 0.71/0.74 powerset: $i > $i)).
% 0.71/0.74 tff(one_sorted_str_type, type, (
% 0.71/0.74 one_sorted_str: $i > $o)).
% 0.71/0.74 tff(1,plain,
% 0.71/0.74 (((~(~one_sorted_str(A!276))) & (~((~element(B!277, powerset(the_carrier(A!276)))) | (subset_complement(the_carrier(A!276), B!277) = subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277))))) <=> (one_sorted_str(A!276) & (~((~element(B!277, powerset(the_carrier(A!276)))) | (subset_complement(the_carrier(A!276), B!277) = subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277)))))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(2,plain,
% 0.71/0.74 ((~![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)))))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(3,plain,
% 0.71/0.74 ((~![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)))))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(4,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')).
% 0.71/0.74 tff(5,plain,
% 0.71/0.74 (~![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))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.71/0.74 tff(6,plain,
% 0.71/0.74 (~![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))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.71/0.74 tff(7,plain,
% 0.71/0.74 (~![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))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.71/0.74 tff(8,plain,
% 0.71/0.74 (~![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))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.71/0.74 tff(9,plain,
% 0.71/0.74 (~![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))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.71/0.74 tff(10,plain,
% 0.71/0.74 (~![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))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.71/0.74 tff(11,plain,
% 0.71/0.74 (~![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))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.71/0.74 tff(12,plain,
% 0.71/0.74 (one_sorted_str(A!276) & (~((~element(B!277, powerset(the_carrier(A!276)))) | (subset_complement(the_carrier(A!276), B!277) = subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.71/0.74 tff(13,plain,
% 0.71/0.74 (one_sorted_str(A!276)),
% 0.71/0.74 inference(and_elim,[status(thm)],[12])).
% 0.71/0.74 tff(14,plain,
% 0.71/0.74 (^[A: $i] : refl(((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(15,plain,
% 0.71/0.74 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.71/0.74 inference(quant_intro,[status(thm)],[14])).
% 0.71/0.74 tff(16,plain,
% 0.71/0.74 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(17,plain,
% 0.71/0.74 (^[A: $i] : rewrite((one_sorted_str(A) => element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(18,plain,
% 0.71/0.74 (![A: $i] : (one_sorted_str(A) => element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.71/0.74 inference(quant_intro,[status(thm)],[17])).
% 0.71/0.74 tff(19,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')).
% 0.71/0.74 tff(20,plain,
% 0.71/0.74 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.71/0.74 tff(21,plain,
% 0.71/0.74 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.71/0.74 tff(22,plain,(
% 0.71/0.74 ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.71/0.74 inference(skolemize,[status(sab)],[21])).
% 0.71/0.74 tff(23,plain,
% 0.71/0.74 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.71/0.74 tff(24,plain,
% 0.71/0.74 (((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!276)) | element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!276)) | element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276))))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(25,plain,
% 0.71/0.74 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!276)) | element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276))))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(26,plain,
% 0.71/0.74 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!276)) | element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276)))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.71/0.74 tff(27,plain,
% 0.71/0.74 (element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276)))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 0.71/0.74 tff(28,plain,
% 0.71/0.74 (~((~element(B!277, powerset(the_carrier(A!276)))) | (subset_complement(the_carrier(A!276), B!277) = subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277)))),
% 0.71/0.74 inference(and_elim,[status(thm)],[12])).
% 0.71/0.75 tff(29,plain,
% 0.71/0.75 (element(B!277, powerset(the_carrier(A!276)))),
% 0.71/0.75 inference(or_elim,[status(thm)],[28])).
% 0.71/0.75 tff(30,plain,
% 0.71/0.75 (^[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)))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(31,plain,
% 0.71/0.75 (![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))))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[30])).
% 0.71/0.75 tff(32,plain,
% 0.71/0.75 (^[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))))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(33,plain,
% 0.71/0.75 (![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))))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[32])).
% 0.71/0.75 tff(34,plain,
% 0.71/0.75 (![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)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(35,plain,
% 0.71/0.75 (^[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))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(36,plain,
% 0.71/0.75 (![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)))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[35])).
% 0.71/0.75 tff(37,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')).
% 0.71/0.75 tff(38,plain,
% 0.71/0.75 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.71/0.75 tff(39,plain,
% 0.71/0.75 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.71/0.75 tff(40,plain,(
% 0.71/0.75 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 0.71/0.75 inference(skolemize,[status(sab)],[39])).
% 0.71/0.75 tff(41,plain,
% 0.71/0.75 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.71/0.75 tff(42,plain,
% 0.71/0.75 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.71/0.75 tff(43,plain,
% 0.71/0.75 (((~![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!277, powerset(the_carrier(A!276)))) | (~element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276)))) | (subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277) = set_difference(cast_as_carrier_subset(A!276), B!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!277, powerset(the_carrier(A!276)))) | (~element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276)))) | (subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277) = set_difference(cast_as_carrier_subset(A!276), B!277)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(44,plain,
% 0.71/0.75 (((subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277) = set_difference(cast_as_carrier_subset(A!276), B!277)) | (~element(B!277, powerset(the_carrier(A!276)))) | (~element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276))))) <=> ((~element(B!277, powerset(the_carrier(A!276)))) | (~element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276)))) | (subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277) = set_difference(cast_as_carrier_subset(A!276), B!277)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(45,plain,
% 0.71/0.75 (((~![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!276), cast_as_carrier_subset(A!276), B!277) = set_difference(cast_as_carrier_subset(A!276), B!277)) | (~element(B!277, powerset(the_carrier(A!276)))) | (~element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276)))))) <=> ((~![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!277, powerset(the_carrier(A!276)))) | (~element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276)))) | (subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277) = set_difference(cast_as_carrier_subset(A!276), B!277))))),
% 0.71/0.75 inference(monotonicity,[status(thm)],[44])).
% 0.71/0.75 tff(46,plain,
% 0.71/0.75 (((~![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!276), cast_as_carrier_subset(A!276), B!277) = set_difference(cast_as_carrier_subset(A!276), B!277)) | (~element(B!277, powerset(the_carrier(A!276)))) | (~element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276)))))) <=> ((~![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!277, powerset(the_carrier(A!276)))) | (~element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276)))) | (subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277) = set_difference(cast_as_carrier_subset(A!276), B!277)))),
% 0.71/0.75 inference(transitivity,[status(thm)],[45, 43])).
% 0.71/0.75 tff(47,plain,
% 0.71/0.75 ((~![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!276), cast_as_carrier_subset(A!276), B!277) = set_difference(cast_as_carrier_subset(A!276), B!277)) | (~element(B!277, powerset(the_carrier(A!276)))) | (~element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276)))))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(48,plain,
% 0.71/0.75 ((~![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!277, powerset(the_carrier(A!276)))) | (~element(cast_as_carrier_subset(A!276), powerset(the_carrier(A!276)))) | (subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277) = set_difference(cast_as_carrier_subset(A!276), B!277))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.71/0.75 tff(49,plain,
% 0.71/0.75 (subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277) = set_difference(cast_as_carrier_subset(A!276), B!277)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[48, 42, 29, 27])).
% 0.71/0.75 tff(50,plain,
% 0.71/0.75 (set_difference(cast_as_carrier_subset(A!276), B!277) = subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277)),
% 0.71/0.75 inference(symmetry,[status(thm)],[49])).
% 0.71/0.75 tff(51,plain,
% 0.71/0.75 (^[A: $i] : refl(((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))) <=> ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(52,plain,
% 0.71/0.75 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))) <=> ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[51])).
% 0.71/0.75 tff(53,plain,
% 0.71/0.75 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))) <=> ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(54,plain,
% 0.71/0.75 (^[A: $i] : rewrite((one_sorted_str(A) => (cast_as_carrier_subset(A) = the_carrier(A))) <=> ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(55,plain,
% 0.71/0.75 (![A: $i] : (one_sorted_str(A) => (cast_as_carrier_subset(A) = the_carrier(A))) <=> ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[54])).
% 0.71/0.75 tff(56,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')).
% 0.71/0.75 tff(57,plain,
% 0.71/0.75 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.71/0.75 tff(58,plain,
% 0.71/0.75 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.71/0.75 tff(59,plain,(
% 0.71/0.75 ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.71/0.75 inference(skolemize,[status(sab)],[58])).
% 0.71/0.75 tff(60,plain,
% 0.71/0.75 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.71/0.75 tff(61,plain,
% 0.71/0.75 (((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!276)) | (cast_as_carrier_subset(A!276) = the_carrier(A!276)))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!276)) | (cast_as_carrier_subset(A!276) = the_carrier(A!276)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(62,plain,
% 0.71/0.75 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!276)) | (cast_as_carrier_subset(A!276) = the_carrier(A!276)))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(63,plain,
% 0.71/0.75 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!276)) | (cast_as_carrier_subset(A!276) = the_carrier(A!276))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.71/0.75 tff(64,plain,
% 0.71/0.75 (cast_as_carrier_subset(A!276) = the_carrier(A!276)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[63, 60, 13])).
% 0.71/0.75 tff(65,plain,
% 0.71/0.75 (set_difference(cast_as_carrier_subset(A!276), B!277) = set_difference(the_carrier(A!276), B!277)),
% 0.71/0.75 inference(monotonicity,[status(thm)],[64])).
% 0.71/0.75 tff(66,plain,
% 0.71/0.75 (set_difference(the_carrier(A!276), B!277) = set_difference(cast_as_carrier_subset(A!276), B!277)),
% 0.71/0.75 inference(symmetry,[status(thm)],[65])).
% 0.71/0.75 tff(67,plain,
% 0.71/0.75 (^[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))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(68,plain,
% 0.71/0.75 (![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)))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[67])).
% 0.71/0.75 tff(69,plain,
% 0.71/0.75 (![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)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(70,plain,
% 0.71/0.75 (^[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))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(71,plain,
% 0.71/0.75 (![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)))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[70])).
% 0.71/0.75 tff(72,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')).
% 0.71/0.75 tff(73,plain,
% 0.71/0.75 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.71/0.75 tff(74,plain,
% 0.71/0.75 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.71/0.75 tff(75,plain,(
% 0.71/0.75 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.71/0.75 inference(skolemize,[status(sab)],[74])).
% 0.71/0.75 tff(76,plain,
% 0.71/0.75 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.71/0.75 tff(77,plain,
% 0.71/0.75 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!277, powerset(the_carrier(A!276)))) | (subset_complement(the_carrier(A!276), B!277) = set_difference(the_carrier(A!276), B!277)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!277, powerset(the_carrier(A!276)))) | (subset_complement(the_carrier(A!276), B!277) = set_difference(the_carrier(A!276), B!277)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(78,plain,
% 0.71/0.75 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!277, powerset(the_carrier(A!276)))) | (subset_complement(the_carrier(A!276), B!277) = set_difference(the_carrier(A!276), B!277)))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(79,plain,
% 0.71/0.75 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!277, powerset(the_carrier(A!276)))) | (subset_complement(the_carrier(A!276), B!277) = set_difference(the_carrier(A!276), B!277))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.71/0.75 tff(80,plain,
% 0.71/0.75 (subset_complement(the_carrier(A!276), B!277) = set_difference(the_carrier(A!276), B!277)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[79, 76, 29])).
% 0.71/0.75 tff(81,plain,
% 0.71/0.75 (subset_complement(the_carrier(A!276), B!277) = subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277)),
% 0.71/0.75 inference(transitivity,[status(thm)],[80, 66, 50])).
% 0.71/0.75 tff(82,plain,
% 0.71/0.75 (~(subset_complement(the_carrier(A!276), B!277) = subset_difference(the_carrier(A!276), cast_as_carrier_subset(A!276), B!277))),
% 0.79/0.77 inference(or_elim,[status(thm)],[28])).
% 0.79/0.77 tff(83,plain,
% 0.79/0.77 ($false),
% 0.79/0.77 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.79/0.77 % SZS output end Proof
%------------------------------------------------------------------------------