%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU308+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:33 AM UTC 2025
% Result : Theorem 0.54s 0.73s
% Output : Proof 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU308+2 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:43:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.54/0.73 % SZS status Theorem
% 0.54/0.73 % SZS output start Proof
% 0.54/0.73 tff(subset_difference_type, type, (
% 0.54/0.73 subset_difference: ( $i * $i * $i ) > $i)).
% 0.54/0.73 tff(tptp_fun_B_206_type, type, (
% 0.54/0.73 tptp_fun_B_206: $i)).
% 0.54/0.73 tff(cast_as_carrier_subset_type, type, (
% 0.54/0.73 cast_as_carrier_subset: $i > $i)).
% 0.54/0.73 tff(tptp_fun_A_205_type, type, (
% 0.54/0.73 tptp_fun_A_205: $i)).
% 0.54/0.73 tff(the_carrier_type, type, (
% 0.54/0.73 the_carrier: $i > $i)).
% 0.54/0.73 tff(subset_complement_type, type, (
% 0.54/0.73 subset_complement: ( $i * $i ) > $i)).
% 0.54/0.73 tff(set_difference_type, type, (
% 0.54/0.73 set_difference: ( $i * $i ) > $i)).
% 0.54/0.73 tff(element_type, type, (
% 0.54/0.73 element: ( $i * $i ) > $o)).
% 0.54/0.73 tff(powerset_type, type, (
% 0.54/0.73 powerset: $i > $i)).
% 0.54/0.73 tff(one_sorted_str_type, type, (
% 0.54/0.73 one_sorted_str: $i > $o)).
% 0.54/0.73 tff(1,plain,
% 0.54/0.73 ((~![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)))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(2,plain,
% 0.54/0.73 ((~![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)))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(3,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')).
% 0.54/0.73 tff(4,plain,
% 0.54/0.73 (~![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))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.54/0.73 tff(5,plain,
% 0.54/0.73 (~![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))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.54/0.73 tff(6,plain,
% 0.54/0.73 (~![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))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.54/0.73 tff(7,plain,
% 0.54/0.73 (~![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))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.54/0.73 tff(8,plain,
% 0.54/0.73 (one_sorted_str(A!205)),
% 0.54/0.73 inference(and_elim,[status(thm)],[7])).
% 0.54/0.73 tff(9,plain,
% 0.54/0.73 (^[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)))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(10,plain,
% 0.54/0.73 (![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))))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[9])).
% 0.54/0.73 tff(11,plain,
% 0.54/0.73 (![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))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(12,plain,
% 0.54/0.73 (^[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)))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(13,plain,
% 0.54/0.73 (![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))))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[12])).
% 0.54/0.73 tff(14,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')).
% 0.54/0.73 tff(15,plain,
% 0.54/0.73 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.54/0.73 tff(16,plain,
% 0.54/0.73 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.54/0.73 tff(17,plain,(
% 0.54/0.73 ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.54/0.73 inference(skolemize,[status(sab)],[16])).
% 0.54/0.73 tff(18,plain,
% 0.54/0.73 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.54/0.73 tff(19,plain,
% 0.54/0.73 (((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!205)) | element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!205)) | element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(20,plain,
% 0.54/0.73 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!205)) | element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205))))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(21,plain,
% 0.54/0.73 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!205)) | element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.54/0.73 tff(22,plain,
% 0.54/0.73 (element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205)))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[21, 18, 8])).
% 0.54/0.73 tff(23,plain,
% 0.54/0.73 (~((~element(B!206, powerset(the_carrier(A!205)))) | (subset_complement(the_carrier(A!205), B!206) = subset_difference(the_carrier(A!205), cast_as_carrier_subset(A!205), B!206)))),
% 0.54/0.73 inference(and_elim,[status(thm)],[7])).
% 0.54/0.73 tff(24,plain,
% 0.54/0.73 (element(B!206, powerset(the_carrier(A!205)))),
% 0.54/0.73 inference(or_elim,[status(thm)],[23])).
% 0.54/0.73 tff(25,plain,
% 0.54/0.73 (^[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)))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(26,plain,
% 0.54/0.73 (![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))))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[25])).
% 0.54/0.73 tff(27,plain,
% 0.54/0.73 (^[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))))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(28,plain,
% 0.54/0.73 (![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))))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[27])).
% 0.54/0.73 tff(29,plain,
% 0.54/0.73 (![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)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(30,plain,
% 0.54/0.73 (^[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))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(31,plain,
% 0.54/0.73 (![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)))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[30])).
% 0.54/0.73 tff(32,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')).
% 0.54/0.73 tff(33,plain,
% 0.54/0.73 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.54/0.73 tff(34,plain,
% 0.54/0.73 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.54/0.73 tff(35,plain,(
% 0.54/0.73 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 0.54/0.73 inference(skolemize,[status(sab)],[34])).
% 0.54/0.73 tff(36,plain,
% 0.54/0.73 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.54/0.73 tff(37,plain,
% 0.54/0.73 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.54/0.73 tff(38,plain,
% 0.54/0.73 (((~![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!206, powerset(the_carrier(A!205)))) | (~element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205)))) | (subset_difference(the_carrier(A!205), cast_as_carrier_subset(A!205), B!206) = set_difference(cast_as_carrier_subset(A!205), B!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!206, powerset(the_carrier(A!205)))) | (~element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205)))) | (subset_difference(the_carrier(A!205), cast_as_carrier_subset(A!205), B!206) = set_difference(cast_as_carrier_subset(A!205), B!206)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(39,plain,
% 0.54/0.73 (((subset_difference(the_carrier(A!205), cast_as_carrier_subset(A!205), B!206) = set_difference(cast_as_carrier_subset(A!205), B!206)) | (~element(B!206, powerset(the_carrier(A!205)))) | (~element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205))))) <=> ((~element(B!206, powerset(the_carrier(A!205)))) | (~element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205)))) | (subset_difference(the_carrier(A!205), cast_as_carrier_subset(A!205), B!206) = set_difference(cast_as_carrier_subset(A!205), B!206)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(40,plain,
% 0.54/0.73 (((~![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!205), cast_as_carrier_subset(A!205), B!206) = set_difference(cast_as_carrier_subset(A!205), B!206)) | (~element(B!206, powerset(the_carrier(A!205)))) | (~element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205)))))) <=> ((~![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!206, powerset(the_carrier(A!205)))) | (~element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205)))) | (subset_difference(the_carrier(A!205), cast_as_carrier_subset(A!205), B!206) = set_difference(cast_as_carrier_subset(A!205), B!206))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[39])).
% 0.54/0.73 tff(41,plain,
% 0.54/0.73 (((~![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!205), cast_as_carrier_subset(A!205), B!206) = set_difference(cast_as_carrier_subset(A!205), B!206)) | (~element(B!206, powerset(the_carrier(A!205)))) | (~element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205)))))) <=> ((~![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!206, powerset(the_carrier(A!205)))) | (~element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205)))) | (subset_difference(the_carrier(A!205), cast_as_carrier_subset(A!205), B!206) = set_difference(cast_as_carrier_subset(A!205), B!206)))),
% 0.54/0.73 inference(transitivity,[status(thm)],[40, 38])).
% 0.54/0.73 tff(42,plain,
% 0.54/0.73 ((~![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!205), cast_as_carrier_subset(A!205), B!206) = set_difference(cast_as_carrier_subset(A!205), B!206)) | (~element(B!206, powerset(the_carrier(A!205)))) | (~element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205)))))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(43,plain,
% 0.54/0.73 ((~![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!206, powerset(the_carrier(A!205)))) | (~element(cast_as_carrier_subset(A!205), powerset(the_carrier(A!205)))) | (subset_difference(the_carrier(A!205), cast_as_carrier_subset(A!205), B!206) = set_difference(cast_as_carrier_subset(A!205), B!206))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.54/0.73 tff(44,plain,
% 0.54/0.73 (subset_difference(the_carrier(A!205), cast_as_carrier_subset(A!205), B!206) = set_difference(cast_as_carrier_subset(A!205), B!206)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[43, 37, 24, 22])).
% 0.54/0.73 tff(45,plain,
% 0.54/0.73 (set_difference(cast_as_carrier_subset(A!205), B!206) = subset_difference(the_carrier(A!205), cast_as_carrier_subset(A!205), B!206)),
% 0.54/0.73 inference(symmetry,[status(thm)],[44])).
% 0.54/0.73 tff(46,plain,
% 0.54/0.73 (^[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))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(47,plain,
% 0.54/0.73 (![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)))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[46])).
% 0.54/0.73 tff(48,plain,
% 0.54/0.73 (![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)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(49,plain,
% 0.54/0.73 (^[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))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(50,plain,
% 0.54/0.73 (![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)))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[49])).
% 0.54/0.73 tff(51,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')).
% 0.54/0.73 tff(52,plain,
% 0.54/0.73 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.54/0.73 tff(53,plain,
% 0.54/0.73 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.54/0.73 tff(54,plain,(
% 0.54/0.73 ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.54/0.73 inference(skolemize,[status(sab)],[53])).
% 0.54/0.73 tff(55,plain,
% 0.54/0.73 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.54/0.73 tff(56,plain,
% 0.54/0.73 (((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!205)) | (cast_as_carrier_subset(A!205) = the_carrier(A!205)))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!205)) | (cast_as_carrier_subset(A!205) = the_carrier(A!205)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(57,plain,
% 0.54/0.73 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!205)) | (cast_as_carrier_subset(A!205) = the_carrier(A!205)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(58,plain,
% 0.54/0.73 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!205)) | (cast_as_carrier_subset(A!205) = the_carrier(A!205))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.54/0.73 tff(59,plain,
% 0.54/0.73 (cast_as_carrier_subset(A!205) = the_carrier(A!205)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[58, 55, 8])).
% 0.54/0.73 tff(60,plain,
% 0.54/0.73 (set_difference(cast_as_carrier_subset(A!205), B!206) = set_difference(the_carrier(A!205), B!206)),
% 0.54/0.73 inference(monotonicity,[status(thm)],[59])).
% 0.54/0.73 tff(61,plain,
% 0.54/0.73 (set_difference(the_carrier(A!205), B!206) = set_difference(cast_as_carrier_subset(A!205), B!206)),
% 0.54/0.73 inference(symmetry,[status(thm)],[60])).
% 0.54/0.73 tff(62,plain,
% 0.54/0.73 (^[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))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(63,plain,
% 0.54/0.73 (![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)))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[62])).
% 0.54/0.73 tff(64,plain,
% 0.54/0.73 (![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)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(65,plain,
% 0.54/0.73 (^[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))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(66,plain,
% 0.54/0.73 (![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)))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[65])).
% 0.54/0.76 tff(67,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')).
% 0.54/0.76 tff(68,plain,
% 0.54/0.76 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.54/0.76 tff(69,plain,
% 0.54/0.76 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.54/0.76 tff(70,plain,(
% 0.54/0.76 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.54/0.76 inference(skolemize,[status(sab)],[69])).
% 0.54/0.76 tff(71,plain,
% 0.54/0.76 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.54/0.76 tff(72,plain,
% 0.54/0.76 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!206, powerset(the_carrier(A!205)))) | (subset_complement(the_carrier(A!205), B!206) = set_difference(the_carrier(A!205), B!206)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!206, powerset(the_carrier(A!205)))) | (subset_complement(the_carrier(A!205), B!206) = set_difference(the_carrier(A!205), B!206)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(73,plain,
% 0.54/0.76 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!206, powerset(the_carrier(A!205)))) | (subset_complement(the_carrier(A!205), B!206) = set_difference(the_carrier(A!205), B!206)))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(74,plain,
% 0.54/0.76 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!206, powerset(the_carrier(A!205)))) | (subset_complement(the_carrier(A!205), B!206) = set_difference(the_carrier(A!205), B!206))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.54/0.76 tff(75,plain,
% 0.54/0.76 (subset_complement(the_carrier(A!205), B!206) = set_difference(the_carrier(A!205), B!206)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[74, 71, 24])).
% 0.54/0.76 tff(76,plain,
% 0.54/0.76 (subset_complement(the_carrier(A!205), B!206) = subset_difference(the_carrier(A!205), cast_as_carrier_subset(A!205), B!206)),
% 0.54/0.76 inference(transitivity,[status(thm)],[75, 61, 45])).
% 0.54/0.76 tff(77,plain,
% 0.54/0.76 (~(subset_complement(the_carrier(A!205), B!206) = subset_difference(the_carrier(A!205), cast_as_carrier_subset(A!205), B!206))),
% 0.54/0.76 inference(or_elim,[status(thm)],[23])).
% 0.54/0.76 tff(78,plain,
% 0.54/0.76 ($false),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.54/0.76 % SZS output end Proof
% 0.54/0.76 % E exiting
%------------------------------------------------------------------------------