%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU309+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:34 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU309+1 : TPTP v9.0.0. Released v3.3.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 06:41:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(tptp_fun_B_6_type, type, (
% 0.12/0.39 tptp_fun_B_6: $i)).
% 0.12/0.39 tff(subset_difference_type, type, (
% 0.12/0.39 subset_difference: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(cast_as_carrier_subset_type, type, (
% 0.12/0.39 cast_as_carrier_subset: $i > $i)).
% 0.12/0.39 tff(tptp_fun_A_5_type, type, (
% 0.12/0.39 tptp_fun_A_5: $i)).
% 0.12/0.39 tff(the_carrier_type, type, (
% 0.12/0.39 the_carrier: $i > $i)).
% 0.12/0.39 tff(subset_intersection2_type, type, (
% 0.12/0.39 subset_intersection2: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(element_type, type, (
% 0.12/0.39 element: ( $i * $i ) > $o)).
% 0.12/0.39 tff(powerset_type, type, (
% 0.12/0.39 powerset: $i > $i)).
% 0.12/0.39 tff(one_sorted_str_type, type, (
% 0.12/0.39 one_sorted_str: $i > $o)).
% 0.12/0.39 tff(set_intersection2_type, type, (
% 0.12/0.39 set_intersection2: ( $i * $i ) > $i)).
% 0.12/0.39 tff(set_difference_type, type, (
% 0.12/0.39 set_difference: ( $i * $i ) > $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 ((~![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 ((~![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(3,axiom,(~![A: $i] : (one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t22_pre_topc')).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (~![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (~![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (~![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (~![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (one_sorted_str(A!5)),
% 0.12/0.39 inference(and_elim,[status(thm)],[7])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (^[A: $i] : refl(((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (^[A: $i] : rewrite(((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[12, 10])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)) <=> ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))), (![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))), ((one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))) <=> (one_sorted_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))))), rewrite((one_sorted_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))), ((one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![A: $i] : (one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.39 tff(17,axiom,(![A: $i] : (one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t15_pre_topc')).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.39 tff(20,plain,(
% 0.12/0.39 ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[19])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))) | ((~one_sorted_str(A!5)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B, cast_as_carrier_subset(A!5)) = B)))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))) | (~one_sorted_str(A!5)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B, cast_as_carrier_subset(A!5)) = B)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))) | ((~one_sorted_str(A!5)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B, cast_as_carrier_subset(A!5)) = B)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_intersection2(the_carrier(A), B, cast_as_carrier_subset(A)) = B)))) | (~one_sorted_str(A!5)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B, cast_as_carrier_subset(A!5)) = B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B, cast_as_carrier_subset(A!5)) = B))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[24, 21, 8])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (~((~element(B!6, powerset(the_carrier(A!5)))) | (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = B!6))),
% 0.12/0.40 inference(and_elim,[status(thm)],[7])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (element(B!6, powerset(the_carrier(A!5)))),
% 0.12/0.40 inference(or_elim,[status(thm)],[26])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B, cast_as_carrier_subset(A!5)) = B))) | ((~element(B!6, powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = B!6))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B, cast_as_carrier_subset(A!5)) = B))) | (~element(B!6, powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = B!6))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B, cast_as_carrier_subset(A!5)) = B))) | ((~element(B!6, powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = B!6))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B, cast_as_carrier_subset(A!5)) = B))) | (~element(B!6, powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = B!6)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = B!6),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[30, 27, 25])).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[32])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[35])).
% 0.12/0.40 tff(37,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')).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.12/0.40 tff(40,plain,(
% 0.12/0.40 ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[39])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!5)) | (cast_as_carrier_subset(A!5) = the_carrier(A!5)))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!5)) | (cast_as_carrier_subset(A!5) = the_carrier(A!5)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!5)) | (cast_as_carrier_subset(A!5) = the_carrier(A!5)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!5)) | (cast_as_carrier_subset(A!5) = the_carrier(A!5))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (cast_as_carrier_subset(A!5) = the_carrier(A!5)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[44, 41, 8])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5)) = subset_intersection2(the_carrier(A!5), B!6, the_carrier(A!5))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[45])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (subset_intersection2(the_carrier(A!5), B!6, the_carrier(A!5)) = subset_intersection2(the_carrier(A!5), B!6, cast_as_carrier_subset(A!5))),
% 0.12/0.40 inference(symmetry,[status(thm)],[46])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (the_carrier(A!5) = cast_as_carrier_subset(A!5)),
% 0.12/0.40 inference(symmetry,[status(thm)],[45])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (element(the_carrier(A!5), powerset(the_carrier(A!5))) <=> element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[48])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5))) <=> element(the_carrier(A!5), powerset(the_carrier(A!5)))),
% 0.12/0.40 inference(symmetry,[status(thm)],[49])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.12/0.40 tff(56,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')).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.12/0.40 tff(59,plain,(
% 0.12/0.40 ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[58])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!5)) | element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!5)) | element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!5)) | element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!5)) | element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[63, 60, 8])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (element(the_carrier(A!5), powerset(the_carrier(A!5)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[64, 50])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (^[A: $i, B: $i, C: $i] : refl(((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A)))) <=> ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A)))) <=> ![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[66])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((element(B, powerset(A)) & element(C, powerset(A))) <=> (~((~element(B, powerset(A))) | (~element(C, powerset(A)))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> (~(~((~element(B, powerset(A))) | (~element(C, powerset(A)))))))), rewrite((~(~((~element(B, powerset(A))) | (~element(C, powerset(A)))))) <=> ((~element(B, powerset(A))) | (~element(C, powerset(A))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> ((~element(B, powerset(A))) | (~element(C, powerset(A)))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> (((~element(B, powerset(A))) | (~element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))))), rewrite((((~element(B, powerset(A))) | (~element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 (^[A: $i, B: $i, C: $i] : rewrite(((element(B, powerset(A)) & element(C, powerset(A))) => (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.12/0.40 tff(73,axiom,(![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => (subset_intersection2(A, B, C) = set_intersection2(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k5_subset_1')).
% 0.12/0.40 tff(74,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.12/0.40 tff(75,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.12/0.40 tff(76,plain,(
% 0.12/0.40 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[75])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.12/0.40 tff(79,plain,
% 0.12/0.40 (((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | (~element(the_carrier(A!5), powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, the_carrier(A!5)) = set_intersection2(B!6, the_carrier(A!5))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(the_carrier(A!5), powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, the_carrier(A!5)) = set_intersection2(B!6, the_carrier(A!5))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 (((subset_intersection2(the_carrier(A!5), B!6, the_carrier(A!5)) = set_intersection2(B!6, the_carrier(A!5))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(the_carrier(A!5), powerset(the_carrier(A!5))))) <=> ((~element(B!6, powerset(the_carrier(A!5)))) | (~element(the_carrier(A!5), powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, the_carrier(A!5)) = set_intersection2(B!6, the_carrier(A!5))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(81,plain,
% 0.12/0.40 (((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((subset_intersection2(the_carrier(A!5), B!6, the_carrier(A!5)) = set_intersection2(B!6, the_carrier(A!5))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(the_carrier(A!5), powerset(the_carrier(A!5)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | (~element(the_carrier(A!5), powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, the_carrier(A!5)) = set_intersection2(B!6, the_carrier(A!5)))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[80])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 (((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((subset_intersection2(the_carrier(A!5), B!6, the_carrier(A!5)) = set_intersection2(B!6, the_carrier(A!5))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(the_carrier(A!5), powerset(the_carrier(A!5)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(the_carrier(A!5), powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, the_carrier(A!5)) = set_intersection2(B!6, the_carrier(A!5))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[81, 79])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((subset_intersection2(the_carrier(A!5), B!6, the_carrier(A!5)) = set_intersection2(B!6, the_carrier(A!5))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(the_carrier(A!5), powerset(the_carrier(A!5)))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(84,plain,
% 0.12/0.40 ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(the_carrier(A!5), powerset(the_carrier(A!5)))) | (subset_intersection2(the_carrier(A!5), B!6, the_carrier(A!5)) = set_intersection2(B!6, the_carrier(A!5)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 (subset_intersection2(the_carrier(A!5), B!6, the_carrier(A!5)) = set_intersection2(B!6, the_carrier(A!5))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[84, 78, 27, 65])).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 (set_intersection2(B!6, the_carrier(A!5)) = subset_intersection2(the_carrier(A!5), B!6, the_carrier(A!5))),
% 0.12/0.40 inference(symmetry,[status(thm)],[85])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[87])).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(90,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.12/0.40 tff(92,plain,(
% 0.12/0.40 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.40 inference(skolemize,[status(sab)],[91])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.12/0.40 tff(94,plain,
% 0.12/0.40 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(the_carrier(A!5), B!6) = set_intersection2(B!6, the_carrier(A!5)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 (set_intersection2(the_carrier(A!5), B!6) = set_intersection2(B!6, the_carrier(A!5))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.12/0.40 tff(96,plain,
% 0.12/0.40 (^[A: $i, B: $i] : refl((set_difference(A, set_difference(A, B)) = set_intersection2(A, B)) <=> (set_difference(A, set_difference(A, B)) = set_intersection2(A, B)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(97,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B)) <=> ![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[96])).
% 0.12/0.40 tff(98,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B)) <=> ![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(99,axiom,(![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t48_xboole_1')).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.12/0.40 tff(101,plain,(
% 0.12/0.40 ![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.12/0.40 inference(skolemize,[status(sab)],[100])).
% 0.12/0.40 tff(102,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.12/0.40 tff(103,plain,
% 0.12/0.40 ((~![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))) | (set_difference(the_carrier(A!5), set_difference(the_carrier(A!5), B!6)) = set_intersection2(the_carrier(A!5), B!6))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(104,plain,
% 0.12/0.40 (set_difference(the_carrier(A!5), set_difference(the_carrier(A!5), B!6)) = set_intersection2(the_carrier(A!5), B!6)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.12/0.40 tff(105,plain,
% 0.12/0.40 (^[A: $i, B: $i, C: $i] : refl(((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)) | (~element(B, powerset(A))) | (~element(C, powerset(A)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(106,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A)))) <=> ![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[105])).
% 0.12/0.40 tff(107,plain,
% 0.12/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((element(B, powerset(A)) & element(C, powerset(A))) <=> (~((~element(B, powerset(A))) | (~element(C, powerset(A)))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> (~(~((~element(B, powerset(A))) | (~element(C, powerset(A)))))))), rewrite((~(~((~element(B, powerset(A))) | (~element(C, powerset(A)))))) <=> ((~element(B, powerset(A))) | (~element(C, powerset(A))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> ((~element(B, powerset(A))) | (~element(C, powerset(A)))))), (((~(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))))), rewrite((((~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(B, powerset(A))) | (~element(C, 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(B, powerset(A))) | (~element(C, powerset(A))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(108,plain,
% 0.12/0.41 (![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(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[107])).
% 0.12/0.41 tff(109,plain,
% 0.12/0.41 (![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)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(110,plain,
% 0.12/0.41 (^[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))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(111,plain,
% 0.12/0.41 (![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)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[110])).
% 0.12/0.41 tff(112,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')).
% 0.12/0.41 tff(113,plain,
% 0.12/0.41 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.12/0.41 tff(114,plain,
% 0.12/0.41 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.12/0.41 tff(115,plain,(
% 0.12/0.41 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[114])).
% 0.12/0.41 tff(116,plain,
% 0.12/0.41 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.12/0.41 tff(117,plain,
% 0.12/0.41 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[116, 106])).
% 0.12/0.41 tff(118,plain,
% 0.12/0.41 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6) = set_difference(cast_as_carrier_subset(A!5), B!6)))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6) = set_difference(cast_as_carrier_subset(A!5), B!6)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 (((subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6) = set_difference(cast_as_carrier_subset(A!5), B!6)) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(B!6, powerset(the_carrier(A!5))))) <=> ((~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6) = set_difference(cast_as_carrier_subset(A!5), B!6)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6) = set_difference(cast_as_carrier_subset(A!5), B!6)) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(B!6, powerset(the_carrier(A!5)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6) = set_difference(cast_as_carrier_subset(A!5), B!6))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[119])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6) = set_difference(cast_as_carrier_subset(A!5), B!6)) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(B!6, powerset(the_carrier(A!5)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6) = set_difference(cast_as_carrier_subset(A!5), B!6)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[120, 118])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6) = set_difference(cast_as_carrier_subset(A!5), B!6)) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(B!6, powerset(the_carrier(A!5)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(B!6, powerset(the_carrier(A!5)))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6) = set_difference(cast_as_carrier_subset(A!5), B!6))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6) = set_difference(cast_as_carrier_subset(A!5), B!6)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[123, 117, 27, 64])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (set_difference(cast_as_carrier_subset(A!5), B!6) = subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)),
% 0.19/0.41 inference(symmetry,[status(thm)],[124])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (set_difference(the_carrier(A!5), B!6) = set_difference(cast_as_carrier_subset(A!5), B!6)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[48])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (set_difference(the_carrier(A!5), B!6) = subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)),
% 0.19/0.41 inference(transitivity,[status(thm)],[126, 125])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (set_difference(the_carrier(A!5), set_difference(the_carrier(A!5), B!6)) = set_difference(cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[48, 127])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (set_difference(cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = set_difference(the_carrier(A!5), set_difference(the_carrier(A!5), B!6))),
% 0.19/0.41 inference(symmetry,[status(thm)],[128])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : refl((element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A)))) <=> (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A)))) <=> ![A: $i, B: $i, C: $i] : (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((element(B, powerset(A)) & element(C, powerset(A))) <=> (~((~element(B, powerset(A))) | (~element(C, powerset(A)))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> (~(~((~element(B, powerset(A))) | (~element(C, powerset(A)))))))), rewrite((~(~((~element(B, powerset(A))) | (~element(C, powerset(A)))))) <=> ((~element(B, powerset(A))) | (~element(C, powerset(A))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> ((~element(B, powerset(A))) | (~element(C, powerset(A)))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | element(subset_difference(A, B, C), powerset(A))) <=> (((~element(B, powerset(A))) | (~element(C, powerset(A)))) | element(subset_difference(A, B, C), powerset(A))))), rewrite((((~element(B, powerset(A))) | (~element(C, powerset(A)))) | element(subset_difference(A, B, C), powerset(A))) <=> (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | element(subset_difference(A, B, C), powerset(A))) <=> (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | element(subset_difference(A, B, C), powerset(A))) <=> ![A: $i, B: $i, C: $i] : (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[132])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | element(subset_difference(A, B, C), powerset(A))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | element(subset_difference(A, B, C), powerset(A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : rewrite(((element(B, powerset(A)) & element(C, powerset(A))) => element(subset_difference(A, B, C), powerset(A))) <=> ((~(element(B, powerset(A)) & element(C, powerset(A)))) | element(subset_difference(A, B, C), powerset(A))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(136,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => element(subset_difference(A, B, C), powerset(A))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | element(subset_difference(A, B, C), powerset(A)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[135])).
% 0.19/0.41 tff(137,axiom,(![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => element(subset_difference(A, B, C), powerset(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_subset_1')).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | element(subset_difference(A, B, C), powerset(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.41 tff(139,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | element(subset_difference(A, B, C), powerset(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.19/0.41 tff(140,plain,(
% 0.19/0.41 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | element(subset_difference(A, B, C), powerset(A)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[139])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.19/0.41 tff(142,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.19/0.41 tff(143,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i] : (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))))) <=> ((~![A: $i, B: $i, C: $i] : (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(B!6, powerset(the_carrier(A!5)))) | element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 ((element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(B!6, powerset(the_carrier(A!5))))) <=> ((~element(B!6, powerset(the_carrier(A!5)))) | element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i] : (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(B!6, powerset(the_carrier(A!5)))))) <=> ((~![A: $i, B: $i, C: $i] : (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[144])).
% 0.19/0.41 tff(146,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i] : (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(B!6, powerset(the_carrier(A!5)))))) <=> ((~![A: $i, B: $i, C: $i] : (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(B!6, powerset(the_carrier(A!5)))) | element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[145, 143])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i] : (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(B!6, powerset(the_carrier(A!5)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i] : (element(subset_difference(A, B, C), powerset(A)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(B!6, powerset(the_carrier(A!5)))) | element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 (element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[148, 142, 27, 64])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5)))) | (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = set_difference(cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5)))) | (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = set_difference(cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 (((subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = set_difference(cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5))))) <=> ((~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5)))) | (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = set_difference(cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = set_difference(cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5)))) | (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = set_difference(cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[151])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = set_difference(cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5)))) | (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = set_difference(cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[152, 150])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | ((subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = set_difference(cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(B, powerset(A))) | (~element(C, powerset(A))))) | (~element(cast_as_carrier_subset(A!5), powerset(the_carrier(A!5)))) | (~element(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6), powerset(the_carrier(A!5)))) | (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = set_difference(cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = set_difference(cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[155, 117, 64, 149])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 (subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = B!6),
% 0.19/0.42 inference(transitivity,[status(thm)],[156, 129, 104, 95, 86, 47, 31])).
% 0.19/0.42 tff(158,plain,
% 0.19/0.42 (~(subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), subset_difference(the_carrier(A!5), cast_as_carrier_subset(A!5), B!6)) = B!6)),
% 0.19/0.42 inference(or_elim,[status(thm)],[26])).
% 0.19/0.42 tff(159,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------