TSTP Solution File: SEU171+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU171+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 07:27:58 EDT 2022
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU171+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 10:13:33 EDT 2022
% 0.21/0.35 % CPUTime :
% 0.21/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.36 Usage: tptp [options] [-file:]file
% 0.21/0.36 -h, -? prints this message.
% 0.21/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.36 -m, -model generate model.
% 0.21/0.36 -p, -proof generate proof.
% 0.21/0.36 -c, -core generate unsat core of named formulas.
% 0.21/0.36 -st, -statistics display statistics.
% 0.21/0.36 -t:timeout set timeout (in second).
% 0.21/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.36 -<param>:<value> configuration parameter and value.
% 0.21/0.36 -o:<output-file> file to place output in.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 tff(empty_type, type, (
% 0.21/0.45 empty: $i > $o)).
% 0.21/0.45 tff(set_difference_type, type, (
% 0.21/0.45 set_difference: ( $i * $i ) > $i)).
% 0.21/0.45 tff(tptp_fun_B_4_type, type, (
% 0.21/0.45 tptp_fun_B_4: $i > $i)).
% 0.21/0.45 tff(tptp_fun_A_6_type, type, (
% 0.21/0.45 tptp_fun_A_6: $i)).
% 0.21/0.45 tff(empty_set_type, type, (
% 0.21/0.45 empty_set: $i)).
% 0.21/0.45 tff(tptp_fun_A_3_type, type, (
% 0.21/0.45 tptp_fun_A_3: $i)).
% 0.21/0.45 tff(element_type, type, (
% 0.21/0.45 element: ( $i * $i ) > $o)).
% 0.21/0.45 tff(powerset_type, type, (
% 0.21/0.45 powerset: $i > $i)).
% 0.21/0.45 tff(in_type, type, (
% 0.21/0.45 in: ( $i * $i ) > $o)).
% 0.21/0.45 tff(tptp_fun_C_8_type, type, (
% 0.21/0.45 tptp_fun_C_8: $i)).
% 0.21/0.45 tff(tptp_fun_B_7_type, type, (
% 0.21/0.45 tptp_fun_B_7: $i)).
% 0.21/0.45 tff(tptp_fun_D_0_type, type, (
% 0.21/0.45 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(subset_complement_type, type, (
% 0.21/0.45 subset_complement: ( $i * $i ) > $i)).
% 0.21/0.45 tff(1,plain,
% 0.21/0.45 (^[A: $i] : refl((set_difference(A, empty_set) = A) <=> (set_difference(A, empty_set) = A))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(2,plain,
% 0.21/0.45 (![A: $i] : (set_difference(A, empty_set) = A) <=> ![A: $i] : (set_difference(A, empty_set) = A)),
% 0.21/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.45 tff(3,plain,
% 0.21/0.45 (![A: $i] : (set_difference(A, empty_set) = A) <=> ![A: $i] : (set_difference(A, empty_set) = A)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(4,axiom,(![A: $i] : (set_difference(A, empty_set) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_boole')).
% 0.21/0.45 tff(5,plain,
% 0.21/0.45 (![A: $i] : (set_difference(A, empty_set) = A)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.45 tff(6,plain,(
% 0.21/0.45 ![A: $i] : (set_difference(A, empty_set) = A)),
% 0.21/0.45 inference(skolemize,[status(sab)],[5])).
% 0.21/0.45 tff(7,plain,
% 0.21/0.45 (![A: $i] : (set_difference(A, empty_set) = A)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.45 tff(8,plain,
% 0.21/0.45 ((~![A: $i] : (set_difference(A, empty_set) = A)) | (set_difference(A!6, empty_set) = A!6)),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(9,plain,
% 0.21/0.45 (set_difference(A!6, empty_set) = A!6),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.45 tff(10,plain,
% 0.21/0.45 (^[A: $i] : refl((~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A))))) <=> (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(11,plain,
% 0.21/0.45 (![A: $i] : (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A))))) <=> ![A: $i] : (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.45 tff(12,plain,
% 0.21/0.45 (^[A: $i] : rewrite((element(tptp_fun_B_4(A), powerset(A)) & empty(tptp_fun_B_4(A))) <=> (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(13,plain,
% 0.21/0.45 (![A: $i] : (element(tptp_fun_B_4(A), powerset(A)) & empty(tptp_fun_B_4(A))) <=> ![A: $i] : (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.45 tff(14,plain,
% 0.21/0.45 (![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B)) <=> ![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(15,axiom,(![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc2_subset_1')).
% 0.21/0.45 tff(16,plain,
% 0.21/0.45 (![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.45 tff(17,plain,(
% 0.21/0.45 ![A: $i] : (element(tptp_fun_B_4(A), powerset(A)) & empty(tptp_fun_B_4(A)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[16])).
% 0.21/0.45 tff(18,plain,
% 0.21/0.45 (![A: $i] : (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 (![A: $i] : (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.45 tff(20,plain,
% 0.21/0.45 ((~![A: $i] : (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A)))))) | (~((~element(tptp_fun_B_4(A!6), powerset(A!6))) | (~empty(tptp_fun_B_4(A!6)))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(21,plain,
% 0.21/0.45 (~((~element(tptp_fun_B_4(A!6), powerset(A!6))) | (~empty(tptp_fun_B_4(A!6))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.21/0.45 tff(22,plain,
% 0.21/0.45 (((~element(tptp_fun_B_4(A!6), powerset(A!6))) | (~empty(tptp_fun_B_4(A!6)))) | empty(tptp_fun_B_4(A!6))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(23,plain,
% 0.21/0.45 (empty(tptp_fun_B_4(A!6))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.21/0.45 tff(24,plain,
% 0.21/0.45 (^[A: $i, B: $i] : refl(((~empty(A)) | (~empty(B)) | (A = B)) <=> ((~empty(A)) | (~empty(B)) | (A = B)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(25,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B)) <=> ![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.45 tff(26,plain,
% 0.21/0.45 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((~empty(A)) | (~empty(B)) | (A = B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((~empty(A)) | (~empty(B)) | (A = B)))))), rewrite((~(~((~empty(A)) | (~empty(B)) | (A = B)))) <=> ((~empty(A)) | (~empty(B)) | (A = B))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((~empty(A)) | (~empty(B)) | (A = B))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(27,plain,
% 0.21/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.45 tff(28,plain,
% 0.21/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(29,plain,
% 0.21/0.45 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(30,plain,
% 0.21/0.45 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.45 tff(31,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 0.21/0.45 tff(32,plain,
% 0.21/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.45 tff(33,plain,
% 0.21/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.21/0.45 tff(34,plain,(
% 0.21/0.45 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[33])).
% 0.21/0.45 tff(35,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.21/0.45 tff(36,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.21/0.45 tff(37,plain,
% 0.21/0.45 (?[A: $i] : empty(A) <=> ?[A: $i] : empty(A)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(38,axiom,(?[A: $i] : empty(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc1_xboole_0')).
% 0.21/0.45 tff(39,plain,
% 0.21/0.45 (?[A: $i] : empty(A)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.45 tff(40,plain,(
% 0.21/0.45 empty(A!3)),
% 0.21/0.45 inference(skolemize,[status(sab)],[39])).
% 0.21/0.45 tff(41,plain,
% 0.21/0.45 (((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(A!3)) | (~empty(tptp_fun_B_4(A!6))) | (A!3 = tptp_fun_B_4(A!6)))) <=> ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(A!3)) | (~empty(tptp_fun_B_4(A!6))) | (A!3 = tptp_fun_B_4(A!6)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(42,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(A!3)) | (~empty(tptp_fun_B_4(A!6))) | (A!3 = tptp_fun_B_4(A!6)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(43,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(A!3)) | (~empty(tptp_fun_B_4(A!6))) | (A!3 = tptp_fun_B_4(A!6))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.45 tff(44,plain,
% 0.21/0.45 (A!3 = tptp_fun_B_4(A!6)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[43, 40, 36, 23])).
% 0.21/0.45 tff(45,plain,
% 0.21/0.45 (empty(empty_set) <=> empty(empty_set)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(46,axiom,(empty(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.21/0.45 tff(47,plain,
% 0.21/0.45 (empty(empty_set)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.45 tff(48,plain,
% 0.21/0.45 (((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(empty_set)) | (~empty(A!3)) | (empty_set = A!3))) <=> ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(empty_set)) | (~empty(A!3)) | (empty_set = A!3))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(49,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(empty_set)) | (~empty(A!3)) | (empty_set = A!3))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(50,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(empty_set)) | (~empty(A!3)) | (empty_set = A!3)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.45 tff(51,plain,
% 0.21/0.45 (empty_set = A!3),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[50, 47, 40, 36])).
% 0.21/0.45 tff(52,plain,
% 0.21/0.45 (empty_set = tptp_fun_B_4(A!6)),
% 0.21/0.45 inference(transitivity,[status(thm)],[51, 44])).
% 0.21/0.45 tff(53,plain,
% 0.21/0.45 (set_difference(A!6, empty_set) = set_difference(A!6, tptp_fun_B_4(A!6))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[52])).
% 0.21/0.45 tff(54,plain,
% 0.21/0.45 (set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(A!6, empty_set)),
% 0.21/0.45 inference(symmetry,[status(thm)],[53])).
% 0.21/0.45 tff(55,plain,
% 0.21/0.45 (set_difference(A!6, tptp_fun_B_4(A!6)) = A!6),
% 0.21/0.45 inference(transitivity,[status(thm)],[54, 9])).
% 0.21/0.45 tff(56,plain,
% 0.21/0.45 (empty(set_difference(A!6, tptp_fun_B_4(A!6))) <=> empty(A!6)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[55])).
% 0.21/0.45 tff(57,plain,
% 0.21/0.45 (empty(A!6) <=> empty(set_difference(A!6, tptp_fun_B_4(A!6)))),
% 0.21/0.45 inference(symmetry,[status(thm)],[56])).
% 0.21/0.45 tff(58,plain,
% 0.21/0.45 (^[A: $i, B: $i] : refl((~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))) <=> (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(59,plain,
% 0.21/0.45 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))) <=> ![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.45 tff(60,plain,
% 0.21/0.45 (^[A: $i, B: $i] : rewrite(((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(61,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(63,plain,
% 0.21/0.45 (^[A: $i, B: $i] : rewrite((((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B)))) <=> ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(64,plain,
% 0.21/0.45 (![A: $i, B: $i] : (((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.45 tff(65,axiom,(![A: $i, B: $i] : (((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_subset_1')).
% 0.21/0.45 tff(66,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.45 tff(68,plain,(
% 0.21/0.45 ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[67])).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))) | (~((~(empty(A!6) | (element(C!8, A!6) <=> in(C!8, A!6)))) | (~((~empty(A!6)) | (element(C!8, A!6) <=> empty(C!8))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 (~((~(empty(A!6) | (element(C!8, A!6) <=> in(C!8, A!6)))) | (~((~empty(A!6)) | (element(C!8, A!6) <=> empty(C!8)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 (((~(empty(A!6) | (element(C!8, A!6) <=> in(C!8, A!6)))) | (~((~empty(A!6)) | (element(C!8, A!6) <=> empty(C!8))))) | (empty(A!6) | (element(C!8, A!6) <=> in(C!8, A!6)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 (empty(A!6) | (element(C!8, A!6) <=> in(C!8, A!6))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[75])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))),
% 0.21/0.45 inference(pull_quant,[status(thm)],[])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B))))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[78])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[79, 77])).
% 0.21/0.46 tff(81,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[80, 76])).
% 0.21/0.46 tff(82,plain,
% 0.21/0.46 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(83,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[82])).
% 0.21/0.46 tff(84,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[83, 81])).
% 0.21/0.46 tff(85,plain,
% 0.21/0.46 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))), rewrite(((C = set_difference(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(C, B, A), B))))) <=> ((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(C, B, A), B)))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) & ((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) & ((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(C, B, A), B)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(86,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[85])).
% 0.21/0.46 tff(87,plain,
% 0.21/0.46 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(C, B, A), B)))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(88,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(C, B, A), B))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[87])).
% 0.21/0.46 tff(89,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(90,axiom,(![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_xboole_0')).
% 0.21/0.46 tff(91,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.46 tff(92,plain,(
% 0.21/0.46 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(C, B, A), B)))))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[91])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(C, B, A), B))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.21/0.46 tff(94,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.21/0.46 tff(95,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[94, 84])).
% 0.21/0.46 tff(96,plain,
% 0.21/0.46 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))) | ((~in(C!8, set_difference(A!6, B!7))) <=> ((~in(C!8, A!6)) | in(C!8, B!7)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))) | ((~in(C!8, set_difference(A!6, B!7))) <=> ((~in(C!8, A!6)) | in(C!8, B!7))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(97,plain,
% 0.21/0.46 ((~(in(C!8, set_difference(A!6, B!7)) <=> ((~in(C!8, A!6)) | in(C!8, B!7)))) <=> ((~in(C!8, set_difference(A!6, B!7))) <=> ((~in(C!8, A!6)) | in(C!8, B!7)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(98,plain,
% 0.21/0.46 (((in(C!8, set_difference(A!6, B!7)) <=> ((~in(C!8, A!6)) | in(C!8, B!7))) | $false) <=> (in(C!8, set_difference(A!6, B!7)) <=> ((~in(C!8, A!6)) | in(C!8, B!7)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(99,plain,
% 0.21/0.46 ((~$true) <=> $false),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(100,plain,
% 0.21/0.46 (($true | (in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), set_difference(A!6, B!7)) <=> ((~in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), A!6)) | in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), B!7)))) <=> $true),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(101,plain,
% 0.21/0.46 ((set_difference(A!6, B!7) = set_difference(A!6, B!7)) <=> $true),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(102,plain,
% 0.21/0.46 (((set_difference(A!6, B!7) = set_difference(A!6, B!7)) | (in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), set_difference(A!6, B!7)) <=> ((~in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), A!6)) | in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), B!7)))) <=> ($true | (in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), set_difference(A!6, B!7)) <=> ((~in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), A!6)) | in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), B!7))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[101])).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 (((set_difference(A!6, B!7) = set_difference(A!6, B!7)) | (in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), set_difference(A!6, B!7)) <=> ((~in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), A!6)) | in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), B!7)))) <=> $true),
% 0.21/0.46 inference(transitivity,[status(thm)],[102, 100])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 ((~((set_difference(A!6, B!7) = set_difference(A!6, B!7)) | (in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), set_difference(A!6, B!7)) <=> ((~in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), A!6)) | in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), B!7))))) <=> (~$true)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[103])).
% 0.21/0.46 tff(105,plain,
% 0.21/0.46 ((~((set_difference(A!6, B!7) = set_difference(A!6, B!7)) | (in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), set_difference(A!6, B!7)) <=> ((~in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), A!6)) | in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), B!7))))) <=> $false),
% 0.21/0.46 inference(transitivity,[status(thm)],[104, 99])).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 ((~(in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7))))) <=> (in(C!8, set_difference(A!6, B!7)) <=> ((~in(C!8, A!6)) | in(C!8, B!7)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 (($false | (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7))))) <=> (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 ((~(set_difference(A!6, B!7) = set_difference(A!6, B!7))) <=> (~$true)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[101])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 ((~(set_difference(A!6, B!7) = set_difference(A!6, B!7))) <=> $false),
% 0.21/0.46 inference(transitivity,[status(thm)],[108, 99])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 (((~(set_difference(A!6, B!7) = set_difference(A!6, B!7))) | (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7))))) <=> ($false | (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[109])).
% 0.21/0.47 tff(111,plain,
% 0.21/0.47 (((~(set_difference(A!6, B!7) = set_difference(A!6, B!7))) | (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7))))) <=> (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[110, 107])).
% 0.21/0.47 tff(112,plain,
% 0.21/0.47 ((~((~(set_difference(A!6, B!7) = set_difference(A!6, B!7))) | (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7)))))) <=> (~(in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[111])).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 ((~((~(set_difference(A!6, B!7) = set_difference(A!6, B!7))) | (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7)))))) <=> (in(C!8, set_difference(A!6, B!7)) <=> ((~in(C!8, A!6)) | in(C!8, B!7)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[112, 106])).
% 0.21/0.47 tff(114,plain,
% 0.21/0.47 (((~((~(set_difference(A!6, B!7) = set_difference(A!6, B!7))) | (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7)))))) | (~((set_difference(A!6, B!7) = set_difference(A!6, B!7)) | (in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), set_difference(A!6, B!7)) <=> ((~in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), A!6)) | in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), B!7)))))) <=> ((in(C!8, set_difference(A!6, B!7)) <=> ((~in(C!8, A!6)) | in(C!8, B!7))) | $false)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[113, 105])).
% 0.21/0.47 tff(115,plain,
% 0.21/0.47 (((~((~(set_difference(A!6, B!7) = set_difference(A!6, B!7))) | (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7)))))) | (~((set_difference(A!6, B!7) = set_difference(A!6, B!7)) | (in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), set_difference(A!6, B!7)) <=> ((~in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), A!6)) | in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), B!7)))))) <=> (in(C!8, set_difference(A!6, B!7)) <=> ((~in(C!8, A!6)) | in(C!8, B!7)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[114, 98])).
% 0.21/0.47 tff(116,plain,
% 0.21/0.47 ((~((~((~(set_difference(A!6, B!7) = set_difference(A!6, B!7))) | (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7)))))) | (~((set_difference(A!6, B!7) = set_difference(A!6, B!7)) | (in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), set_difference(A!6, B!7)) <=> ((~in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), A!6)) | in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), B!7))))))) <=> (~(in(C!8, set_difference(A!6, B!7)) <=> ((~in(C!8, A!6)) | in(C!8, B!7))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[115])).
% 0.21/0.47 tff(117,plain,
% 0.21/0.47 ((~((~((~(set_difference(A!6, B!7) = set_difference(A!6, B!7))) | (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7)))))) | (~((set_difference(A!6, B!7) = set_difference(A!6, B!7)) | (in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), set_difference(A!6, B!7)) <=> ((~in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), A!6)) | in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), B!7))))))) <=> ((~in(C!8, set_difference(A!6, B!7))) <=> ((~in(C!8, A!6)) | in(C!8, B!7)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[116, 97])).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))) | (~((~((~(set_difference(A!6, B!7) = set_difference(A!6, B!7))) | (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7)))))) | (~((set_difference(A!6, B!7) = set_difference(A!6, B!7)) | (in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), set_difference(A!6, B!7)) <=> ((~in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), A!6)) | in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), B!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))) | ((~in(C!8, set_difference(A!6, B!7))) <=> ((~in(C!8, A!6)) | in(C!8, B!7))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))) | (~((~((~(set_difference(A!6, B!7) = set_difference(A!6, B!7))) | (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7)))))) | (~((set_difference(A!6, B!7) = set_difference(A!6, B!7)) | (in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), set_difference(A!6, B!7)) <=> ((~in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), A!6)) | in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), B!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))) | ((~in(C!8, set_difference(A!6, B!7))) <=> ((~in(C!8, A!6)) | in(C!8, B!7))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[118, 96])).
% 0.21/0.47 tff(120,plain,
% 0.21/0.47 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))) | (~((~((~(set_difference(A!6, B!7) = set_difference(A!6, B!7))) | (in(C!8, set_difference(A!6, B!7)) <=> (~((~in(C!8, A!6)) | in(C!8, B!7)))))) | (~((set_difference(A!6, B!7) = set_difference(A!6, B!7)) | (in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), set_difference(A!6, B!7)) <=> ((~in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), A!6)) | in(tptp_fun_D_0(set_difference(A!6, B!7), B!7, A!6), B!7)))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(121,plain,
% 0.21/0.47 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)))))))) | ((~in(C!8, set_difference(A!6, B!7))) <=> ((~in(C!8, A!6)) | in(C!8, B!7)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.47 tff(122,plain,
% 0.21/0.47 ((~in(C!8, set_difference(A!6, B!7))) <=> ((~in(C!8, A!6)) | in(C!8, B!7))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[121, 95])).
% 0.21/0.47 tff(123,plain,
% 0.21/0.47 (((~(A!6 = empty_set)) & (element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))))) <=> ((~(A!6 = empty_set)) & element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(124,plain,
% 0.21/0.47 (((~(~element(B!7, powerset(A!6)))) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6))))) <=> (element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(125,plain,
% 0.21/0.47 (((~(A!6 = empty_set)) & ((~(~element(B!7, powerset(A!6)))) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))))) <=> ((~(A!6 = empty_set)) & (element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[124])).
% 0.21/0.47 tff(126,plain,
% 0.21/0.47 (((~(A!6 = empty_set)) & ((~(~element(B!7, powerset(A!6)))) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))))) <=> ((~(A!6 = empty_set)) & element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[125, 123])).
% 0.21/0.47 tff(127,plain,
% 0.21/0.47 ((~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))) <=> (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(128,plain,
% 0.21/0.47 ((~![A: $i] : ((~(A = empty_set)) => ![B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B))))))) <=> (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(129,axiom,(~![A: $i] : ((~(A = empty_set)) => ![B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t50_subset_1')).
% 0.21/0.47 tff(130,plain,
% 0.21/0.47 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[130, 127])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[132, 127])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[133, 127])).
% 0.21/0.47 tff(135,plain,
% 0.21/0.47 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[135, 127])).
% 0.21/0.47 tff(137,plain,
% 0.21/0.47 ((~(A!6 = empty_set)) & element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[136, 126])).
% 0.21/0.47 tff(138,plain,
% 0.21/0.47 (element(B!7, powerset(A!6))),
% 0.21/0.47 inference(and_elim,[status(thm)],[137])).
% 0.21/0.47 tff(139,plain,
% 0.21/0.47 (^[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))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(140,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[139])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(142,plain,
% 0.21/0.47 (^[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))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(143,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[142])).
% 0.21/0.47 tff(144,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')).
% 0.21/0.47 tff(145,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.21/0.47 tff(146,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.21/0.47 tff(147,plain,(
% 0.21/0.47 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[146])).
% 0.21/0.47 tff(148,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.21/0.47 tff(149,plain,
% 0.21/0.47 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!7, powerset(A!6))) | (subset_complement(A!6, B!7) = set_difference(A!6, B!7)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!7, powerset(A!6))) | (subset_complement(A!6, B!7) = set_difference(A!6, B!7)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(150,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!7, powerset(A!6))) | (subset_complement(A!6, B!7) = set_difference(A!6, B!7)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(151,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!7, powerset(A!6))) | (subset_complement(A!6, B!7) = set_difference(A!6, B!7))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.47 tff(152,plain,
% 0.21/0.47 (subset_complement(A!6, B!7) = set_difference(A!6, B!7)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[151, 148, 138])).
% 0.21/0.47 tff(153,plain,
% 0.21/0.47 (set_difference(A!6, B!7) = subset_complement(A!6, B!7)),
% 0.21/0.47 inference(symmetry,[status(thm)],[152])).
% 0.21/0.47 tff(154,plain,
% 0.21/0.47 (in(C!8, set_difference(A!6, B!7)) <=> in(C!8, subset_complement(A!6, B!7))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[153])).
% 0.21/0.47 tff(155,plain,
% 0.21/0.47 (in(C!8, subset_complement(A!6, B!7)) <=> in(C!8, set_difference(A!6, B!7))),
% 0.21/0.47 inference(symmetry,[status(thm)],[154])).
% 0.21/0.47 tff(156,plain,
% 0.21/0.47 ((~in(C!8, subset_complement(A!6, B!7))) <=> (~in(C!8, set_difference(A!6, B!7)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[155])).
% 0.21/0.47 tff(157,plain,
% 0.21/0.47 (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))),
% 0.21/0.47 inference(and_elim,[status(thm)],[137])).
% 0.21/0.47 tff(158,plain,
% 0.21/0.47 (~in(C!8, subset_complement(A!6, B!7))),
% 0.21/0.47 inference(or_elim,[status(thm)],[157])).
% 0.21/0.47 tff(159,plain,
% 0.21/0.47 (~in(C!8, set_difference(A!6, B!7))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[158, 156])).
% 0.21/0.47 tff(160,plain,
% 0.21/0.47 ((~((~in(C!8, set_difference(A!6, B!7))) <=> ((~in(C!8, A!6)) | in(C!8, B!7)))) | in(C!8, set_difference(A!6, B!7)) | ((~in(C!8, A!6)) | in(C!8, B!7))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(161,plain,
% 0.21/0.47 ((~in(C!8, A!6)) | in(C!8, B!7)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[160, 159, 122])).
% 0.21/0.47 tff(162,plain,
% 0.21/0.47 (~in(C!8, B!7)),
% 0.21/0.47 inference(or_elim,[status(thm)],[157])).
% 0.21/0.47 tff(163,plain,
% 0.21/0.47 ((~((~in(C!8, A!6)) | in(C!8, B!7))) | (~in(C!8, A!6)) | in(C!8, B!7)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(164,plain,
% 0.21/0.47 ((~((~in(C!8, A!6)) | in(C!8, B!7))) | (~in(C!8, A!6))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.21/0.47 tff(165,plain,
% 0.21/0.47 (~in(C!8, A!6)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[164, 161])).
% 0.21/0.47 tff(166,plain,
% 0.21/0.47 (element(C!8, A!6)),
% 0.21/0.47 inference(or_elim,[status(thm)],[157])).
% 0.21/0.47 tff(167,plain,
% 0.21/0.47 ((~(element(C!8, A!6) <=> in(C!8, A!6))) | (~element(C!8, A!6)) | in(C!8, A!6)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(168,plain,
% 0.21/0.47 ((~(element(C!8, A!6) <=> in(C!8, A!6))) | in(C!8, A!6)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.21/0.47 tff(169,plain,
% 0.21/0.47 (~(element(C!8, A!6) <=> in(C!8, A!6))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[168, 165])).
% 0.21/0.47 tff(170,plain,
% 0.21/0.47 ((~(empty(A!6) | (element(C!8, A!6) <=> in(C!8, A!6)))) | empty(A!6) | (element(C!8, A!6) <=> in(C!8, A!6))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(171,plain,
% 0.21/0.47 (empty(A!6)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[170, 169, 74])).
% 0.21/0.47 tff(172,plain,
% 0.21/0.47 (empty(set_difference(A!6, tptp_fun_B_4(A!6)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[171, 57])).
% 0.21/0.47 tff(173,plain,
% 0.21/0.47 (A!3 = empty_set),
% 0.21/0.47 inference(symmetry,[status(thm)],[51])).
% 0.21/0.47 tff(174,plain,
% 0.21/0.47 (tptp_fun_B_4(A!6) = A!3),
% 0.21/0.47 inference(symmetry,[status(thm)],[44])).
% 0.21/0.47 tff(175,plain,
% 0.21/0.47 ((~![A: $i] : (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A)))))) | (~((~element(tptp_fun_B_4(powerset(A!6)), powerset(powerset(A!6)))) | (~empty(tptp_fun_B_4(powerset(A!6))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(176,plain,
% 0.21/0.47 (~((~element(tptp_fun_B_4(powerset(A!6)), powerset(powerset(A!6)))) | (~empty(tptp_fun_B_4(powerset(A!6)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[175, 19])).
% 0.21/0.47 tff(177,plain,
% 0.21/0.47 (((~element(tptp_fun_B_4(powerset(A!6)), powerset(powerset(A!6)))) | (~empty(tptp_fun_B_4(powerset(A!6))))) | empty(tptp_fun_B_4(powerset(A!6)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(178,plain,
% 0.21/0.47 (empty(tptp_fun_B_4(powerset(A!6)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.21/0.47 tff(179,plain,
% 0.21/0.47 (((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(tptp_fun_B_4(A!6))) | (~empty(tptp_fun_B_4(powerset(A!6)))) | (tptp_fun_B_4(A!6) = tptp_fun_B_4(powerset(A!6))))) <=> ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(tptp_fun_B_4(A!6))) | (~empty(tptp_fun_B_4(powerset(A!6)))) | (tptp_fun_B_4(A!6) = tptp_fun_B_4(powerset(A!6))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(180,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(tptp_fun_B_4(A!6))) | (~empty(tptp_fun_B_4(powerset(A!6)))) | (tptp_fun_B_4(A!6) = tptp_fun_B_4(powerset(A!6))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(181,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(tptp_fun_B_4(A!6))) | (~empty(tptp_fun_B_4(powerset(A!6)))) | (tptp_fun_B_4(A!6) = tptp_fun_B_4(powerset(A!6)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.21/0.47 tff(182,plain,
% 0.21/0.47 (tptp_fun_B_4(A!6) = tptp_fun_B_4(powerset(A!6))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[181, 36, 23, 178])).
% 0.21/0.47 tff(183,plain,
% 0.21/0.47 (tptp_fun_B_4(powerset(A!6)) = tptp_fun_B_4(A!6)),
% 0.21/0.47 inference(symmetry,[status(thm)],[182])).
% 0.21/0.47 tff(184,plain,
% 0.21/0.47 (tptp_fun_B_4(powerset(A!6)) = empty_set),
% 0.21/0.47 inference(transitivity,[status(thm)],[183, 174, 173])).
% 0.21/0.47 tff(185,plain,
% 0.21/0.47 ((set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6))) <=> (A!6 = empty_set)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[55, 184])).
% 0.21/0.47 tff(186,plain,
% 0.21/0.47 ((A!6 = empty_set) <=> (set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6)))),
% 0.21/0.47 inference(symmetry,[status(thm)],[185])).
% 0.21/0.47 tff(187,plain,
% 0.21/0.47 ((~(A!6 = empty_set)) <=> (~(set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[186])).
% 0.21/0.47 tff(188,plain,
% 0.21/0.47 (~(A!6 = empty_set)),
% 0.21/0.47 inference(and_elim,[status(thm)],[137])).
% 0.21/0.47 tff(189,plain,
% 0.21/0.47 (~(set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.21/0.47 tff(190,plain,
% 0.21/0.47 (((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(tptp_fun_B_4(powerset(A!6)))) | (~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6))))) <=> ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(tptp_fun_B_4(powerset(A!6)))) | (~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(191,plain,
% 0.21/0.47 (((~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (~empty(tptp_fun_B_4(powerset(A!6)))) | (set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6)))) <=> ((~empty(tptp_fun_B_4(powerset(A!6)))) | (~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(192,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (~empty(tptp_fun_B_4(powerset(A!6)))) | (set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6))))) <=> ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(tptp_fun_B_4(powerset(A!6)))) | (~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[191])).
% 0.21/0.48 tff(193,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (~empty(tptp_fun_B_4(powerset(A!6)))) | (set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6))))) <=> ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(tptp_fun_B_4(powerset(A!6)))) | (~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[192, 190])).
% 0.21/0.48 tff(194,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (~empty(tptp_fun_B_4(powerset(A!6)))) | (set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(195,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(tptp_fun_B_4(powerset(A!6)))) | (~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.21/0.48 tff(196,plain,
% 0.21/0.48 ((~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (set_difference(A!6, tptp_fun_B_4(A!6)) = tptp_fun_B_4(powerset(A!6)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[195, 36, 178])).
% 0.21/0.48 tff(197,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[196, 189, 172])).
% 0.21/0.48 % SZS output end Proof
%------------------------------------------------------------------------------