TSTP Solution File: SEU137+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU137+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 07:27:41 EDT 2022
% Result : Theorem 3.89s 4.13s
% Output : Proof 3.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SEU137+1 : TPTP v8.1.0. Released v3.3.0.
% 0.05/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.32 % Computer : n023.cluster.edu
% 0.09/0.32 % Model : x86_64 x86_64
% 0.09/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.32 % Memory : 8042.1875MB
% 0.09/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32 % CPULimit : 300
% 0.09/0.32 % WCLimit : 300
% 0.09/0.32 % DateTime : Sat Sep 3 09:58:33 EDT 2022
% 0.09/0.33 % CPUTime :
% 0.09/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.33 Usage: tptp [options] [-file:]file
% 0.09/0.33 -h, -? prints this message.
% 0.09/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.33 -m, -model generate model.
% 0.09/0.33 -p, -proof generate proof.
% 0.09/0.33 -c, -core generate unsat core of named formulas.
% 0.09/0.33 -st, -statistics display statistics.
% 0.09/0.33 -t:timeout set timeout (in second).
% 0.09/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.33 -<param>:<value> configuration parameter and value.
% 0.09/0.33 -o:<output-file> file to place output in.
% 3.89/4.13 % SZS status Theorem
% 3.89/4.13 % SZS output start Proof
% 3.89/4.13 tff(in_type, type, (
% 3.89/4.13 in: ( $i * $i ) > $o)).
% 3.89/4.13 tff(set_union2_type, type, (
% 3.89/4.13 set_union2: ( $i * $i ) > $i)).
% 3.89/4.13 tff(tptp_fun_A_3_type, type, (
% 3.89/4.13 tptp_fun_A_3: $i)).
% 3.89/4.13 tff(tptp_fun_A_7_type, type, (
% 3.89/4.13 tptp_fun_A_7: $i)).
% 3.89/4.13 tff(tptp_fun_D_0_type, type, (
% 3.89/4.13 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 3.89/4.13 tff(set_difference_type, type, (
% 3.89/4.13 set_difference: ( $i * $i ) > $i)).
% 3.89/4.13 tff(tptp_fun_B_6_type, type, (
% 3.89/4.13 tptp_fun_B_6: $i)).
% 3.89/4.13 tff(empty_set_type, type, (
% 3.89/4.13 empty_set: $i)).
% 3.89/4.13 tff(empty_type, type, (
% 3.89/4.13 empty: $i > $o)).
% 3.89/4.13 tff(tptp_fun_C_5_type, type, (
% 3.89/4.13 tptp_fun_C_5: ( $i * $i ) > $i)).
% 3.89/4.13 tff(subset_type, type, (
% 3.89/4.13 subset: ( $i * $i ) > $o)).
% 3.89/4.13 tff(tptp_fun_D_2_type, type, (
% 3.89/4.13 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 3.89/4.13 tff(tptp_fun_C_1_type, type, (
% 3.89/4.13 tptp_fun_C_1: ( $i * $i ) > $i)).
% 3.89/4.13 tff(1,plain,
% 3.89/4.13 (^[A: $i] : refl((set_union2(A, empty_set) = A) <=> (set_union2(A, empty_set) = A))),
% 3.89/4.13 inference(bind,[status(th)],[])).
% 3.89/4.13 tff(2,plain,
% 3.89/4.13 (![A: $i] : (set_union2(A, empty_set) = A) <=> ![A: $i] : (set_union2(A, empty_set) = A)),
% 3.89/4.13 inference(quant_intro,[status(thm)],[1])).
% 3.89/4.13 tff(3,plain,
% 3.89/4.13 (![A: $i] : (set_union2(A, empty_set) = A) <=> ![A: $i] : (set_union2(A, empty_set) = A)),
% 3.89/4.13 inference(rewrite,[status(thm)],[])).
% 3.89/4.13 tff(4,axiom,(![A: $i] : (set_union2(A, empty_set) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_boole')).
% 3.89/4.13 tff(5,plain,
% 3.89/4.13 (![A: $i] : (set_union2(A, empty_set) = A)),
% 3.89/4.13 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.89/4.13 tff(6,plain,(
% 3.89/4.13 ![A: $i] : (set_union2(A, empty_set) = A)),
% 3.89/4.13 inference(skolemize,[status(sab)],[5])).
% 3.89/4.13 tff(7,plain,
% 3.89/4.13 (![A: $i] : (set_union2(A, empty_set) = A)),
% 3.89/4.13 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.89/4.13 tff(8,plain,
% 3.89/4.13 ((~![A: $i] : (set_union2(A, empty_set) = A)) | (set_union2(A!7, empty_set) = A!7)),
% 3.89/4.13 inference(quant_inst,[status(thm)],[])).
% 3.89/4.13 tff(9,plain,
% 3.89/4.13 (set_union2(A!7, empty_set) = A!7),
% 3.89/4.13 inference(unit_resolution,[status(thm)],[8, 7])).
% 3.89/4.13 tff(10,plain,
% 3.89/4.13 (^[A: $i, B: $i] : refl(((A = B) | (~empty(A)) | (~empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B))))),
% 3.89/4.13 inference(bind,[status(th)],[])).
% 3.89/4.13 tff(11,plain,
% 3.89/4.13 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 3.89/4.13 inference(quant_intro,[status(thm)],[10])).
% 3.89/4.13 tff(12,plain,
% 3.89/4.13 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((A = B) | (~empty(A)) | (~empty(B))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((A = B) | (~empty(A)) | (~empty(B))))))), rewrite((~(~((A = B) | (~empty(A)) | (~empty(B))))) <=> ((A = B) | (~empty(A)) | (~empty(B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B)))))),
% 3.89/4.13 inference(bind,[status(th)],[])).
% 3.89/4.13 tff(13,plain,
% 3.89/4.13 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 3.89/4.13 inference(quant_intro,[status(thm)],[12])).
% 3.89/4.13 tff(14,plain,
% 3.89/4.13 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.89/4.13 inference(rewrite,[status(thm)],[])).
% 3.89/4.13 tff(15,plain,
% 3.89/4.13 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 3.89/4.13 inference(bind,[status(th)],[])).
% 3.89/4.13 tff(16,plain,
% 3.89/4.13 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.89/4.13 inference(quant_intro,[status(thm)],[15])).
% 3.89/4.13 tff(17,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 3.89/4.13 tff(18,plain,
% 3.89/4.13 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.89/4.13 inference(modus_ponens,[status(thm)],[17, 16])).
% 3.89/4.13 tff(19,plain,
% 3.89/4.13 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.89/4.13 inference(modus_ponens,[status(thm)],[18, 14])).
% 3.89/4.13 tff(20,plain,(
% 3.89/4.13 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.89/4.13 inference(skolemize,[status(sab)],[19])).
% 3.89/4.13 tff(21,plain,
% 3.89/4.13 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 3.89/4.13 inference(modus_ponens,[status(thm)],[20, 13])).
% 3.89/4.13 tff(22,plain,
% 3.89/4.13 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 3.89/4.13 inference(modus_ponens,[status(thm)],[21, 11])).
% 3.89/4.13 tff(23,plain,
% 3.89/4.13 (?[A: $i] : empty(A) <=> ?[A: $i] : empty(A)),
% 3.89/4.13 inference(rewrite,[status(thm)],[])).
% 3.89/4.13 tff(24,axiom,(?[A: $i] : empty(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc1_xboole_0')).
% 3.89/4.13 tff(25,plain,
% 3.89/4.13 (?[A: $i] : empty(A)),
% 3.89/4.13 inference(modus_ponens,[status(thm)],[24, 23])).
% 3.89/4.13 tff(26,plain,(
% 3.89/4.13 empty(A!3)),
% 3.89/4.13 inference(skolemize,[status(sab)],[25])).
% 3.89/4.13 tff(27,plain,
% 3.89/4.13 (empty(empty_set) <=> empty(empty_set)),
% 3.89/4.13 inference(rewrite,[status(thm)],[])).
% 3.89/4.13 tff(28,axiom,(empty(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 3.89/4.13 tff(29,plain,
% 3.89/4.13 (empty(empty_set)),
% 3.89/4.13 inference(modus_ponens,[status(thm)],[28, 27])).
% 3.89/4.13 tff(30,plain,
% 3.89/4.13 (((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((empty_set = A!3) | (~empty(empty_set)) | (~empty(A!3)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (empty_set = A!3) | (~empty(empty_set)) | (~empty(A!3)))),
% 3.89/4.13 inference(rewrite,[status(thm)],[])).
% 3.89/4.13 tff(31,plain,
% 3.89/4.13 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((empty_set = A!3) | (~empty(empty_set)) | (~empty(A!3)))),
% 3.89/4.13 inference(quant_inst,[status(thm)],[])).
% 3.89/4.13 tff(32,plain,
% 3.89/4.13 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (empty_set = A!3) | (~empty(empty_set)) | (~empty(A!3))),
% 3.89/4.13 inference(modus_ponens,[status(thm)],[31, 30])).
% 3.89/4.13 tff(33,plain,
% 3.89/4.13 (empty_set = A!3),
% 3.89/4.13 inference(unit_resolution,[status(thm)],[32, 29, 26, 22])).
% 3.89/4.13 tff(34,plain,
% 3.89/4.13 (set_union2(A!7, empty_set) = set_union2(A!7, A!3)),
% 3.89/4.13 inference(monotonicity,[status(thm)],[33])).
% 3.89/4.13 tff(35,plain,
% 3.89/4.13 (set_union2(A!7, A!3) = set_union2(A!7, empty_set)),
% 3.89/4.13 inference(symmetry,[status(thm)],[34])).
% 3.89/4.13 tff(36,plain,
% 3.89/4.13 (set_union2(A!7, A!3) = A!7),
% 3.89/4.13 inference(transitivity,[status(thm)],[35, 9])).
% 3.89/4.13 tff(37,plain,
% 3.89/4.13 (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)) <=> in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)),
% 3.89/4.13 inference(monotonicity,[status(thm)],[36])).
% 3.89/4.13 tff(38,plain,
% 3.89/4.13 (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7) <=> in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))),
% 3.89/4.13 inference(symmetry,[status(thm)],[37])).
% 3.89/4.13 tff(39,plain,
% 3.89/4.13 ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)) <=> (~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)))),
% 3.89/4.13 inference(monotonicity,[status(thm)],[38])).
% 3.89/4.13 tff(40,plain,
% 3.89/4.13 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 3.89/4.13 inference(bind,[status(th)],[])).
% 3.89/4.13 tff(41,plain,
% 3.89/4.13 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 3.89/4.13 inference(quant_intro,[status(thm)],[40])).
% 3.89/4.13 tff(42,plain,
% 3.89/4.13 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 3.89/4.13 inference(rewrite,[status(thm)],[])).
% 3.89/4.13 tff(43,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 3.89/4.13 tff(44,plain,
% 3.89/4.13 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 3.89/4.13 inference(modus_ponens,[status(thm)],[43, 42])).
% 3.89/4.13 tff(45,plain,(
% 3.89/4.13 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 3.89/4.13 inference(skolemize,[status(sab)],[44])).
% 3.89/4.13 tff(46,plain,
% 3.89/4.13 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 3.89/4.13 inference(modus_ponens,[status(thm)],[45, 41])).
% 3.89/4.13 tff(47,plain,
% 3.89/4.13 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(B!6, A!3) = set_union2(A!3, B!6))),
% 3.89/4.13 inference(quant_inst,[status(thm)],[])).
% 3.89/4.13 tff(48,plain,
% 3.89/4.13 (set_union2(B!6, A!3) = set_union2(A!3, B!6)),
% 3.89/4.13 inference(unit_resolution,[status(thm)],[47, 46])).
% 3.89/4.13 tff(49,plain,
% 3.89/4.13 (set_union2(B!6, empty_set) = set_union2(B!6, A!3)),
% 3.89/4.13 inference(monotonicity,[status(thm)],[33])).
% 3.89/4.13 tff(50,plain,
% 3.89/4.13 ((~![A: $i] : (set_union2(A, empty_set) = A)) | (set_union2(B!6, empty_set) = B!6)),
% 3.89/4.13 inference(quant_inst,[status(thm)],[])).
% 3.89/4.13 tff(51,plain,
% 3.89/4.13 (set_union2(B!6, empty_set) = B!6),
% 3.89/4.13 inference(unit_resolution,[status(thm)],[50, 7])).
% 3.89/4.13 tff(52,plain,
% 3.89/4.13 (B!6 = set_union2(B!6, empty_set)),
% 3.89/4.13 inference(symmetry,[status(thm)],[51])).
% 3.89/4.13 tff(53,plain,
% 3.89/4.13 (B!6 = set_union2(A!3, B!6)),
% 3.89/4.13 inference(transitivity,[status(thm)],[52, 49, 48])).
% 3.89/4.13 tff(54,plain,
% 3.89/4.13 (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), B!6) <=> in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))),
% 3.89/4.13 inference(monotonicity,[status(thm)],[53])).
% 3.89/4.13 tff(55,plain,
% 3.89/4.13 (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6)) <=> in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), B!6)),
% 3.89/4.13 inference(symmetry,[status(thm)],[54])).
% 3.89/4.13 tff(56,plain,
% 3.89/4.13 ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), B!6))),
% 3.89/4.13 inference(monotonicity,[status(thm)],[55])).
% 3.89/4.13 tff(57,assumption,(~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))), introduced(assumption)).
% 3.89/4.13 tff(58,plain,
% 3.89/4.13 (~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), B!6)),
% 3.89/4.13 inference(modus_ponens,[status(thm)],[57, 56])).
% 3.89/4.13 tff(59,plain,
% 3.89/4.13 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 3.89/4.13 inference(bind,[status(th)],[])).
% 3.89/4.13 tff(60,plain,
% 3.89/4.13 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 3.89/4.13 inference(quant_intro,[status(thm)],[59])).
% 3.89/4.13 tff(61,plain,
% 3.89/4.13 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 3.89/4.13 inference(pull_quant,[status(thm)],[])).
% 3.89/4.13 tff(62,plain,
% 3.89/4.13 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 3.89/4.14 inference(bind,[status(th)],[])).
% 3.89/4.14 tff(63,plain,
% 3.89/4.14 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 3.89/4.14 inference(quant_intro,[status(thm)],[62])).
% 3.89/4.14 tff(64,plain,
% 3.89/4.14 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 3.89/4.14 inference(transitivity,[status(thm)],[63, 61])).
% 3.89/4.14 tff(65,plain,
% 3.89/4.14 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 3.89/4.14 inference(transitivity,[status(thm)],[64, 60])).
% 3.89/4.14 tff(66,plain,
% 3.89/4.14 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 3.89/4.14 inference(bind,[status(th)],[])).
% 3.89/4.14 tff(67,plain,
% 3.89/4.14 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 3.89/4.14 inference(quant_intro,[status(thm)],[66])).
% 3.89/4.14 tff(68,plain,
% 3.89/4.14 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 3.89/4.14 inference(transitivity,[status(thm)],[67, 65])).
% 3.89/4.14 tff(69,plain,
% 3.89/4.14 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 3.89/4.14 inference(bind,[status(th)],[])).
% 3.89/4.14 tff(70,plain,
% 3.89/4.14 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 3.89/4.14 inference(quant_intro,[status(thm)],[69])).
% 3.89/4.14 tff(71,plain,
% 3.89/4.14 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))),
% 3.89/4.14 inference(bind,[status(th)],[])).
% 3.89/4.14 tff(72,plain,
% 3.89/4.14 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))),
% 3.89/4.14 inference(quant_intro,[status(thm)],[71])).
% 3.89/4.14 tff(73,plain,
% 3.89/4.14 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 3.89/4.14 inference(rewrite,[status(thm)],[])).
% 3.89/4.14 tff(74,plain,
% 3.89/4.14 (^[A: $i, B: $i, C: $i] : rewrite(((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))))),
% 3.89/4.14 inference(bind,[status(th)],[])).
% 3.89/4.14 tff(75,plain,
% 3.89/4.14 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 3.89/4.14 inference(quant_intro,[status(thm)],[74])).
% 3.89/4.14 tff(76,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_xboole_0')).
% 3.89/4.14 tff(77,plain,
% 3.89/4.14 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 3.89/4.14 inference(modus_ponens,[status(thm)],[76, 75])).
% 3.89/4.14 tff(78,plain,
% 3.89/4.14 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 3.89/4.14 inference(modus_ponens,[status(thm)],[77, 73])).
% 3.89/4.14 tff(79,plain,(
% 3.89/4.14 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))),
% 3.89/4.14 inference(skolemize,[status(sab)],[78])).
% 3.89/4.14 tff(80,plain,
% 3.89/4.14 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))),
% 3.89/4.14 inference(modus_ponens,[status(thm)],[79, 72])).
% 3.89/4.14 tff(81,plain,
% 3.89/4.14 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 3.89/4.14 inference(modus_ponens,[status(thm)],[80, 70])).
% 3.89/4.14 tff(82,plain,
% 3.89/4.14 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 3.89/4.14 inference(modus_ponens,[status(thm)],[81, 68])).
% 3.89/4.14 tff(83,plain,
% 3.89/4.14 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (~((~((~(set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7)))) | (in(tptp_fun_C_5(A!7, A!3), set_union2(A!3, B!6)) <=> (in(tptp_fun_C_5(A!7, A!3), A!7) | in(tptp_fun_C_5(A!7, A!3), set_difference(B!6, A!7)))))) | (~((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (~((~((~(set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7)))) | (in(tptp_fun_C_5(A!7, A!3), set_union2(A!3, B!6)) <=> (in(tptp_fun_C_5(A!7, A!3), A!7) | in(tptp_fun_C_5(A!7, A!3), set_difference(B!6, A!7)))))) | (~((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7))))))))),
% 3.89/4.14 inference(rewrite,[status(thm)],[])).
% 3.89/4.14 tff(84,plain,
% 3.89/4.14 ((~((~((~(set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7)))) | (in(tptp_fun_C_5(A!7, A!3), set_union2(A!3, B!6)) <=> (in(tptp_fun_C_5(A!7, A!3), set_difference(B!6, A!7)) | in(tptp_fun_C_5(A!7, A!3), A!7))))) | (~((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7))))))) <=> (~((~((~(set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7)))) | (in(tptp_fun_C_5(A!7, A!3), set_union2(A!3, B!6)) <=> (in(tptp_fun_C_5(A!7, A!3), A!7) | in(tptp_fun_C_5(A!7, A!3), set_difference(B!6, A!7)))))) | (~((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)))))))),
% 3.89/4.14 inference(rewrite,[status(thm)],[])).
% 3.89/4.14 tff(85,plain,
% 3.89/4.14 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (~((~((~(set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7)))) | (in(tptp_fun_C_5(A!7, A!3), set_union2(A!3, B!6)) <=> (in(tptp_fun_C_5(A!7, A!3), set_difference(B!6, A!7)) | in(tptp_fun_C_5(A!7, A!3), A!7))))) | (~((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (~((~((~(set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7)))) | (in(tptp_fun_C_5(A!7, A!3), set_union2(A!3, B!6)) <=> (in(tptp_fun_C_5(A!7, A!3), A!7) | in(tptp_fun_C_5(A!7, A!3), set_difference(B!6, A!7)))))) | (~((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7))))))))),
% 3.89/4.14 inference(monotonicity,[status(thm)],[84])).
% 3.89/4.14 tff(86,plain,
% 3.89/4.15 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (~((~((~(set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7)))) | (in(tptp_fun_C_5(A!7, A!3), set_union2(A!3, B!6)) <=> (in(tptp_fun_C_5(A!7, A!3), set_difference(B!6, A!7)) | in(tptp_fun_C_5(A!7, A!3), A!7))))) | (~((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (~((~((~(set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7)))) | (in(tptp_fun_C_5(A!7, A!3), set_union2(A!3, B!6)) <=> (in(tptp_fun_C_5(A!7, A!3), A!7) | in(tptp_fun_C_5(A!7, A!3), set_difference(B!6, A!7)))))) | (~((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7))))))))),
% 3.89/4.15 inference(transitivity,[status(thm)],[85, 83])).
% 3.89/4.15 tff(87,plain,
% 3.89/4.15 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (~((~((~(set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7)))) | (in(tptp_fun_C_5(A!7, A!3), set_union2(A!3, B!6)) <=> (in(tptp_fun_C_5(A!7, A!3), set_difference(B!6, A!7)) | in(tptp_fun_C_5(A!7, A!3), A!7))))) | (~((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)))))))),
% 3.89/4.15 inference(quant_inst,[status(thm)],[])).
% 3.89/4.15 tff(88,plain,
% 3.89/4.15 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (~((~((~(set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7)))) | (in(tptp_fun_C_5(A!7, A!3), set_union2(A!3, B!6)) <=> (in(tptp_fun_C_5(A!7, A!3), A!7) | in(tptp_fun_C_5(A!7, A!3), set_difference(B!6, A!7)))))) | (~((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)))))))),
% 3.89/4.15 inference(modus_ponens,[status(thm)],[87, 86])).
% 3.89/4.15 tff(89,plain,
% 3.89/4.15 (~((~((~(set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7)))) | (in(tptp_fun_C_5(A!7, A!3), set_union2(A!3, B!6)) <=> (in(tptp_fun_C_5(A!7, A!3), A!7) | in(tptp_fun_C_5(A!7, A!3), set_difference(B!6, A!7)))))) | (~((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7))))))),
% 3.89/4.15 inference(unit_resolution,[status(thm)],[88, 82])).
% 3.89/4.15 tff(90,plain,
% 3.89/4.15 (((~((~(set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7)))) | (in(tptp_fun_C_5(A!7, A!3), set_union2(A!3, B!6)) <=> (in(tptp_fun_C_5(A!7, A!3), A!7) | in(tptp_fun_C_5(A!7, A!3), set_difference(B!6, A!7)))))) | (~((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)))))) | ((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7))))),
% 3.89/4.15 inference(tautology,[status(thm)],[])).
% 3.89/4.15 tff(91,plain,
% 3.89/4.15 ((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)))),
% 3.89/4.15 inference(unit_resolution,[status(thm)],[90, 89])).
% 3.89/4.15 tff(92,plain,
% 3.89/4.15 (set_union2(B!6, A!3) = set_union2(B!6, empty_set)),
% 3.89/4.15 inference(symmetry,[status(thm)],[49])).
% 3.89/4.15 tff(93,plain,
% 3.89/4.15 (set_union2(A!3, B!6) = set_union2(B!6, A!3)),
% 3.89/4.15 inference(symmetry,[status(thm)],[48])).
% 3.89/4.15 tff(94,plain,
% 3.89/4.15 (set_union2(A!3, B!6) = B!6),
% 3.89/4.15 inference(transitivity,[status(thm)],[93, 92, 51])).
% 3.89/4.15 tff(95,plain,
% 3.89/4.15 ((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) <=> (B!6 = set_union2(A!7, set_difference(B!6, A!7)))),
% 3.89/4.15 inference(monotonicity,[status(thm)],[94])).
% 3.89/4.15 tff(96,plain,
% 3.89/4.15 ((B!6 = set_union2(A!7, set_difference(B!6, A!7))) <=> (set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7)))),
% 3.89/4.15 inference(symmetry,[status(thm)],[95])).
% 3.89/4.15 tff(97,plain,
% 3.89/4.15 ((~(B!6 = set_union2(A!7, set_difference(B!6, A!7)))) <=> (~(set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))))),
% 3.89/4.15 inference(monotonicity,[status(thm)],[96])).
% 3.89/4.15 tff(98,plain,
% 3.89/4.15 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 3.89/4.15 inference(rewrite,[status(thm)],[])).
% 3.89/4.15 tff(99,plain,
% 3.89/4.15 ((~![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 3.89/4.15 inference(rewrite,[status(thm)],[])).
% 3.89/4.15 tff(100,axiom,(~![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t45_xboole_1')).
% 3.89/4.15 tff(101,plain,
% 3.89/4.15 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 3.89/4.15 inference(modus_ponens,[status(thm)],[100, 99])).
% 3.89/4.15 tff(102,plain,
% 3.89/4.15 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 3.89/4.15 inference(modus_ponens,[status(thm)],[101, 98])).
% 3.89/4.15 tff(103,plain,
% 3.89/4.15 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 3.89/4.15 inference(modus_ponens,[status(thm)],[102, 98])).
% 3.89/4.15 tff(104,plain,
% 3.89/4.15 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 3.89/4.15 inference(modus_ponens,[status(thm)],[103, 98])).
% 3.89/4.15 tff(105,plain,
% 3.89/4.15 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 3.89/4.15 inference(modus_ponens,[status(thm)],[104, 98])).
% 3.89/4.15 tff(106,plain,
% 3.89/4.15 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 3.89/4.15 inference(modus_ponens,[status(thm)],[105, 98])).
% 3.89/4.15 tff(107,plain,
% 3.89/4.15 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 3.89/4.15 inference(modus_ponens,[status(thm)],[106, 98])).
% 3.96/4.16 tff(108,plain,(
% 3.96/4.16 ~((~subset(A!7, B!6)) | (B!6 = set_union2(A!7, set_difference(B!6, A!7))))),
% 3.96/4.16 inference(skolemize,[status(sab)],[107])).
% 3.96/4.16 tff(109,plain,
% 3.96/4.16 (~(B!6 = set_union2(A!7, set_difference(B!6, A!7)))),
% 3.96/4.16 inference(or_elim,[status(thm)],[108])).
% 3.96/4.16 tff(110,plain,
% 3.96/4.16 (~(set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7)))),
% 3.96/4.16 inference(modus_ponens,[status(thm)],[109, 97])).
% 3.96/4.16 tff(111,plain,
% 3.96/4.16 ((~((set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7))))) | (set_union2(A!3, B!6) = set_union2(A!7, set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)))),
% 3.96/4.16 inference(tautology,[status(thm)],[])).
% 3.96/4.16 tff(112,plain,
% 3.96/4.16 ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7))),
% 3.96/4.16 inference(unit_resolution,[status(thm)],[111, 110, 91])).
% 3.96/4.16 tff(113,plain,
% 3.96/4.16 ((~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6)) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7))),
% 3.96/4.16 inference(tautology,[status(thm)],[])).
% 3.96/4.16 tff(114,plain,
% 3.96/4.16 (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6)) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7))),
% 3.96/4.16 inference(unit_resolution,[status(thm)],[113, 112])).
% 3.96/4.16 tff(115,plain,
% 3.96/4.16 (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)),
% 3.96/4.16 inference(unit_resolution,[status(thm)],[114, 57])).
% 3.96/4.16 tff(116,plain,
% 3.96/4.16 (((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))),
% 3.96/4.16 inference(tautology,[status(thm)],[])).
% 3.96/4.16 tff(117,plain,
% 3.96/4.16 ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))),
% 3.96/4.16 inference(unit_resolution,[status(thm)],[116, 57])).
% 3.96/4.16 tff(118,assumption,((~((set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3))) | (in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_difference(B!6, A!7)) <=> ((~in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!3, B!6))) | in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!7, A!3)))))) | (~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)))))))), introduced(assumption)).
% 3.96/4.16 tff(119,plain,
% 3.96/4.16 (^[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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))))),
% 3.96/4.16 inference(bind,[status(th)],[])).
% 3.96/4.16 tff(120,plain,
% 3.96/4.16 (![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 3.96/4.16 inference(quant_intro,[status(thm)],[119])).
% 3.96/4.16 tff(121,plain,
% 3.96/4.16 (![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 3.96/4.16 inference(pull_quant,[status(thm)],[])).
% 3.96/4.16 tff(122,plain,
% 3.96/4.16 (^[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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))))),
% 3.96/4.16 inference(bind,[status(th)],[])).
% 3.96/4.16 tff(123,plain,
% 3.96/4.16 (![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 3.96/4.16 inference(quant_intro,[status(thm)],[122])).
% 3.96/4.16 tff(124,plain,
% 3.96/4.16 (![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 3.96/4.16 inference(transitivity,[status(thm)],[123, 121])).
% 3.96/4.16 tff(125,plain,
% 3.96/4.16 (![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 3.96/4.16 inference(transitivity,[status(thm)],[124, 120])).
% 3.96/4.16 tff(126,plain,
% 3.96/4.16 (^[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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))))),
% 3.96/4.16 inference(bind,[status(th)],[])).
% 3.96/4.16 tff(127,plain,
% 3.96/4.16 (![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 3.96/4.16 inference(quant_intro,[status(thm)],[126])).
% 3.96/4.16 tff(128,plain,
% 3.96/4.16 (![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 3.96/4.16 inference(transitivity,[status(thm)],[127, 125])).
% 3.96/4.16 tff(129,plain,
% 3.96/4.16 (^[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_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))) <=> ((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(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_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))))),
% 3.96/4.16 inference(bind,[status(th)],[])).
% 3.96/4.16 tff(130,plain,
% 3.96/4.16 (![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_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 3.96/4.16 inference(quant_intro,[status(thm)],[129])).
% 3.96/4.16 tff(131,plain,
% 3.96/4.16 (^[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_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(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_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))))),
% 3.96/4.16 inference(bind,[status(th)],[])).
% 3.96/4.16 tff(132,plain,
% 3.96/4.16 (![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_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(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_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))),
% 3.97/4.16 inference(quant_intro,[status(thm)],[131])).
% 3.97/4.16 tff(133,plain,
% 3.97/4.16 (![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)))))),
% 3.97/4.16 inference(rewrite,[status(thm)],[])).
% 3.97/4.16 tff(134,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')).
% 3.97/4.16 tff(135,plain,
% 3.97/4.16 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[134, 133])).
% 3.97/4.16 tff(136,plain,(
% 3.97/4.16 ![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_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))))),
% 3.97/4.16 inference(skolemize,[status(sab)],[135])).
% 3.97/4.16 tff(137,plain,
% 3.97/4.16 (![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_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[136, 132])).
% 3.97/4.16 tff(138,plain,
% 3.97/4.16 (![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[137, 130])).
% 3.97/4.16 tff(139,plain,
% 3.97/4.16 (![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[138, 128])).
% 3.97/4.16 tff(140,plain,
% 3.97/4.16 (((~![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3))) | (in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_difference(B!6, A!7)) <=> ((~in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!3, B!6))) | in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!7, A!3)))))) | (~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)))))))))) <=> ((~![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3))) | (in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_difference(B!6, A!7)) <=> ((~in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!3, B!6))) | in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!7, A!3)))))) | (~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))))))))))),
% 3.97/4.17 inference(rewrite,[status(thm)],[])).
% 3.97/4.17 tff(141,plain,
% 3.97/4.17 ((~((~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))))))) | (~((set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3))) | (in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_difference(B!6, A!7)) <=> ((~in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!3, B!6))) | in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!7, A!3)))))))) <=> (~((~((set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3))) | (in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_difference(B!6, A!7)) <=> ((~in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!3, B!6))) | in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!7, A!3)))))) | (~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)))))))))),
% 3.97/4.17 inference(rewrite,[status(thm)],[])).
% 3.97/4.17 tff(142,plain,
% 3.97/4.17 (((~![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))))))) | (~((set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3))) | (in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_difference(B!6, A!7)) <=> ((~in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!3, B!6))) | in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!7, A!3))))))))) <=> ((~![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3))) | (in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_difference(B!6, A!7)) <=> ((~in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!3, B!6))) | in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!7, A!3)))))) | (~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))))))))))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[141])).
% 3.97/4.17 tff(143,plain,
% 3.97/4.17 (((~![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))))))) | (~((set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3))) | (in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_difference(B!6, A!7)) <=> ((~in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!3, B!6))) | in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!7, A!3))))))))) <=> ((~![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3))) | (in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_difference(B!6, A!7)) <=> ((~in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!3, B!6))) | in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!7, A!3)))))) | (~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))))))))))),
% 3.97/4.17 inference(transitivity,[status(thm)],[142, 140])).
% 3.97/4.17 tff(144,plain,
% 3.97/4.17 ((~![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_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))))))) | (~((set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3))) | (in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_difference(B!6, A!7)) <=> ((~in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!3, B!6))) | in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!7, A!3))))))))),
% 3.97/4.17 inference(quant_inst,[status(thm)],[])).
% 3.97/4.17 tff(145,plain,
% 3.97/4.17 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3))) | (in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_difference(B!6, A!7)) <=> ((~in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!3, B!6))) | in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!7, A!3)))))) | (~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)))))))))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[144, 143])).
% 3.97/4.18 tff(146,plain,
% 3.97/4.18 ($false),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[145, 139, 118])).
% 3.97/4.18 tff(147,plain,(~((~((set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3))) | (in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_difference(B!6, A!7)) <=> ((~in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!3, B!6))) | in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!7, A!3)))))) | (~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))))))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.18 tff(148,plain,
% 3.97/4.18 (((~((set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3))) | (in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_difference(B!6, A!7)) <=> ((~in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!3, B!6))) | in(tptp_fun_D_2(set_difference(B!6, A!7), set_union2(A!7, A!3), set_union2(A!3, B!6)), set_union2(A!7, A!3)))))) | (~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)))))))) | ((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))))))),
% 3.97/4.18 inference(tautology,[status(thm)],[])).
% 3.97/4.18 tff(149,plain,
% 3.97/4.18 ((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[148, 147])).
% 3.97/4.18 tff(150,plain,
% 3.97/4.18 (set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)) = set_difference(B!6, A!7)),
% 3.97/4.18 inference(monotonicity,[status(thm)],[94, 36])).
% 3.97/4.18 tff(151,plain,
% 3.97/4.18 (set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3))),
% 3.97/4.18 inference(symmetry,[status(thm)],[150])).
% 3.97/4.18 tff(152,plain,
% 3.97/4.18 ((~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))))))) | (~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)))))),
% 3.97/4.18 inference(tautology,[status(thm)],[])).
% 3.97/4.18 tff(153,plain,
% 3.97/4.18 ((~((~(set_difference(B!6, A!7) = set_difference(set_union2(A!3, B!6), set_union2(A!7, A!3)))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))))))) | (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[152, 151])).
% 3.97/4.18 tff(154,plain,
% 3.97/4.18 (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[153, 149])).
% 3.97/4.18 tff(155,plain,
% 3.97/4.18 ((~(in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)))))) | (~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7))) | (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))))),
% 3.97/4.18 inference(tautology,[status(thm)],[])).
% 3.97/4.18 tff(156,plain,
% 3.97/4.18 ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7))) | (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[155, 154])).
% 3.97/4.18 tff(157,plain,
% 3.97/4.18 (~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[156, 117])).
% 3.97/4.18 tff(158,plain,
% 3.97/4.18 ((~(in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)),
% 3.97/4.18 inference(tautology,[status(thm)],[])).
% 3.97/4.18 tff(159,plain,
% 3.97/4.18 (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[158, 157, 115])).
% 3.97/4.18 tff(160,plain,
% 3.97/4.18 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 3.97/4.18 inference(bind,[status(th)],[])).
% 3.97/4.18 tff(161,plain,
% 3.97/4.18 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 3.97/4.18 inference(quant_intro,[status(thm)],[160])).
% 3.97/4.18 tff(162,plain,
% 3.97/4.18 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 3.97/4.18 inference(bind,[status(th)],[])).
% 3.97/4.18 tff(163,plain,
% 3.97/4.18 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 3.97/4.18 inference(quant_intro,[status(thm)],[162])).
% 3.97/4.18 tff(164,plain,
% 3.97/4.18 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 3.97/4.18 inference(transitivity,[status(thm)],[163, 161])).
% 3.97/4.18 tff(165,plain,
% 3.97/4.18 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))))),
% 3.97/4.18 inference(bind,[status(th)],[])).
% 3.97/4.18 tff(166,plain,
% 3.97/4.18 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 3.97/4.18 inference(quant_intro,[status(thm)],[165])).
% 3.97/4.18 tff(167,plain,
% 3.97/4.18 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 3.97/4.18 inference(rewrite,[status(thm)],[])).
% 3.97/4.18 tff(168,plain,
% 3.97/4.18 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 3.97/4.18 inference(bind,[status(th)],[])).
% 3.97/4.18 tff(169,plain,
% 3.97/4.18 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 3.97/4.18 inference(quant_intro,[status(thm)],[168])).
% 3.97/4.18 tff(170,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 3.97/4.19 tff(171,plain,
% 3.97/4.19 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[170, 169])).
% 3.97/4.19 tff(172,plain,
% 3.97/4.19 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[171, 167])).
% 3.97/4.19 tff(173,plain,(
% 3.97/4.19 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))),
% 3.97/4.19 inference(skolemize,[status(sab)],[172])).
% 3.97/4.19 tff(174,plain,
% 3.97/4.19 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[173, 166])).
% 3.97/4.19 tff(175,plain,
% 3.97/4.19 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[174, 164])).
% 3.97/4.19 tff(176,plain,
% 3.97/4.19 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))) | (~((~((~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6)))) | (~(subset(A!7, B!6) | (~((~in(tptp_fun_C_1(B!6, A!7), A!7)) | in(tptp_fun_C_1(B!6, A!7), B!6)))))))),
% 3.97/4.19 inference(quant_inst,[status(thm)],[])).
% 3.97/4.19 tff(177,plain,
% 3.97/4.19 (~((~((~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6)))) | (~(subset(A!7, B!6) | (~((~in(tptp_fun_C_1(B!6, A!7), A!7)) | in(tptp_fun_C_1(B!6, A!7), B!6))))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[176, 175])).
% 3.97/4.19 tff(178,plain,
% 3.97/4.19 (((~((~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6)))) | (~(subset(A!7, B!6) | (~((~in(tptp_fun_C_1(B!6, A!7), A!7)) | in(tptp_fun_C_1(B!6, A!7), B!6)))))) | ((~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6)))),
% 3.97/4.19 inference(tautology,[status(thm)],[])).
% 3.97/4.19 tff(179,plain,
% 3.97/4.19 ((~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[178, 177])).
% 3.97/4.19 tff(180,plain,
% 3.97/4.19 (subset(A!7, B!6)),
% 3.97/4.19 inference(or_elim,[status(thm)],[108])).
% 3.97/4.19 tff(181,plain,
% 3.97/4.19 ((~((~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6)))) | (~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6))),
% 3.97/4.19 inference(tautology,[status(thm)],[])).
% 3.97/4.19 tff(182,plain,
% 3.97/4.19 ((~((~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6)))) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[181, 180])).
% 3.97/4.19 tff(183,plain,
% 3.97/4.19 (![C: $i] : ((~in(C, A!7)) | in(C, B!6))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[182, 179])).
% 3.97/4.19 tff(184,plain,
% 3.97/4.19 (((~![C: $i] : ((~in(C, A!7)) | in(C, B!6))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), B!6))) <=> ((~![C: $i] : ((~in(C, A!7)) | in(C, B!6))) | (~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), B!6))),
% 3.97/4.19 inference(rewrite,[status(thm)],[])).
% 3.97/4.19 tff(185,plain,
% 3.97/4.19 ((~![C: $i] : ((~in(C, A!7)) | in(C, B!6))) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), B!6))),
% 3.97/4.19 inference(quant_inst,[status(thm)],[])).
% 3.97/4.19 tff(186,plain,
% 3.97/4.19 ((~![C: $i] : ((~in(C, A!7)) | in(C, B!6))) | (~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), B!6)),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[185, 184])).
% 3.97/4.19 tff(187,plain,
% 3.97/4.19 ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), B!6)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[186, 183])).
% 3.97/4.19 tff(188,plain,
% 3.97/4.19 (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), B!6)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[187, 159])).
% 3.97/4.19 tff(189,plain,
% 3.97/4.19 ($false),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[188, 58])).
% 3.97/4.19 tff(190,plain,(in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.19 tff(191,plain,
% 3.97/4.19 ((~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) <=> (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)))) | (~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | (~(in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)))),
% 3.97/4.19 inference(tautology,[status(thm)],[])).
% 3.97/4.19 tff(192,plain,
% 3.97/4.19 ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | (~(in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[191, 112])).
% 3.97/4.19 tff(193,plain,
% 3.97/4.19 (~(in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[192, 190])).
% 3.97/4.19 tff(194,plain,
% 3.97/4.19 ((in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)) | (~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7))),
% 3.97/4.19 inference(tautology,[status(thm)],[])).
% 3.97/4.19 tff(195,plain,
% 3.97/4.19 (~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[194, 193])).
% 3.97/4.19 tff(196,plain,
% 3.97/4.19 (~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[195, 39])).
% 3.97/4.19 tff(197,plain,
% 3.97/4.19 ((in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), A!7)) | (~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)))),
% 3.97/4.19 inference(tautology,[status(thm)],[])).
% 3.97/4.19 tff(198,plain,
% 3.97/4.19 (~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[197, 193])).
% 3.97/4.19 tff(199,plain,
% 3.97/4.19 ((~(in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) <=> (~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)))))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)))),
% 3.97/4.19 inference(tautology,[status(thm)],[])).
% 3.97/4.19 tff(200,plain,
% 3.97/4.19 (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_difference(B!6, A!7)) | ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[199, 154])).
% 3.97/4.19 tff(201,plain,
% 3.97/4.19 ((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[200, 198])).
% 3.97/4.19 tff(202,plain,
% 3.97/4.19 ((~((~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3)))) | (~in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!3, B!6))) | in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))),
% 3.97/4.20 inference(tautology,[status(thm)],[])).
% 3.97/4.20 tff(203,plain,
% 3.97/4.20 (in(tptp_fun_D_0(set_union2(A!3, B!6), set_difference(B!6, A!7), A!7), set_union2(A!7, A!3))),
% 3.97/4.20 inference(unit_resolution,[status(thm)],[202, 201, 190])).
% 3.97/4.20 tff(204,plain,
% 3.97/4.20 ($false),
% 3.97/4.20 inference(unit_resolution,[status(thm)],[203, 196])).
% 3.97/4.20 % SZS output end Proof
%------------------------------------------------------------------------------