TSTP Solution File: SET578+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET578+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 05:07:05 EDT 2022
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET578+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 06:58:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(member_type, type, (
% 0.21/0.42 member: ( $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_B_4_type, type, (
% 0.21/0.42 tptp_fun_B_4: $i)).
% 0.21/0.42 tff(tptp_fun_D_1_type, type, (
% 0.21/0.42 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.21/0.42 tff(intersection_type, type, (
% 0.21/0.42 intersection: ( $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_C_3_type, type, (
% 0.21/0.42 tptp_fun_C_3: $i)).
% 0.21/0.42 tff(tptp_fun_D_2_type, type, (
% 0.21/0.42 tptp_fun_D_2: $i)).
% 0.21/0.42 tff(1,assumption,(~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))), introduced(assumption)).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (^[E: $i] : refl((member(E, B!4) <=> (~((~member(E, C!3)) | (~member(E, D!2))))) <=> (member(E, B!4) <=> (~((~member(E, C!3)) | (~member(E, D!2))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (![E: $i] : (member(E, B!4) <=> (~((~member(E, C!3)) | (~member(E, D!2))))) <=> ![E: $i] : (member(E, B!4) <=> (~((~member(E, C!3)) | (~member(E, D!2)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (^[E: $i] : rewrite((member(E, B!4) <=> (member(E, C!3) & member(E, D!2))) <=> (member(E, B!4) <=> (~((~member(E, C!3)) | (~member(E, D!2))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (![E: $i] : (member(E, B!4) <=> (member(E, C!3) & member(E, D!2))) <=> ![E: $i] : (member(E, B!4) <=> (~((~member(E, C!3)) | (~member(E, D!2)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 ((![E: $i] : (member(E, B!4) <=> (member(E, C!3) & member(E, D!2))) & (~(B!4 = intersection(C!3, D!2)))) <=> (![E: $i] : (member(E, B!4) <=> (member(E, C!3) & member(E, D!2))) & (~(B!4 = intersection(C!3, D!2))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 ((~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 ((~![B: $i, C: $i, D: $i] : (![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D))) => (B = intersection(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(9,axiom,(~![B: $i, C: $i, D: $i] : (![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D))) => (B = intersection(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th19')).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[13, 7])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[15, 7])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (![E: $i] : (member(E, B!4) <=> (member(E, C!3) & member(E, D!2))) & (~(B!4 = intersection(C!3, D!2)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 (![E: $i] : (member(E, B!4) <=> (member(E, C!3) & member(E, D!2)))),
% 0.21/0.42 inference(and_elim,[status(thm)],[17])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 (![E: $i] : (member(E, B!4) <=> (~((~member(E, C!3)) | (~member(E, D!2)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[18, 5])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 (![E: $i] : (member(E, B!4) <=> (~((~member(E, C!3)) | (~member(E, D!2)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[19, 3])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 ((~![E: $i] : (member(E, B!4) <=> (~((~member(E, C!3)) | (~member(E, D!2)))))) | (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 ((~(member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))))) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4) | ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4) | ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[24, 1])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 (^[B: $i, C: $i, D: $i] : refl((member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 (^[B: $i, C: $i, D: $i] : rewrite((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(31,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersection_defn')).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.42 tff(33,plain,(
% 0.21/0.42 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[32])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 ((member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3))))) <=> (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[37])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[38, 36])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[41, 35])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 ((~(member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))))) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) | ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) | ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[44, 1])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.21/0.43 inference(pull_quant,[status(thm)],[])).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 (^[B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> (~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))))), pull_quant((~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C))))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(50,plain,
% 0.21/0.43 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[50, 48])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[51, 47])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[54, 52])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (^[B: $i, C: $i] : rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(61,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_member_defn')).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.43 tff(63,plain,(
% 0.21/0.43 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[62])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))) | (~((~((~(intersection(D!2, C!3) = B!4)) | (member(tptp_fun_D_1(intersection(D!2, C!3), C!3), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(intersection(D!2, C!3), C!3), B!4)))) | (~((intersection(D!2, C!3) = B!4) | ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (~((~((~(intersection(D!2, C!3) = B!4)) | (member(tptp_fun_D_1(intersection(D!2, C!3), C!3), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(intersection(D!2, C!3), C!3), B!4)))) | (~((intersection(D!2, C!3) = B!4) | ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (((~((~(intersection(D!2, C!3) = B!4)) | (member(tptp_fun_D_1(intersection(D!2, C!3), C!3), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(intersection(D!2, C!3), C!3), B!4)))) | (~((intersection(D!2, C!3) = B!4) | ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))))) | ((intersection(D!2, C!3) = B!4) | ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 ((intersection(D!2, C!3) = B!4) | ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 ((intersection(C!3, D!2) = B!4) <=> (B!4 = intersection(C!3, D!2))),
% 0.21/0.43 inference(commutativity,[status(thm)],[])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(75,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.43 tff(77,plain,(
% 0.21/0.43 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.21/0.43 inference(skolemize,[status(sab)],[76])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(C!3, D!2) = intersection(D!2, C!3))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (intersection(C!3, D!2) = intersection(D!2, C!3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 (intersection(D!2, C!3) = intersection(C!3, D!2)),
% 0.21/0.43 inference(symmetry,[status(thm)],[80])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 ((intersection(D!2, C!3) = B!4) <=> (intersection(C!3, D!2) = B!4)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[81])).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 ((intersection(D!2, C!3) = B!4) <=> (B!4 = intersection(C!3, D!2))),
% 0.21/0.43 inference(transitivity,[status(thm)],[82, 71])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 ((B!4 = intersection(C!3, D!2)) <=> (intersection(D!2, C!3) = B!4)),
% 0.21/0.43 inference(symmetry,[status(thm)],[83])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 ((~(B!4 = intersection(C!3, D!2))) <=> (~(intersection(D!2, C!3) = B!4))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 (~(B!4 = intersection(C!3, D!2))),
% 0.21/0.43 inference(and_elim,[status(thm)],[17])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (~(intersection(D!2, C!3) = B!4)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 ((~((intersection(D!2, C!3) = B!4) | ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)))) | (intersection(D!2, C!3) = B!4) | ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[88, 87, 70])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 ((~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[91, 45, 25])).
% 0.21/0.43 tff(93,plain,((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 ((~(member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)) | (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)) | (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[94, 22])).
% 0.21/0.44 tff(96,plain,
% 0.21/0.44 (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[95, 93])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 ((~(member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) | (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(98,plain,
% 0.21/0.44 ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) | (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[97, 42])).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[98, 93])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 ((~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(101,plain,
% 0.21/0.44 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[100, 89])).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[101, 99, 96])).
% 0.21/0.44 % SZS output end Proof
%------------------------------------------------------------------------------