%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET012-2 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 : Mon Jun 24 14:19:59 EDT 2024
% Result : Unsatisfiable 65.07s 65.21s
% Output : CNFRefutation 65.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SET012-2 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.05/0.09 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.29 % Computer : n032.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Sun Jun 23 17:24:23 EDT 2024
% 0.08/0.29 % CPUTime :
% 0.13/0.46 start to proof:theBenchmark
% 65.07/65.20 %-------------------------------------------
% 65.07/65.20 % File :CSE---1.7
% 65.07/65.20 % Problem :theBenchmark
% 65.07/65.20 % Transform :cnf
% 65.07/65.20 % Format :tptp:raw
% 65.07/65.20 % Command :java -jar mcs_scs.jar %d %s
% 65.07/65.20
% 65.07/65.20 % Result :Theorem 64.690000s
% 65.07/65.20 % Output :CNFRefutation 64.690000s
% 65.07/65.20 %-------------------------------------------
% 65.07/65.21 %--------------------------------------------------------------------------
% 65.07/65.21 % File : SET012-2 : TPTP v8.2.0. Bugfixed v2.1.0.
% 65.07/65.21 % Domain : Set Theory
% 65.07/65.21 % Problem : Complement is an involution
% 65.07/65.21 % Version : [MOW76] axioms : Especial.
% 65.07/65.21 % Theorem formulation : Modified.
% 65.07/65.21 % English :
% 65.07/65.21
% 65.07/65.21 % Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% 65.07/65.21 % Source : [ANL]
% 65.07/65.21 % Names : compl.ver1.in [ANL]
% 65.07/65.21
% 65.07/65.21 % Status : Unsatisfiable
% 65.07/65.21 % Rating : 0.17 v8.2.0, 0.14 v8.1.0, 0.00 v7.4.0, 0.33 v7.0.0, 0.25 v6.3.0, 0.29 v6.2.0, 0.11 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.38 v5.4.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.36 v5.0.0, 0.43 v4.1.0, 0.38 v4.0.1, 0.40 v4.0.0, 0.43 v3.4.0, 0.25 v3.3.0, 0.33 v2.7.0, 0.25 v2.6.0, 0.67 v2.5.0, 0.00 v2.1.0
% 65.07/65.21 % Syntax : Number of clauses : 24 ( 6 unt; 3 nHn; 18 RR)
% 65.07/65.21 % Number of literals : 48 ( 0 equ; 24 neg)
% 65.07/65.21 % Maximal clause size : 3 ( 2 avg)
% 65.07/65.21 % Maximal term depth : 2 ( 1 avg)
% 65.07/65.21 % Number of predicates : 4 ( 4 usr; 0 prp; 2-2 aty)
% 65.07/65.21 % Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% 65.07/65.21 % Number of variables : 48 ( 5 sgn)
% 65.07/65.21 % SPC : CNF_UNS_RFO_NEQ_NHN
% 65.07/65.21
% 65.07/65.21 % Comments :
% 65.07/65.21 % Bugfixes : v2.1.0 - Bugfix in SET002-0.eq
% 65.07/65.21 %--------------------------------------------------------------------------
% 65.07/65.21 %----Include set axioms
% 65.07/65.21 include('Axioms/SET002-0.ax').
% 65.07/65.21 %--------------------------------------------------------------------------
% 65.07/65.21 cnf(complement_of_a_is_b,hypothesis,
% 65.07/65.21 equal_sets(complement(a),b) ).
% 65.07/65.21
% 65.07/65.21 cnf(complement_of_b_is_c,hypothesis,
% 65.07/65.21 equal_sets(complement(b),c) ).
% 65.07/65.21
% 65.07/65.21 cnf(prove_a_equals_c,negated_conjecture,
% 65.07/65.21 ~ equal_sets(a,c) ).
% 65.07/65.21
% 65.07/65.21 %--------------------------------------------------------------------------
% 65.07/65.21 %-------------------------------------------
% 65.07/65.21 % Proof found
% 65.07/65.21 % SZS status Theorem for theBenchmark
% 65.07/65.21 % SZS output start Proof
% 65.07/65.21 %ClaNum:24(EqnAxiom:0)
% 65.07/65.21 %VarNum:97(SingletonVarNum:48)
% 65.07/65.21 %MaxLitNum:3
% 65.07/65.21 %MaxfuncDepth:1
% 65.07/65.21 %SharedTerms:9
% 65.07/65.21 %goalClause: 5
% 65.07/65.21 %singleGoalClaCount:1
% 65.07/65.21 [5]~P1(a1,a4)
% 65.07/65.21 [3]P1(f2(a1),a3)
% 65.07/65.21 [4]P1(f2(a3),a4)
% 65.07/65.21 [1]P1(x11,x11)
% 65.07/65.21 [2]P2(x21,x21)
% 65.07/65.21 [6]~P3(x61,a5)
% 65.07/65.21 [8]~P1(x82,x81)+P4(x81,x82)
% 65.07/65.21 [9]~P1(x91,x92)+P4(x91,x92)
% 65.07/65.21 [10]~P1(x102,x101)+P1(x101,x102)
% 65.07/65.21 [11]~P2(x112,x111)+P2(x111,x112)
% 65.07/65.21 [7]P3(x71,x72)+P3(x71,f2(x72))
% 65.07/65.21 [12]P4(x121,x122)+P3(f6(x121,x122),x121)
% 65.07/65.21 [13]~P3(x131,x132)+~P3(x131,f2(x132))
% 65.07/65.21 [22]P4(x221,x222)+~P3(f6(x221,x222),x222)
% 65.07/65.21 [18]~P3(x181,x183)+P3(x181,f8(x182,x183))
% 65.07/65.21 [19]~P3(x191,x192)+P3(x191,f8(x192,x193))
% 65.07/65.21 [20]P3(x201,x202)+~P3(x201,f7(x203,x202))
% 65.07/65.21 [21]P3(x211,x212)+~P3(x211,f7(x212,x213))
% 65.07/65.21 [15]~P4(x151,x152)+~P4(x152,x151)+P1(x151,x152)
% 65.07/65.21 [14]~P4(x143,x142)+P3(x141,x142)+~P3(x141,x143)
% 65.07/65.21 [16]~P1(x161,x163)+P1(x161,x162)+~P1(x163,x162)
% 65.07/65.21 [17]~P2(x171,x173)+P2(x171,x172)+~P2(x173,x172)
% 65.07/65.21 [23]~P3(x231,x233)+~P3(x231,x232)+P3(x231,f7(x232,x233))
% 65.07/65.21 [24]P3(x241,x242)+P3(x241,x243)+~P3(x241,f8(x243,x242))
% 65.07/65.21 %EqnAxiom
% 65.07/65.21
% 65.07/65.21 %-------------------------------------------
% 65.07/65.22 cnf(25,plain,
% 65.07/65.22 (~P1(a4,a1)),
% 65.07/65.22 inference(scs_inference,[],[5,10])).
% 65.07/65.22 cnf(27,plain,
% 65.07/65.22 (P4(a5,x271)),
% 65.07/65.22 inference(scs_inference,[],[5,6,10,12])).
% 65.07/65.22 cnf(31,plain,
% 65.07/65.22 (~P3(x311,f2(a1))+P3(x311,a3)),
% 65.07/65.22 inference(scs_inference,[],[3,9,14])).
% 65.07/65.22 cnf(32,plain,
% 65.07/65.22 (P3(x321,f2(f7(x322,a5)))),
% 65.07/65.22 inference(scs_inference,[],[6,7,20])).
% 65.07/65.22 cnf(33,plain,
% 65.07/65.22 (~P3(x331,f7(x332,a5))),
% 65.07/65.22 inference(scs_inference,[],[32,13])).
% 65.07/65.22 cnf(35,plain,
% 65.07/65.22 (P4(f7(x351,a5),x352)),
% 65.07/65.22 inference(scs_inference,[],[32,13,12])).
% 65.07/65.22 cnf(37,plain,
% 65.07/65.22 (P4(f2(a1),x371)+P3(f6(f2(a1),x371),a3)),
% 65.07/65.22 inference(scs_inference,[],[31,12])).
% 65.07/65.22 cnf(41,plain,
% 65.07/65.22 (P1(a5,f7(x411,a5))),
% 65.07/65.22 inference(scs_inference,[],[27,35,15])).
% 65.07/65.22 cnf(45,plain,
% 65.07/65.22 (P1(f2(a1),a5)+P3(f6(f2(a1),a5),a3)),
% 65.07/65.22 inference(scs_inference,[],[27,37,15])).
% 65.07/65.22 cnf(51,plain,
% 65.07/65.22 (P3(x511,f2(a5))),
% 65.07/65.22 inference(scs_inference,[],[32,33,23,7])).
% 65.07/65.22 cnf(59,plain,
% 65.07/65.22 (P1(a5,f2(a1))+P3(f6(f2(a1),a5),a3)),
% 65.07/65.22 inference(scs_inference,[],[10,45])).
% 65.07/65.22 cnf(60,plain,
% 65.07/65.22 (P1(a5,a3)+P3(f6(f2(a1),a5),a3)),
% 65.07/65.22 inference(scs_inference,[],[3,59,16])).
% 65.07/65.22 cnf(66,plain,
% 65.07/65.22 (P4(f2(a1),a3)),
% 65.07/65.22 inference(scs_inference,[],[3,10,8])).
% 65.07/65.22 cnf(67,plain,
% 65.07/65.22 (P1(a3,f2(a1))+~P4(a3,f2(a1))),
% 65.07/65.22 inference(scs_inference,[],[66,15])).
% 65.07/65.22 cnf(85,plain,
% 65.07/65.22 (~P4(a4,a1)+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[25,10,15])).
% 65.07/65.22 cnf(86,plain,
% 65.07/65.22 (P3(f6(a4,a1),a4)+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[85,12])).
% 65.07/65.22 cnf(87,plain,
% 65.07/65.22 (~P3(f6(a1,a4),a4)+P3(f6(a4,a1),a4)),
% 65.07/65.22 inference(scs_inference,[],[86,22])).
% 65.07/65.22 cnf(94,plain,
% 65.07/65.22 (~P4(a1,a4)+~P3(f6(a4,a1),a1)),
% 65.07/65.22 inference(scs_inference,[],[85,22])).
% 65.07/65.22 cnf(95,plain,
% 65.07/65.22 (~P4(a1,a4)+P3(f6(a4,a1),f2(a1))),
% 65.07/65.22 inference(scs_inference,[],[94,7])).
% 65.07/65.22 cnf(98,plain,
% 65.07/65.22 (~P4(a4,a1)+~P3(f6(a1,a4),a4)),
% 65.07/65.22 inference(scs_inference,[],[85,22])).
% 65.07/65.22 cnf(153,plain,
% 65.07/65.22 (~P3(x1531,f2(a1))+~P3(x1531,f2(a3))),
% 65.07/65.22 inference(scs_inference,[],[31,13])).
% 65.07/65.22 cnf(185,plain,
% 65.07/65.22 (P3(f6(a4,a1),a3)+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[31,95])).
% 65.07/65.22 cnf(186,plain,
% 65.07/65.22 (P3(f6(a4,a1),a3)+~P3(f6(a1,a4),a4)),
% 65.07/65.22 inference(scs_inference,[],[185,22])).
% 65.07/65.22 cnf(255,plain,
% 65.07/65.22 (P1(a3,f2(a1))),
% 65.07/65.22 inference(scs_inference,[],[3,67,8])).
% 65.07/65.22 cnf(281,plain,
% 65.07/65.22 (~P3(f6(a4,a1),a1)+~P3(f6(a1,a4),a4)),
% 65.07/65.22 inference(scs_inference,[],[94,22])).
% 65.07/65.22 cnf(335,plain,
% 65.07/65.22 (~P4(f2(a5),a1)+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[51,94,14])).
% 65.07/65.22 cnf(386,plain,
% 65.07/65.22 (~P1(a1,f2(a5))+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[335,8])).
% 65.07/65.22 cnf(394,plain,
% 65.07/65.22 (~P1(f2(a5),a1)+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[386,10])).
% 65.07/65.22 cnf(428,plain,
% 65.07/65.22 (~P4(f2(a5),a1)+~P3(f6(a1,a4),a4)),
% 65.07/65.22 inference(scs_inference,[],[335,22])).
% 65.07/65.22 cnf(483,plain,
% 65.07/65.22 (~P1(a1,f2(a5))+~P3(f6(a1,a4),a4)),
% 65.07/65.22 inference(scs_inference,[],[386,22])).
% 65.07/65.22 cnf(490,plain,
% 65.07/65.22 (~P1(f2(a5),a1)+~P3(f6(a1,a4),a4)),
% 65.07/65.22 inference(scs_inference,[],[394,22])).
% 65.07/65.22 cnf(611,plain,
% 65.07/65.22 (P3(x6111,a1)+~P3(x6111,f2(a3))),
% 65.07/65.22 inference(scs_inference,[],[153,7])).
% 65.07/65.22 cnf(627,plain,
% 65.07/65.22 (P4(x6271,a1)+~P3(f6(x6271,a1),f2(a3))),
% 65.07/65.22 inference(scs_inference,[],[611,22])).
% 65.07/65.22 cnf(649,plain,
% 65.07/65.22 (~P4(f2(a5),f2(a3))+P3(x6491,a1)),
% 65.07/65.22 inference(scs_inference,[],[51,611,14])).
% 65.07/65.22 cnf(743,plain,
% 65.07/65.22 (~P4(a3,f7(x7431,a5))+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[33,185,14])).
% 65.07/65.22 cnf(820,plain,
% 65.07/65.22 (~P4(f2(a5),f2(a3))+~P3(f6(a1,a4),a4)),
% 65.07/65.22 inference(scs_inference,[],[649,281])).
% 65.07/65.22 cnf(821,plain,
% 65.07/65.22 (~P1(f2(a3),f2(a5))+~P3(f6(a1,a4),a4)),
% 65.07/65.22 inference(scs_inference,[],[820,8])).
% 65.07/65.22 cnf(888,plain,
% 65.07/65.22 (~P1(f7(x8881,a5),a3)+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[743,8])).
% 65.07/65.22 cnf(893,plain,
% 65.07/65.22 (~P3(f6(a1,a4),a4)+~P4(a3,f7(x8931,a5))),
% 65.07/65.22 inference(scs_inference,[],[743,22])).
% 65.07/65.22 cnf(897,plain,
% 65.07/65.22 (~P1(a3,f7(x8971,a5))+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[743,9])).
% 65.07/65.22 cnf(1153,plain,
% 65.07/65.22 (~P3(f6(a1,a4),a4)+~P1(f7(x11531,a5),a3)),
% 65.07/65.22 inference(scs_inference,[],[888,22])).
% 65.07/65.22 cnf(1157,plain,
% 65.07/65.22 (~P1(a3,a5)+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[41,897,16])).
% 65.07/65.22 cnf(1158,plain,
% 65.07/65.22 (~P1(a5,a3)+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[1157,10])).
% 65.07/65.22 cnf(1159,plain,
% 65.07/65.22 (~P4(a3,a5)+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[27,1158,15])).
% 65.07/65.22 cnf(1160,plain,
% 65.07/65.22 (~P4(a1,a4)+P3(f6(a3,a5),a3)),
% 65.07/65.22 inference(scs_inference,[],[1159,12])).
% 65.07/65.22 cnf(1161,plain,
% 65.07/65.22 (P3(f6(a3,a5),a3)+~P3(f6(a1,a4),a4)),
% 65.07/65.22 inference(scs_inference,[],[1160,22])).
% 65.07/65.22 cnf(1169,plain,
% 65.07/65.22 (~P1(a3,a5)+~P3(f6(a1,a4),a4)),
% 65.07/65.22 inference(scs_inference,[],[1157,22])).
% 65.07/65.22 cnf(1182,plain,
% 65.07/65.22 (~P1(a5,f2(a1))+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[3,1158,16])).
% 65.07/65.22 cnf(1183,plain,
% 65.07/65.22 (~P1(f2(a1),a5)+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[1182,10])).
% 65.07/65.22 cnf(1196,plain,
% 65.07/65.22 (~P4(a3,a5)+~P3(f6(a1,a4),a4)),
% 65.07/65.22 inference(scs_inference,[],[1159,22])).
% 65.07/65.22 cnf(1204,plain,
% 65.07/65.22 (~P4(f2(a1),a5)+~P4(a1,a4)),
% 65.07/65.22 inference(scs_inference,[],[27,1182,15])).
% 65.07/65.22 cnf(1207,plain,
% 65.07/65.22 (~P1(a5,f2(a1))+~P3(f6(a1,a4),a4)),
% 65.07/65.22 inference(scs_inference,[],[1182,22])).
% 65.07/65.22 cnf(1220,plain,
% 65.07/65.22 (~P1(f2(a1),a5)+~P3(f6(a1,a4),a4)),
% 65.07/65.22 inference(scs_inference,[],[1183,22])).
% 65.07/65.22 cnf(1228,plain,
% 65.07/65.22 (~P4(f2(a1),a5)+~P3(f6(a1,a4),a4)),
% 65.07/65.22 inference(scs_inference,[],[1204,22])).
% 65.07/65.22 cnf(1232,plain,
% 65.07/65.22 (~P3(f6(a1,a4),a4)+~P1(a3,f7(x12321,a5))),
% 65.07/65.22 inference(scs_inference,[],[897,22])).
% 65.07/65.22 cnf(1617,plain,
% 65.07/65.22 (~P4(a3,f7(x16171,a5))+P1(a5,a3)),
% 65.07/65.22 inference(scs_inference,[],[33,60,14])).
% 65.07/65.22 cnf(1627,plain,
% 65.07/65.22 (~P1(f7(x16271,a5),a3)+P1(a5,a3)),
% 65.07/65.22 inference(scs_inference,[],[1617,8])).
% 65.07/65.22 cnf(1700,plain,
% 65.07/65.22 (~P1(f7(x17001,a5),f2(a1))+P1(a5,a3)),
% 65.07/65.22 inference(scs_inference,[],[3,1627,16])).
% 65.07/65.22 cnf(1701,plain,
% 65.07/65.22 (P4(a3,a5)+~P1(f7(x17011,a5),f2(a1))),
% 65.07/65.22 inference(scs_inference,[],[1700,8])).
% 65.07/65.22 cnf(2083,plain,
% 65.07/65.22 (P4(f2(a3),a4)),
% 65.07/65.22 inference(scs_inference,[],[4,10,8,9])).
% 65.07/65.22 cnf(2085,plain,
% 65.07/65.23 (~P3(x20851,a4)+P3(x20851,f2(a3))),
% 65.07/65.23 inference(scs_inference,[],[4,10,8,9,14])).
% 65.07/65.23 cnf(2089,plain,
% 65.07/65.23 (~P3(f6(a4,a1),a4)+~P4(a1,a4)),
% 65.07/65.23 inference(scs_inference,[],[4,10,8,9,14,611,94])).
% 65.07/65.23 cnf(2090,plain,
% 65.07/65.23 (~P3(f6(a4,a1),a4)+P4(a4,a1)),
% 65.07/65.23 inference(scs_inference,[],[4,10,8,9,14,611,94,627])).
% 65.07/65.23 cnf(2116,plain,
% 65.07/65.23 (P4(a3,f2(a1))),
% 65.07/65.23 inference(scs_inference,[],[255,9])).
% 65.07/65.23 cnf(2148,plain,
% 65.07/65.23 (~P3(f6(a1,a4),f2(a3))+~P3(f6(a4,a1),f7(x21481,a4))),
% 65.07/65.23 inference(scs_inference,[],[2083,14,2085,98,1169,1196,2090,1701,428,483,490,1207,1220,1228,893,1153,1232,87,186,281,821,1161,7,20])).
% 65.07/65.23 cnf(2156,plain,
% 65.07/65.23 (~P3(f6(a1,a4),f2(a3))+~P3(f6(a1,a4),f2(a4))),
% 65.07/65.23 inference(scs_inference,[],[2083,14,2085,98,1169,1196,2090,1701,428,483,490,1207,1220,1228,893,1153,1232,87,186,281,821,1161,7,20,21,18,19,13])).
% 65.07/65.23 cnf(2253,plain,
% 65.07/65.23 (P3(f6(a1,a4),a3)+~P3(f6(a4,a1),f7(x22531,a4))),
% 65.07/65.23 inference(scs_inference,[],[2148,7])).
% 65.07/65.23 cnf(2254,plain,
% 65.07/65.23 (~P3(f6(a4,a1),a4)+P3(f6(a1,a4),a3)),
% 65.07/65.23 inference(scs_inference,[],[51,2253,23])).
% 65.07/65.23 cnf(2607,plain,
% 65.07/65.23 (~P4(a1,a4)+P4(a4,a1)),
% 65.07/65.23 inference(scs_inference,[],[2089,12])).
% 65.07/65.23 cnf(2611,plain,
% 65.07/65.23 (~P4(a1,a4)),
% 65.07/65.23 inference(scs_inference,[],[2607,85])).
% 65.07/65.23 cnf(2632,plain,
% 65.07/65.23 (~P3(f6(a1,a4),f2(a3))),
% 65.07/65.23 inference(scs_inference,[],[2611,22,12,23,24,21,7,20,18,19,13,2156])).
% 65.07/65.23 cnf(2633,plain,
% 65.07/65.23 (~P3(f6(a1,a4),a3)),
% 65.07/65.23 inference(scs_inference,[],[2611,2116,22,12,23,24,21,7,20,18,19,13,2156,14])).
% 65.07/65.23 cnf(2640,plain,
% 65.07/65.23 (~P3(f6(a4,a1),a4)),
% 65.07/65.23 inference(scs_inference,[],[2633,2254])).
% 65.07/65.23 cnf(2651,plain,
% 65.07/65.23 ($false),
% 65.07/65.23 inference(scs_inference,[],[2632,2640,2633,21,7]),
% 65.07/65.23 ['proof']).
% 65.07/65.23 % SZS output end Proof
% 65.07/65.23 % Total time :64.690000s
%------------------------------------------------------------------------------