TSTP Solution File: SET787-1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET787-1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 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 : Thu Aug 31 14:31:02 EDT 2023
% Result : Unsatisfiable 1.17s 1.24s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET787-1 : TPTP v8.1.2. Released v2.7.0.
% 0.03/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n023.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
% 0.13/0.34 % DateTime : Sat Aug 26 10:35:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.48/0.57 start to proof:theBenchmark
% 1.17/1.23 %-------------------------------------------
% 1.17/1.23 % File :CSE---1.6
% 1.17/1.23 % Problem :theBenchmark
% 1.17/1.23 % Transform :cnf
% 1.17/1.23 % Format :tptp:raw
% 1.17/1.23 % Command :java -jar mcs_scs.jar %d %s
% 1.17/1.23
% 1.17/1.23 % Result :Theorem 0.620000s
% 1.17/1.23 % Output :CNFRefutation 0.620000s
% 1.17/1.23 %-------------------------------------------
% 1.17/1.24 %--------------------------------------------------------------------------
% 1.17/1.24 % File : SET787-1 : TPTP v8.1.2. Released v2.7.0.
% 1.17/1.24 % Domain : Set Theory
% 1.17/1.24 % Problem : un_eq_Union_2_c2
% 1.17/1.24 % Version : Especial.
% 1.17/1.24 % English :
% 1.17/1.24
% 1.17/1.24 % Refs : [Men03] Meng (2003), Email to G. Sutcliffe
% 1.17/1.24 % Source : [Men03]
% 1.17/1.24 % Names :
% 1.17/1.24
% 1.17/1.24 % Status : Unsatisfiable
% 1.17/1.24 % Rating : 0.10 v8.1.0, 0.00 v7.5.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.00 v6.3.0, 0.09 v6.2.0, 0.00 v6.1.0, 0.07 v6.0.0, 0.00 v5.4.0, 0.05 v5.3.0, 0.11 v5.2.0, 0.06 v5.1.0, 0.12 v5.0.0, 0.07 v4.1.0, 0.15 v4.0.1, 0.18 v4.0.0, 0.09 v3.7.0, 0.00 v3.4.0, 0.08 v3.3.0, 0.14 v3.2.0, 0.15 v3.1.0, 0.27 v2.7.0
% 1.17/1.24 % Syntax : Number of clauses : 14 ( 3 unt; 2 nHn; 11 RR)
% 1.17/1.24 % Number of literals : 26 ( 2 equ; 12 neg)
% 1.17/1.24 % Maximal clause size : 3 ( 1 avg)
% 1.17/1.24 % Maximal term depth : 4 ( 1 avg)
% 1.17/1.24 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 1.17/1.24 % Number of functors : 15 ( 15 usr; 4 con; 0-2 aty)
% 1.17/1.24 % Number of variables : 28 ( 4 sgn)
% 1.17/1.24 % SPC : CNF_UNS_RFO_SEQ_NHN
% 1.17/1.24
% 1.17/1.24 % Comments : Problem coming out of an Isabelle proof.
% 1.17/1.24 %--------------------------------------------------------------------------
% 1.17/1.24 %----two clauses for UnionE
% 1.17/1.24 cnf(clause119,axiom,
% 1.17/1.24 ( ~ member(U,union(V))
% 1.17/1.24 | member(U,unionE_sk1(U,V)) ) ).
% 1.17/1.24
% 1.17/1.24 cnf(clause120,axiom,
% 1.17/1.24 ( ~ member(U,union(V))
% 1.17/1.24 | member(unionE_sk1(U,V),V) ) ).
% 1.17/1.24
% 1.17/1.24 %----two clauses for subsetI
% 1.17/1.24 cnf(clause131,axiom,
% 1.17/1.24 ( member(subsetI_sk1(A,B),A)
% 1.17/1.24 | subset(A,B) ) ).
% 1.17/1.24
% 1.17/1.24 cnf(clause132,axiom,
% 1.17/1.24 ( ~ member(subsetI_sk1(A,B),B)
% 1.17/1.24 | subset(A,B) ) ).
% 1.17/1.24
% 1.17/1.24 %----consE
% 1.17/1.24 cnf(clause112,axiom,
% 1.17/1.24 ( ~ member(U,cons(V,W))
% 1.17/1.24 | U = V
% 1.17/1.24 | member(U,W) ) ).
% 1.17/1.24
% 1.17/1.24 %----UnI1
% 1.17/1.24 cnf(unI1,axiom,
% 1.17/1.24 ( ~ member(C,A)
% 1.17/1.24 | member(C,un(A,B)) ) ).
% 1.17/1.24
% 1.17/1.24 %----UnI2
% 1.17/1.24 cnf(unI2,axiom,
% 1.17/1.24 ( ~ member(C,B)
% 1.17/1.24 | member(C,un(A,B)) ) ).
% 1.17/1.24
% 1.17/1.24 %----emptyE
% 1.17/1.24 cnf(clause158,axiom,
% 1.17/1.24 ~ member(X,eptset) ).
% 1.17/1.24
% 1.17/1.24 %----converseI
% 1.17/1.24 cnf(clause10,axiom,
% 1.17/1.24 ( ~ member(pair(U,V),W)
% 1.17/1.24 | member(pair(V,U),converse(W)) ) ).
% 1.17/1.24
% 1.17/1.24 %----converseD
% 1.17/1.24 cnf(converseD,axiom,
% 1.17/1.24 ( ~ member(pair(A,B),converse(R))
% 1.17/1.24 | member(pair(B,A),R) ) ).
% 1.17/1.24
% 1.17/1.24 %----two clauses for converseE
% 1.17/1.24 cnf(converseE_1,axiom,
% 1.17/1.24 ( ~ member(YX,converse(R))
% 1.17/1.24 | YX = pair(converseE_sk2(YX),converseE_sk1(YX)) ) ).
% 1.17/1.24
% 1.17/1.24 cnf(converseE_2,axiom,
% 1.17/1.24 ( ~ member(YX,converse(R))
% 1.17/1.24 | member(pair(converse_sk1(YX),converse_sk2(YX)),R) ) ).
% 1.17/1.24
% 1.17/1.24 %----lemma Un_eq_Union: "A Un B = Union({A, B})"
% 1.17/1.24 %Set {A,B} is represented as cons(A,cons(B,0)).
% 1.17/1.24 cnf(un_eq_Union_2_c1,negated_conjecture,
% 1.17/1.24 member(sk2,union(cons(a,cons(b,eptset)))) ).
% 1.17/1.24
% 1.17/1.24 cnf(un_eq_Union_2_c2,negated_conjecture,
% 1.17/1.24 ~ member(sk2,un(a,b)) ).
% 1.17/1.24
% 1.17/1.24 %--------------------------------------------------------------------------
% 1.17/1.24 %-------------------------------------------
% 1.17/1.24 % Proof found
% 1.17/1.24 % SZS status Theorem for theBenchmark
% 1.17/1.24 % SZS output start Proof
% 1.17/1.24 %ClaNum:37(EqnAxiom:23)
% 1.17/1.24 %VarNum:60(SingletonVarNum:28)
% 1.17/1.24 %MaxLitNum:3
% 1.17/1.24 %MaxfuncDepth:3
% 1.17/1.24 %SharedTerms:10
% 1.17/1.24 %goalClause: 24 26
% 1.17/1.24 %singleGoalClaCount:2
% 1.17/1.24 [26]~P1(a1,f13(a2,a3))
% 1.17/1.24 [24]P1(a1,f12(f5(a2,f5(a3,a4))))
% 1.17/1.24 [25]~P1(x251,a4)
% 1.17/1.24 [27]P2(x271,x272)+P1(f14(x271,x272),x271)
% 1.17/1.24 [31]~P1(x311,f12(x312))+P1(x311,f15(x311,x312))
% 1.17/1.24 [32]~P1(x321,f12(x322))+P1(f15(x321,x322),x322)
% 1.17/1.24 [33]P2(x331,x332)+~P1(f14(x331,x332),x332)
% 1.17/1.24 [28]~P1(x281,f8(x282))+E(f11(f6(x281),f7(x281)),x281)
% 1.17/1.24 [35]~P1(x351,f8(x352))+P1(f11(f9(x351),f10(x351)),x352)
% 1.17/1.24 [29]~P1(x291,x293)+P1(x291,f13(x292,x293))
% 1.17/1.24 [30]~P1(x301,x302)+P1(x301,f13(x302,x303))
% 1.17/1.24 [36]~P1(f11(x362,x361),x363)+P1(f11(x361,x362),f8(x363))
% 1.17/1.24 [37]~P1(f11(x372,x371),f8(x373))+P1(f11(x371,x372),x373)
% 1.17/1.24 [34]E(x341,x342)+P1(x341,x343)+~P1(x341,f5(x342,x343))
% 1.17/1.24 %EqnAxiom
% 1.17/1.24 [1]E(x11,x11)
% 1.17/1.24 [2]E(x22,x21)+~E(x21,x22)
% 1.17/1.24 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.17/1.24 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43))
% 1.17/1.24 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52))
% 1.17/1.24 [6]~E(x61,x62)+E(f8(x61),f8(x62))
% 1.17/1.24 [7]~E(x71,x72)+E(f12(x71),f12(x72))
% 1.17/1.24 [8]~E(x81,x82)+E(f13(x81,x83),f13(x82,x83))
% 1.17/1.24 [9]~E(x91,x92)+E(f13(x93,x91),f13(x93,x92))
% 1.17/1.24 [10]~E(x101,x102)+E(f14(x101,x103),f14(x102,x103))
% 1.17/1.24 [11]~E(x111,x112)+E(f14(x113,x111),f14(x113,x112))
% 1.17/1.24 [12]~E(x121,x122)+E(f6(x121),f6(x122))
% 1.17/1.24 [13]~E(x131,x132)+E(f7(x131),f7(x132))
% 1.18/1.24 [14]~E(x141,x142)+E(f11(x141,x143),f11(x142,x143))
% 1.18/1.24 [15]~E(x151,x152)+E(f11(x153,x151),f11(x153,x152))
% 1.18/1.24 [16]~E(x161,x162)+E(f9(x161),f9(x162))
% 1.18/1.24 [17]~E(x171,x172)+E(f15(x171,x173),f15(x172,x173))
% 1.18/1.24 [18]~E(x181,x182)+E(f15(x183,x181),f15(x183,x182))
% 1.18/1.24 [19]~E(x191,x192)+E(f10(x191),f10(x192))
% 1.18/1.24 [20]P1(x202,x203)+~E(x201,x202)+~P1(x201,x203)
% 1.18/1.24 [21]P1(x213,x212)+~E(x211,x212)+~P1(x213,x211)
% 1.18/1.24 [22]P2(x222,x223)+~E(x221,x222)+~P2(x221,x223)
% 1.18/1.24 [23]P2(x233,x232)+~E(x231,x232)+~P2(x233,x231)
% 1.18/1.24
% 1.18/1.24 %-------------------------------------------
% 1.18/1.24 cnf(38,plain,
% 1.18/1.24 (~P1(a1,a2)),
% 1.18/1.24 inference(scs_inference,[],[26,30])).
% 1.18/1.24 cnf(39,plain,
% 1.18/1.24 (~P1(a1,a3)),
% 1.18/1.24 inference(scs_inference,[],[26,30,29])).
% 1.18/1.24 cnf(41,plain,
% 1.18/1.24 (~P1(x411,a4)),
% 1.18/1.24 inference(rename_variables,[],[25])).
% 1.18/1.24 cnf(43,plain,
% 1.18/1.24 (~P1(x431,f8(a4))),
% 1.18/1.24 inference(scs_inference,[],[25,41,26,30,29,27,35])).
% 1.18/1.24 cnf(44,plain,
% 1.18/1.24 (~P1(x441,a4)),
% 1.18/1.24 inference(rename_variables,[],[25])).
% 1.18/1.24 cnf(46,plain,
% 1.18/1.24 (~P1(x461,f12(a4))),
% 1.18/1.24 inference(scs_inference,[],[25,41,44,26,30,29,27,35,32])).
% 1.18/1.24 cnf(47,plain,
% 1.18/1.24 (~P1(x471,a4)),
% 1.18/1.24 inference(rename_variables,[],[25])).
% 1.18/1.24 cnf(53,plain,
% 1.18/1.24 (~E(a4,f12(f5(a2,f5(a3,a4))))),
% 1.18/1.24 inference(scs_inference,[],[24,25,41,44,47,26,30,29,27,35,32,37,21,2])).
% 1.18/1.24 cnf(54,plain,
% 1.18/1.24 (P1(a1,f15(a1,f5(a2,f5(a3,a4))))),
% 1.18/1.24 inference(scs_inference,[],[24,25,41,44,47,26,30,29,27,35,32,37,21,2,31])).
% 1.18/1.24 cnf(61,plain,
% 1.18/1.24 (P1(f15(a1,f5(a2,f5(a3,a4))),f5(a2,f5(a3,a4)))),
% 1.18/1.24 inference(scs_inference,[],[24,32])).
% 1.18/1.24 cnf(63,plain,
% 1.18/1.24 (~E(f12(f5(a2,f5(a3,a4))),f13(a2,a3))),
% 1.18/1.24 inference(scs_inference,[],[24,26,32,21])).
% 1.18/1.24 cnf(67,plain,
% 1.18/1.24 (~P1(x671,f12(f12(a4)))),
% 1.18/1.25 inference(scs_inference,[],[46,32])).
% 1.18/1.25 cnf(70,plain,
% 1.18/1.25 (E(f15(a1,f5(a2,f5(a3,a4))),a2)+P1(f15(a1,f5(a2,f5(a3,a4))),f5(a3,a4))),
% 1.18/1.25 inference(scs_inference,[],[61,46,32,34])).
% 1.18/1.25 cnf(73,plain,
% 1.18/1.25 (P1(a2,f5(a2,f5(a3,a4)))+P1(f15(a1,f5(a2,f5(a3,a4))),f5(a3,a4))),
% 1.18/1.25 inference(scs_inference,[],[38,61,46,54,32,34,21,22,20])).
% 1.18/1.25 cnf(74,plain,
% 1.18/1.25 (E(a2,f15(a1,f5(a2,f5(a3,a4))))+P1(f15(a1,f5(a2,f5(a3,a4))),f5(a3,a4))),
% 1.18/1.25 inference(scs_inference,[],[38,61,46,54,32,34,21,22,20,2])).
% 1.18/1.25 cnf(79,plain,
% 1.18/1.25 (~E(f15(a1,f5(a2,f5(a3,a4))),f13(a2,a3))),
% 1.18/1.25 inference(scs_inference,[],[26,25,63,54,2,34,21])).
% 1.18/1.25 cnf(82,plain,
% 1.18/1.25 (~P1(f15(a1,f5(a2,f5(a3,a4))),f5(f13(a2,a3),a4))),
% 1.18/1.25 inference(scs_inference,[],[25,79,34])).
% 1.18/1.25 cnf(83,plain,
% 1.18/1.25 (~P1(x831,a4)),
% 1.18/1.25 inference(rename_variables,[],[25])).
% 1.18/1.25 cnf(85,plain,
% 1.18/1.25 (~E(f5(a2,f5(a3,a4)),a4)),
% 1.18/1.25 inference(scs_inference,[],[25,83,79,61,34,21])).
% 1.18/1.25 cnf(88,plain,
% 1.18/1.25 (~P1(x881,f12(f12(a4)))),
% 1.18/1.25 inference(rename_variables,[],[67])).
% 1.18/1.25 cnf(91,plain,
% 1.18/1.25 (~P1(x911,f12(f12(a4)))),
% 1.18/1.25 inference(rename_variables,[],[67])).
% 1.18/1.25 cnf(93,plain,
% 1.18/1.25 (~P1(x931,f8(f12(f12(a4))))),
% 1.18/1.25 inference(scs_inference,[],[25,83,67,88,91,79,61,34,21,27,37,35])).
% 1.18/1.25 cnf(97,plain,
% 1.18/1.25 (~E(a4,f5(a2,f5(a3,a4)))),
% 1.18/1.25 inference(scs_inference,[],[39,85,20,2])).
% 1.18/1.25 cnf(99,plain,
% 1.18/1.25 (~P1(x991,f12(f8(a4)))),
% 1.18/1.25 inference(scs_inference,[],[43,32])).
% 1.18/1.25 cnf(105,plain,
% 1.18/1.25 (~P1(x1051,f8(a4))),
% 1.18/1.25 inference(rename_variables,[],[43])).
% 1.18/1.25 cnf(107,plain,
% 1.18/1.25 (~E(f15(a1,f5(a2,f5(a3,a4))),a3)),
% 1.18/1.25 inference(scs_inference,[],[39,43,97,54,34,21])).
% 1.18/1.25 cnf(109,plain,
% 1.18/1.25 (~P1(x1091,f8(a4))),
% 1.18/1.25 inference(rename_variables,[],[43])).
% 1.18/1.25 cnf(111,plain,
% 1.18/1.25 (~P1(x1111,f8(f8(a4)))),
% 1.18/1.25 inference(scs_inference,[],[39,43,105,109,97,54,34,21,27,35])).
% 1.18/1.25 cnf(153,plain,
% 1.18/1.25 (~P1(x1531,f12(a4))),
% 1.18/1.25 inference(rename_variables,[],[46])).
% 1.18/1.25 cnf(155,plain,
% 1.18/1.25 (~E(f5(a2,f5(a3,a4)),f12(a4))),
% 1.18/1.25 inference(scs_inference,[],[46,153,53,61,34,21])).
% 1.18/1.25 cnf(195,plain,
% 1.18/1.25 (~E(f5(a2,f5(a3,a4)),f5(f13(a2,a3),a4))),
% 1.18/1.25 inference(scs_inference,[],[53,82,43,61,34,21])).
% 1.18/1.25 cnf(270,plain,
% 1.18/1.25 (~E(f12(a4),f5(a2,f5(a3,a4)))),
% 1.18/1.25 inference(scs_inference,[],[93,155,61,21,2])).
% 1.18/1.25 cnf(280,plain,
% 1.18/1.25 (~P1(x2801,f12(f8(a4)))),
% 1.18/1.25 inference(rename_variables,[],[99])).
% 1.18/1.25 cnf(283,plain,
% 1.18/1.25 (~E(f15(a1,f5(a2,f5(a3,a4))),f12(f8(a4)))),
% 1.18/1.25 inference(scs_inference,[],[99,280,195,270,54,34,2,21])).
% 1.18/1.25 cnf(299,plain,
% 1.18/1.25 (~P1(f15(a1,f5(a2,f5(a3,a4))),f5(a3,a4))),
% 1.18/1.25 inference(scs_inference,[],[107,111,283,25,54,2,21,34])).
% 1.18/1.25 cnf(305,plain,
% 1.18/1.25 (E(f15(a1,f5(a2,f5(a3,a4))),a2)),
% 1.18/1.25 inference(scs_inference,[],[299,70])).
% 1.18/1.25 cnf(306,plain,
% 1.18/1.25 (P1(a2,f5(a2,f5(a3,a4)))),
% 1.18/1.25 inference(scs_inference,[],[299,73])).
% 1.18/1.25 cnf(307,plain,
% 1.18/1.25 (E(a2,f15(a1,f5(a2,f5(a3,a4))))),
% 1.18/1.25 inference(scs_inference,[],[299,74])).
% 1.18/1.25 cnf(314,plain,
% 1.18/1.25 ($false),
% 1.18/1.25 inference(scs_inference,[],[305,299,307,306,38,54,30,29,20,21]),
% 1.18/1.25 ['proof']).
% 1.18/1.25 % SZS output end Proof
% 1.18/1.25 % Total time :0.620000s
%------------------------------------------------------------------------------