%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET787-1 : TPTP v8.2.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %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 : Mon Jun 24 14:22:28 EDT 2024
% Result : Unsatisfiable 109.67s 109.73s
% Output : CNFRefutation 109.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET787-1 : TPTP v8.2.0. Released v2.7.0.
% 0.04/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 : Sun Jun 23 12:53:54 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.52/0.57 start to proof:theBenchmark
% 109.67/109.72 %-------------------------------------------
% 109.67/109.72 % File :CSE---1.7
% 109.67/109.72 % Problem :theBenchmark
% 109.67/109.72 % Transform :cnf
% 109.67/109.72 % Format :tptp:raw
% 109.67/109.72 % Command :java -jar mcs_scs.jar %d %s
% 109.67/109.72
% 109.67/109.72 % Result :Theorem 109.120000s
% 109.67/109.72 % Output :CNFRefutation 109.120000s
% 109.67/109.72 %-------------------------------------------
% 109.67/109.73 %--------------------------------------------------------------------------
% 109.67/109.73 % File : SET787-1 : TPTP v8.2.0. Released v2.7.0.
% 109.67/109.73 % Domain : Set Theory
% 109.67/109.73 % Problem : un_eq_Union_2_c2
% 109.67/109.73 % Version : Especial.
% 109.67/109.73 % English :
% 109.67/109.73
% 109.67/109.73 % Refs : [Men03] Meng (2003), Email to G. Sutcliffe
% 109.67/109.73 % Source : [Men03]
% 109.67/109.73 % Names :
% 109.67/109.73
% 109.67/109.73 % Status : Unsatisfiable
% 109.67/109.73 % 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
% 109.67/109.73 % Syntax : Number of clauses : 14 ( 3 unt; 2 nHn; 11 RR)
% 109.67/109.73 % Number of literals : 26 ( 2 equ; 12 neg)
% 109.67/109.73 % Maximal clause size : 3 ( 1 avg)
% 109.67/109.73 % Maximal term depth : 4 ( 1 avg)
% 109.67/109.73 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 109.67/109.73 % Number of functors : 15 ( 15 usr; 4 con; 0-2 aty)
% 109.67/109.73 % Number of variables : 28 ( 4 sgn)
% 109.67/109.73 % SPC : CNF_UNS_RFO_SEQ_NHN
% 109.67/109.73
% 109.67/109.73 % Comments : Problem coming out of an Isabelle proof.
% 109.67/109.73 %--------------------------------------------------------------------------
% 109.67/109.73 %----two clauses for UnionE
% 109.67/109.73 cnf(clause119,axiom,
% 109.67/109.73 ( ~ member(U,union(V))
% 109.67/109.73 | member(U,unionE_sk1(U,V)) ) ).
% 109.67/109.73
% 109.67/109.73 cnf(clause120,axiom,
% 109.67/109.73 ( ~ member(U,union(V))
% 109.67/109.73 | member(unionE_sk1(U,V),V) ) ).
% 109.67/109.73
% 109.67/109.73 %----two clauses for subsetI
% 109.67/109.73 cnf(clause131,axiom,
% 109.67/109.73 ( member(subsetI_sk1(A,B),A)
% 109.67/109.73 | subset(A,B) ) ).
% 109.67/109.73
% 109.67/109.73 cnf(clause132,axiom,
% 109.67/109.73 ( ~ member(subsetI_sk1(A,B),B)
% 109.67/109.73 | subset(A,B) ) ).
% 109.67/109.73
% 109.67/109.73 %----consE
% 109.67/109.73 cnf(clause112,axiom,
% 109.67/109.73 ( ~ member(U,cons(V,W))
% 109.67/109.73 | U = V
% 109.67/109.73 | member(U,W) ) ).
% 109.67/109.73
% 109.67/109.73 %----UnI1
% 109.67/109.73 cnf(unI1,axiom,
% 109.67/109.73 ( ~ member(C,A)
% 109.67/109.73 | member(C,un(A,B)) ) ).
% 109.67/109.73
% 109.67/109.73 %----UnI2
% 109.67/109.73 cnf(unI2,axiom,
% 109.67/109.73 ( ~ member(C,B)
% 109.67/109.73 | member(C,un(A,B)) ) ).
% 109.67/109.73
% 109.67/109.73 %----emptyE
% 109.67/109.73 cnf(clause158,axiom,
% 109.67/109.73 ~ member(X,eptset) ).
% 109.67/109.73
% 109.67/109.73 %----converseI
% 109.67/109.73 cnf(clause10,axiom,
% 109.67/109.73 ( ~ member(pair(U,V),W)
% 109.67/109.73 | member(pair(V,U),converse(W)) ) ).
% 109.67/109.73
% 109.67/109.73 %----converseD
% 109.67/109.73 cnf(converseD,axiom,
% 109.67/109.73 ( ~ member(pair(A,B),converse(R))
% 109.67/109.73 | member(pair(B,A),R) ) ).
% 109.67/109.73
% 109.67/109.73 %----two clauses for converseE
% 109.67/109.73 cnf(converseE_1,axiom,
% 109.67/109.73 ( ~ member(YX,converse(R))
% 109.67/109.73 | YX = pair(converseE_sk2(YX),converseE_sk1(YX)) ) ).
% 109.67/109.73
% 109.67/109.73 cnf(converseE_2,axiom,
% 109.67/109.73 ( ~ member(YX,converse(R))
% 109.67/109.73 | member(pair(converse_sk1(YX),converse_sk2(YX)),R) ) ).
% 109.67/109.73
% 109.67/109.73 %----lemma Un_eq_Union: "A Un B = Union({A, B})"
% 109.67/109.73 %Set {A,B} is represented as cons(A,cons(B,0)).
% 109.67/109.73 cnf(un_eq_Union_2_c1,negated_conjecture,
% 109.67/109.73 member(sk2,union(cons(a,cons(b,eptset)))) ).
% 109.67/109.73
% 109.67/109.73 cnf(un_eq_Union_2_c2,negated_conjecture,
% 109.67/109.73 ~ member(sk2,un(a,b)) ).
% 109.67/109.73
% 109.67/109.73 %--------------------------------------------------------------------------
% 109.67/109.73 %-------------------------------------------
% 109.67/109.73 % Proof found
% 109.67/109.73 % SZS status Theorem for theBenchmark
% 109.67/109.73 % SZS output start Proof
% 109.67/109.73 %ClaNum:37(EqnAxiom:23)
% 109.67/109.73 %VarNum:60(SingletonVarNum:28)
% 109.67/109.73 %MaxLitNum:3
% 109.67/109.73 %MaxfuncDepth:3
% 109.67/109.73 %SharedTerms:10
% 109.67/109.73 %goalClause: 24 26
% 109.67/109.73 %singleGoalClaCount:2
% 109.67/109.73 [26]~P1(a1,f13(a2,a3))
% 109.67/109.73 [24]P1(a1,f12(f5(a2,f5(a3,a4))))
% 109.67/109.73 [25]~P1(x251,a4)
% 109.67/109.73 [27]P2(x271,x272)+P1(f14(x271,x272),x271)
% 109.67/109.73 [31]~P1(x311,f12(x312))+P1(x311,f15(x311,x312))
% 109.67/109.73 [32]~P1(x321,f12(x322))+P1(f15(x321,x322),x322)
% 109.67/109.73 [33]P2(x331,x332)+~P1(f14(x331,x332),x332)
% 109.67/109.73 [28]~P1(x281,f8(x282))+E(f11(f6(x281),f7(x281)),x281)
% 109.67/109.73 [35]~P1(x351,f8(x352))+P1(f11(f9(x351),f10(x351)),x352)
% 109.67/109.73 [29]~P1(x291,x293)+P1(x291,f13(x292,x293))
% 109.67/109.73 [30]~P1(x301,x302)+P1(x301,f13(x302,x303))
% 109.67/109.73 [36]~P1(f11(x362,x361),x363)+P1(f11(x361,x362),f8(x363))
% 109.67/109.73 [37]~P1(f11(x372,x371),f8(x373))+P1(f11(x371,x372),x373)
% 109.67/109.73 [34]E(x341,x342)+P1(x341,x343)+~P1(x341,f5(x342,x343))
% 109.67/109.73 %EqnAxiom
% 109.67/109.73 [1]E(x11,x11)
% 109.67/109.73 [2]E(x22,x21)+~E(x21,x22)
% 109.75/109.73 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 109.75/109.73 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43))
% 109.75/109.73 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52))
% 109.75/109.73 [6]~E(x61,x62)+E(f8(x61),f8(x62))
% 109.75/109.73 [7]~E(x71,x72)+E(f12(x71),f12(x72))
% 109.75/109.73 [8]~E(x81,x82)+E(f13(x81,x83),f13(x82,x83))
% 109.75/109.73 [9]~E(x91,x92)+E(f13(x93,x91),f13(x93,x92))
% 109.75/109.73 [10]~E(x101,x102)+E(f14(x101,x103),f14(x102,x103))
% 109.75/109.73 [11]~E(x111,x112)+E(f14(x113,x111),f14(x113,x112))
% 109.75/109.73 [12]~E(x121,x122)+E(f6(x121),f6(x122))
% 109.75/109.73 [13]~E(x131,x132)+E(f7(x131),f7(x132))
% 109.75/109.73 [14]~E(x141,x142)+E(f11(x141,x143),f11(x142,x143))
% 109.75/109.73 [15]~E(x151,x152)+E(f11(x153,x151),f11(x153,x152))
% 109.75/109.73 [16]~E(x161,x162)+E(f9(x161),f9(x162))
% 109.75/109.73 [17]~E(x171,x172)+E(f15(x171,x173),f15(x172,x173))
% 109.75/109.73 [18]~E(x181,x182)+E(f15(x183,x181),f15(x183,x182))
% 109.75/109.73 [19]~E(x191,x192)+E(f10(x191),f10(x192))
% 109.75/109.73 [20]P1(x202,x203)+~E(x201,x202)+~P1(x201,x203)
% 109.75/109.73 [21]P1(x213,x212)+~E(x211,x212)+~P1(x213,x211)
% 109.75/109.73 [22]P2(x222,x223)+~E(x221,x222)+~P2(x221,x223)
% 109.75/109.73 [23]P2(x233,x232)+~E(x231,x232)+~P2(x233,x231)
% 109.75/109.73
% 109.75/109.73 %-------------------------------------------
% 109.75/109.74 cnf(38,plain,
% 109.75/109.74 (~P1(a1,a3)),
% 109.75/109.74 inference(scs_inference,[],[26,29])).
% 109.75/109.74 cnf(40,plain,
% 109.75/109.74 (~P1(a1,a2)),
% 109.75/109.74 inference(scs_inference,[],[26,29,30])).
% 109.75/109.74 cnf(42,plain,
% 109.75/109.74 (~P1(x421,f12(a4))),
% 109.75/109.74 inference(scs_inference,[],[26,25,29,30,32])).
% 109.75/109.74 cnf(43,plain,
% 109.75/109.74 (~P1(x431,a4)),
% 109.75/109.74 inference(rename_variables,[],[25])).
% 109.75/109.74 cnf(46,plain,
% 109.75/109.74 (~P1(x461,a4)),
% 109.75/109.74 inference(rename_variables,[],[25])).
% 109.75/109.74 cnf(48,plain,
% 109.75/109.74 (~P1(x481,f8(a4))),
% 109.75/109.74 inference(scs_inference,[],[26,25,43,46,29,30,32,27,35])).
% 109.75/109.74 cnf(51,plain,
% 109.75/109.74 (~P1(f11(x511,x512),f8(f12(a4)))),
% 109.75/109.74 inference(scs_inference,[],[26,25,43,46,29,30,32,27,35,37])).
% 109.75/109.74 cnf(62,plain,
% 109.75/109.74 (~P1(x621,f12(a4))),
% 109.75/109.74 inference(rename_variables,[],[42])).
% 109.75/109.74 cnf(64,plain,
% 109.75/109.74 (~P1(x641,f8(f12(a4)))),
% 109.75/109.74 inference(scs_inference,[],[42,62,51,37,32,35])).
% 109.75/109.74 cnf(89,plain,
% 109.75/109.74 (~P1(x891,f8(a4))),
% 109.75/109.74 inference(rename_variables,[],[48])).
% 109.75/109.74 cnf(91,plain,
% 109.75/109.74 (~P1(x911,f12(f8(a4)))),
% 109.75/109.74 inference(scs_inference,[],[48,89,37,32])).
% 109.75/109.74 cnf(166,plain,
% 109.75/109.74 (~E(f5(a2,f5(a3,a4)),a4)),
% 109.75/109.74 inference(scs_inference,[],[42,24,21,7])).
% 109.75/109.74 cnf(172,plain,
% 109.75/109.74 (~E(f12(f5(a2,f5(a3,a4))),f8(a4))),
% 109.75/109.74 inference(scs_inference,[],[48,24,21])).
% 109.75/109.74 cnf(181,plain,
% 109.75/109.74 (~E(f12(f5(a2,f5(a3,a4))),f8(f12(a4)))),
% 109.75/109.74 inference(scs_inference,[],[64,24,21])).
% 109.75/109.74 cnf(189,plain,
% 109.75/109.74 (~E(f12(f5(a2,f5(a3,a4))),f12(f8(a4)))),
% 109.75/109.74 inference(scs_inference,[],[91,24,21])).
% 109.75/109.74 cnf(191,plain,
% 109.75/109.74 (~E(f5(a2,f5(a3,a4)),f8(a4))),
% 109.75/109.74 inference(scs_inference,[],[91,24,21,7])).
% 109.75/109.74 cnf(193,plain,
% 109.75/109.74 (~E(f8(a4),f5(a2,f5(a3,a4)))),
% 109.75/109.74 inference(scs_inference,[],[189,2,7])).
% 109.75/109.74 cnf(1596,plain,
% 109.75/109.74 (P1(a1,f15(a1,f5(a2,f5(a3,a4))))),
% 109.75/109.74 inference(scs_inference,[],[172,24,2,31])).
% 109.75/109.74 cnf(1598,plain,
% 109.75/109.74 (P1(f15(a1,f5(a2,f5(a3,a4))),f5(a2,f5(a3,a4)))),
% 109.75/109.74 inference(scs_inference,[],[172,24,2,31,32])).
% 109.75/109.74 cnf(1716,plain,
% 109.75/109.74 (~E(f8(f12(a4)),f12(f5(a2,f5(a3,a4))))),
% 109.75/109.74 inference(scs_inference,[],[181,2])).
% 109.75/109.74 cnf(1775,plain,
% 109.75/109.74 (~P1(f5(a2,f5(a3,a4)),f5(a4,a4))),
% 109.75/109.74 inference(scs_inference,[],[25,166,34])).
% 109.75/109.74 cnf(1803,plain,
% 109.75/109.74 (~E(f15(a1,f5(a2,f5(a3,a4))),a2)),
% 109.75/109.74 inference(scs_inference,[],[25,1716,40,193,1596,34,3,21])).
% 109.75/109.74 cnf(1814,plain,
% 109.75/109.74 (~P1(f5(a2,f5(a3,a4)),f5(f8(a4),f5(a4,a4)))),
% 109.75/109.74 inference(scs_inference,[],[1775,191,34])).
% 109.75/109.74 cnf(1930,plain,
% 109.75/109.74 (~E(f15(a1,f5(a2,f5(a3,a4))),a3)),
% 109.75/109.74 inference(scs_inference,[],[38,1814,166,1596,34,21])).
% 109.75/109.74 cnf(3804,plain,
% 109.75/109.74 (~P1(f15(a1,f5(a2,f5(a3,a4))),f5(a3,a4))),
% 109.75/109.74 inference(scs_inference,[],[1930,25,34])).
% 109.75/109.74 cnf(4888,plain,
% 109.75/109.74 ($false),
% 109.75/109.74 inference(scs_inference,[],[3804,1803,1598,34]),
% 109.75/109.74 ['proof']).
% 109.75/109.75 % SZS output end Proof
% 109.75/109.75 % Total time :109.120000s
%------------------------------------------------------------------------------