%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET002-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 14:19:56 EDT 2024
% Result : Unsatisfiable 0.54s 0.82s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET002-1 : TPTP v8.2.0. Released v1.0.0.
% 0.10/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.32 % Computer : n018.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jun 23 18:04:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.54/0.58 start to proof:theBenchmark
% 0.54/0.82 %-------------------------------------------
% 0.54/0.82 % File :CSE---1.7
% 0.54/0.82 % Problem :theBenchmark
% 0.54/0.82 % Transform :cnf
% 0.54/0.82 % Format :tptp:raw
% 0.54/0.82 % Command :java -jar mcs_scs.jar %d %s
% 0.54/0.82
% 0.54/0.82 % Result :Theorem 0.190000s
% 0.54/0.82 % Output :CNFRefutation 0.190000s
% 0.54/0.82 %-------------------------------------------
% 0.54/0.82 %--------------------------------------------------------------------------
% 0.54/0.82 % File : SET002-1 : TPTP v8.2.0. Released v1.0.0.
% 0.54/0.82 % Domain : Set Theory
% 0.54/0.82 % Problem : Idempotency of union
% 0.54/0.82 % Version : [LS74] axioms.
% 0.54/0.82 % English :
% 0.54/0.82
% 0.54/0.82 % Refs : [LS74] Lawrence & Starkey (1974), Experimental Tests of Resol
% 0.54/0.82 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 0.54/0.82 % Source : [SPRFN]
% 0.54/0.82 % Names : ls103 [LS74]
% 0.54/0.82 % : ls103 [WM76]
% 0.54/0.82
% 0.54/0.82 % Status : Unsatisfiable
% 0.54/0.82 % Rating : 0.00 v5.0.0, 0.07 v4.1.0, 0.00 v2.0.0
% 0.54/0.82 % Syntax : Number of clauses : 14 ( 2 unt; 3 nHn; 12 RR)
% 0.54/0.82 % Number of literals : 36 ( 0 equ; 18 neg)
% 0.54/0.82 % Maximal clause size : 4 ( 2 avg)
% 0.54/0.82 % Maximal term depth : 2 ( 1 avg)
% 0.54/0.82 % Number of predicates : 4 ( 4 usr; 0 prp; 2-3 aty)
% 0.54/0.82 % Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% 0.54/0.82 % Number of variables : 34 ( 2 sgn)
% 0.54/0.82 % SPC : CNF_UNS_RFO_NEQ_NHN
% 0.54/0.82
% 0.54/0.82 % Comments :
% 0.54/0.82 %--------------------------------------------------------------------------
% 0.54/0.82 %----Include the member and subset axioms
% 0.54/0.82 include('Axioms/SET001-0.ax').
% 0.54/0.82 %----Include the member and union axioms
% 0.54/0.82 include('Axioms/SET001-1.ax').
% 0.54/0.82 %--------------------------------------------------------------------------
% 0.54/0.82 cnf(a_union_a_is_aUa,hypothesis,
% 0.54/0.82 union(a,a,aUa) ).
% 0.54/0.82
% 0.54/0.82 cnf(prove_a_equals_aUa,negated_conjecture,
% 0.54/0.82 ~ equal_sets(aUa,a) ).
% 0.54/0.82
% 0.54/0.82 %--------------------------------------------------------------------------
% 0.54/0.82 %-------------------------------------------
% 0.54/0.82 % Proof found
% 0.54/0.82 % SZS status Theorem for theBenchmark
% 0.54/0.82 % SZS output start Proof
% 0.54/0.83 %ClaNum:14(EqnAxiom:0)
% 0.54/0.83 %VarNum:90(SingletonVarNum:34)
% 0.54/0.83 %MaxLitNum:4
% 0.54/0.83 %MaxfuncDepth:1
% 0.54/0.83 %SharedTerms:4
% 0.54/0.83 %goalClause: 2
% 0.54/0.83 %singleGoalClaCount:1
% 0.54/0.83 [1]P1(a1,a1,a2)
% 0.54/0.83 [2]~P2(a2,a1)
% 0.54/0.83 [3]~P2(x32,x31)+P3(x31,x32)
% 0.54/0.83 [4]~P2(x41,x42)+P3(x41,x42)
% 0.54/0.83 [5]P3(x51,x52)+P4(f3(x51,x52),x51)
% 0.54/0.83 [8]P3(x81,x82)+~P4(f3(x81,x82),x82)
% 0.54/0.83 [7]~P3(x71,x72)+~P3(x72,x71)+P2(x71,x72)
% 0.54/0.83 [6]~P3(x63,x62)+P4(x61,x62)+~P4(x61,x63)
% 0.54/0.83 [13]P1(x131,x132,x133)+~P4(f4(x131,x132,x133),x133)+~P4(f4(x131,x132,x133),x132)
% 0.54/0.83 [14]P1(x141,x142,x143)+~P4(f4(x141,x142,x143),x143)+~P4(f4(x141,x142,x143),x141)
% 0.54/0.83 [9]P4(x91,x92)+~P1(x94,x93,x92)+~P4(x91,x93)
% 0.54/0.83 [10]P4(x101,x102)+~P1(x103,x104,x102)+~P4(x101,x103)
% 0.54/0.83 [12]P1(x121,x122,x123)+P4(f4(x121,x122,x123),x123)+P4(f4(x121,x122,x123),x122)+P4(f4(x121,x122,x123),x121)
% 0.54/0.83 [11]~P1(x113,x112,x114)+P4(x111,x112)+P4(x111,x113)+~P4(x111,x114)
% 0.54/0.83 %EqnAxiom
% 0.54/0.83
% 0.54/0.83 %-------------------------------------------
% 0.54/0.83 cnf(17,plain,
% 0.54/0.83 (~P3(a2,a1)+P4(f3(a1,a2),a1)),
% 0.54/0.83 inference(scs_inference,[],[2,5,7])).
% 0.54/0.83 cnf(24,plain,
% 0.54/0.83 (~P3(x241,x242)+P3(x241,x243)+P4(f3(x241,x243),x242)),
% 0.54/0.83 inference(scs_inference,[],[6,5])).
% 0.54/0.83 cnf(25,plain,
% 0.54/0.83 (P4(f3(a1,a2),a2)+~P3(a2,a1)),
% 0.54/0.83 inference(scs_inference,[],[1,10,17])).
% 0.54/0.83 cnf(26,plain,
% 0.54/0.83 (P3(a1,a2)+~P3(a2,a1)),
% 0.54/0.83 inference(scs_inference,[],[25,8])).
% 0.54/0.83 cnf(27,plain,
% 0.54/0.83 (~P3(a2,a1)),
% 0.54/0.83 inference(scs_inference,[],[2,26,7])).
% 0.54/0.83 cnf(49,plain,
% 0.54/0.83 (P4(f3(a2,a1),x491)+~P2(x491,a2)),
% 0.54/0.83 inference(scs_inference,[],[27,3,24])).
% 0.54/0.83 cnf(50,plain,
% 0.54/0.83 (P4(f3(a2,a1),a1)+~P2(a2,a2)),
% 0.54/0.83 inference(scs_inference,[],[1,49,11])).
% 0.54/0.83 cnf(51,plain,
% 0.54/0.83 (~P3(a2,a2)+P4(f3(a2,a1),a1)),
% 0.54/0.83 inference(scs_inference,[],[50,7])).
% 0.54/0.83 cnf(52,plain,
% 0.54/0.83 (P4(f3(a2,a2),a2)+P4(f3(a2,a1),a1)),
% 0.54/0.83 inference(scs_inference,[],[51,5])).
% 0.54/0.83 cnf(53,plain,
% 0.54/0.83 (P3(a2,a2)+P4(f3(a2,a1),a1)),
% 0.54/0.83 inference(scs_inference,[],[52,8])).
% 0.54/0.83 cnf(54,plain,
% 0.54/0.83 (P4(f3(a2,a1),a1)),
% 0.54/0.83 inference(scs_inference,[],[53,51])).
% 0.54/0.83 cnf(56,plain,
% 0.54/0.83 ($false),
% 0.54/0.83 inference(scs_inference,[],[27,54,8]),
% 0.54/0.83 ['proof']).
% 0.54/0.83 % SZS output end Proof
% 0.54/0.83 % Total time :0.190000s
%------------------------------------------------------------------------------