TSTP Solution File: SET002-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n013.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 14:27:44 EDT 2023
% Result : Unsatisfiable 0.19s 0.66s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n013.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 16:24:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.19/0.65 %-------------------------------------------
% 0.19/0.65 % File :CSE---1.6
% 0.19/0.65 % Problem :theBenchmark
% 0.19/0.65 % Transform :cnf
% 0.19/0.65 % Format :tptp:raw
% 0.19/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.65
% 0.19/0.65 % Result :Theorem 0.030000s
% 0.19/0.65 % Output :CNFRefutation 0.030000s
% 0.19/0.65 %-------------------------------------------
% 0.19/0.65 %--------------------------------------------------------------------------
% 0.19/0.65 % File : SET002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.19/0.65 % Domain : Set Theory
% 0.19/0.65 % Problem : Idempotency of union
% 0.19/0.65 % Version : [LS74] axioms.
% 0.19/0.65 % English :
% 0.19/0.65
% 0.19/0.65 % Refs : [LS74] Lawrence & Starkey (1974), Experimental Tests of Resol
% 0.19/0.65 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 0.19/0.65 % Source : [SPRFN]
% 0.19/0.65 % Names : ls103 [LS74]
% 0.19/0.65 % : ls103 [WM76]
% 0.19/0.65
% 0.19/0.65 % Status : Unsatisfiable
% 0.19/0.65 % Rating : 0.00 v5.0.0, 0.07 v4.1.0, 0.00 v2.0.0
% 0.19/0.66 % Syntax : Number of clauses : 14 ( 2 unt; 3 nHn; 12 RR)
% 0.19/0.66 % Number of literals : 36 ( 0 equ; 18 neg)
% 0.19/0.66 % Maximal clause size : 4 ( 2 avg)
% 0.19/0.66 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.66 % Number of predicates : 4 ( 4 usr; 0 prp; 2-3 aty)
% 0.19/0.66 % Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% 0.19/0.66 % Number of variables : 34 ( 2 sgn)
% 0.19/0.66 % SPC : CNF_UNS_RFO_NEQ_NHN
% 0.19/0.66
% 0.19/0.66 % Comments :
% 0.19/0.66 %--------------------------------------------------------------------------
% 0.19/0.66 %----Include the member and subset axioms
% 0.19/0.66 include('Axioms/SET001-0.ax').
% 0.19/0.66 %----Include the member and union axioms
% 0.19/0.66 include('Axioms/SET001-1.ax').
% 0.19/0.66 %--------------------------------------------------------------------------
% 0.19/0.66 cnf(a_union_a_is_aUa,hypothesis,
% 0.19/0.66 union(a,a,aUa) ).
% 0.19/0.66
% 0.19/0.66 cnf(prove_a_equals_aUa,negated_conjecture,
% 0.19/0.66 ~ equal_sets(aUa,a) ).
% 0.19/0.66
% 0.19/0.66 %--------------------------------------------------------------------------
% 0.19/0.66 %-------------------------------------------
% 0.19/0.66 % Proof found
% 0.19/0.66 % SZS status Theorem for theBenchmark
% 0.19/0.66 % SZS output start Proof
% 0.19/0.66 %ClaNum:14(EqnAxiom:0)
% 0.19/0.66 %VarNum:90(SingletonVarNum:34)
% 0.19/0.66 %MaxLitNum:4
% 0.19/0.66 %MaxfuncDepth:1
% 0.19/0.66 %SharedTerms:4
% 0.19/0.66 %goalClause: 2
% 0.19/0.66 %singleGoalClaCount:1
% 0.19/0.66 [1]P1(a1,a1,a2)
% 0.19/0.66 [2]~P2(a2,a1)
% 0.19/0.66 [3]~P2(x32,x31)+P3(x31,x32)
% 0.19/0.66 [4]~P2(x41,x42)+P3(x41,x42)
% 0.19/0.66 [5]P3(x51,x52)+P4(f3(x51,x52),x51)
% 0.19/0.66 [8]P3(x81,x82)+~P4(f3(x81,x82),x82)
% 0.19/0.66 [7]~P3(x71,x72)+~P3(x72,x71)+P2(x71,x72)
% 0.19/0.66 [6]~P3(x63,x62)+P4(x61,x62)+~P4(x61,x63)
% 0.19/0.66 [13]P1(x131,x132,x133)+~P4(f4(x131,x132,x133),x133)+~P4(f4(x131,x132,x133),x132)
% 0.19/0.66 [14]P1(x141,x142,x143)+~P4(f4(x141,x142,x143),x143)+~P4(f4(x141,x142,x143),x141)
% 0.19/0.66 [9]P4(x91,x92)+~P1(x94,x93,x92)+~P4(x91,x93)
% 0.19/0.66 [10]P4(x101,x102)+~P1(x103,x104,x102)+~P4(x101,x103)
% 0.19/0.66 [12]P1(x121,x122,x123)+P4(f4(x121,x122,x123),x123)+P4(f4(x121,x122,x123),x122)+P4(f4(x121,x122,x123),x121)
% 0.19/0.66 [11]~P1(x113,x112,x114)+P4(x111,x112)+P4(x111,x113)+~P4(x111,x114)
% 0.19/0.66 %EqnAxiom
% 0.19/0.66
% 0.19/0.66 %-------------------------------------------
% 0.19/0.66 cnf(15,plain,
% 0.19/0.66 (~P3(a1,a2)+~P3(a2,a1)),
% 0.19/0.66 inference(scs_inference,[],[2,7])).
% 0.19/0.66 cnf(20,plain,
% 0.19/0.66 (~P4(x201,a1)+P4(x201,a2)),
% 0.19/0.66 inference(scs_inference,[],[1,10])).
% 0.19/0.66 cnf(28,plain,
% 0.19/0.66 (P3(x281,a2)+~P4(f3(x281,a2),a1)),
% 0.19/0.66 inference(scs_inference,[],[20,8])).
% 0.19/0.66 cnf(30,plain,
% 0.19/0.66 (~P3(a2,a1)+~P4(f3(a1,a2),a1)),
% 0.19/0.66 inference(scs_inference,[],[28,15])).
% 0.19/0.66 cnf(31,plain,
% 0.19/0.66 (P4(x311,a1)+~P4(x311,a2)),
% 0.19/0.66 inference(scs_inference,[],[1,11])).
% 0.19/0.66 cnf(32,plain,
% 0.19/0.66 (~P4(f3(a1,a2),a2)+~P3(a2,a1)),
% 0.19/0.66 inference(scs_inference,[],[1,11,30])).
% 0.19/0.66 cnf(33,plain,
% 0.19/0.66 (P3(a2,x331)+P4(f3(a2,x331),a1)),
% 0.19/0.66 inference(scs_inference,[],[31,5])).
% 0.19/0.66 cnf(34,plain,
% 0.19/0.66 (~P4(f3(a1,a2),a2)+~P4(f3(a2,a1),a1)),
% 0.19/0.66 inference(scs_inference,[],[32,8])).
% 0.19/0.66 cnf(35,plain,
% 0.19/0.66 (P4(f3(a2,a1),a1)+~P4(f3(a1,a2),a1)),
% 0.19/0.66 inference(scs_inference,[],[33,30])).
% 0.19/0.66 cnf(37,plain,
% 0.19/0.66 (~P4(f3(a1,a2),a1)+~P4(f3(a2,a1),a1)),
% 0.19/0.66 inference(scs_inference,[],[34,20])).
% 0.19/0.66 cnf(38,plain,
% 0.19/0.66 (P3(a1,a2)+P4(f3(a2,a1),a1)),
% 0.19/0.66 inference(scs_inference,[],[35,5])).
% 0.19/0.66 cnf(39,plain,
% 0.19/0.66 (P4(f3(a2,a1),a2)+P3(a1,a2)),
% 0.19/0.66 inference(scs_inference,[],[1,38,9])).
% 0.19/0.66 cnf(40,plain,
% 0.19/0.66 (~P3(a2,a1)+P4(f3(a2,a1),a2)),
% 0.19/0.66 inference(scs_inference,[],[39,15])).
% 0.19/0.66 cnf(41,plain,
% 0.19/0.66 (P4(f3(a2,a1),a2)+P4(f3(a2,a1),a1)),
% 0.19/0.66 inference(scs_inference,[],[40,33])).
% 0.19/0.66 cnf(42,plain,
% 0.19/0.66 (P3(a1,a2)+~P4(f3(a2,a1),a1)),
% 0.19/0.66 inference(scs_inference,[],[37,5])).
% 0.19/0.66 cnf(46,plain,
% 0.19/0.66 (P4(f3(a2,a1),a2)),
% 0.19/0.66 inference(scs_inference,[],[1,41,9])).
% 0.19/0.66 cnf(56,plain,
% 0.19/0.66 ($false),
% 0.19/0.66 inference(scs_inference,[],[46,2,31,8,7,42]),
% 0.19/0.66 ['proof']).
% 0.19/0.66 % SZS output end Proof
% 0.19/0.66 % Total time :0.030000s
%------------------------------------------------------------------------------