TSTP Solution File: GRP001-5 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP001-5 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 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 : Thu Aug 31 00:10:29 EDT 2023
% Result : Unsatisfiable 0.14s 0.52s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GRP001-5 : TPTP v8.1.2. Released v1.0.0.
% 0.05/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Aug 28 21:20:16 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.47 start to proof:theBenchmark
% 0.14/0.51 %-------------------------------------------
% 0.14/0.51 % File :CSE---1.6
% 0.14/0.51 % Problem :theBenchmark
% 0.14/0.51 % Transform :cnf
% 0.14/0.51 % Format :tptp:raw
% 0.14/0.51 % Command :java -jar mcs_scs.jar %d %s
% 0.14/0.51
% 0.14/0.51 % Result :Theorem 0.000000s
% 0.14/0.51 % Output :CNFRefutation 0.000000s
% 0.14/0.51 %-------------------------------------------
% 0.14/0.52 %------------------------------------------------------------------------------
% 0.14/0.52 % File : GRP001-5 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.52 % Domain : Group Theory
% 0.14/0.52 % Problem : X^2 = identity => commutativity
% 0.14/0.52 % Version : [Cha70] axioms : Incomplete.
% 0.14/0.52 % English : If the square of every element is the identity, the system
% 0.14/0.52 % is commutative.
% 0.14/0.52
% 0.14/0.52 % Refs : [Luc68] Luckham (1968), Some Tree-paring Strategies for Theore
% 0.14/0.52 % : [Lov69] Loveland (1969), Theorem-provers Combining Model Elimi
% 0.14/0.52 % : [Cha70] Chang (1970), The Unit Proof and the Input Proof in Th
% 0.14/0.52 % : [MRS72] Michie et al. (1972), G-deduction
% 0.14/0.52 % : [RR+72] Reboh et al. (1972), Study of automatic theorem provin
% 0.14/0.52 % : [CL73] Chang & Lee (1973), Symbolic Logic and Mechanical Theo
% 0.14/0.52 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 0.14/0.52 % Source : [Cha70]
% 0.14/0.52 % Names : Example 4 [Luc68]
% 0.14/0.52 % : Example 1 [Lov69]
% 0.14/0.52 % : Example 2 [Cha70]
% 0.14/0.52 % : ROB2 [MRS72]
% 0.14/0.52 % : GROUP2 [RR+72]
% 0.14/0.52 % : Example 2 [CL73]
% 0.14/0.52 % : GROUP2 [WM76]
% 0.14/0.52 % : ROB2 [WM76]
% 0.14/0.52 % : EX2 [SPRFN]
% 0.14/0.52
% 0.14/0.52 % Status : Unsatisfiable
% 0.14/0.52 % Rating : 0.00 v2.2.0, 0.11 v2.1.0, 0.00 v2.0.0
% 0.14/0.52 % Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 4 RR)
% 0.14/0.52 % Number of literals : 13 ( 0 equ; 7 neg)
% 0.14/0.52 % Maximal clause size : 4 ( 1 avg)
% 0.14/0.52 % Maximal term depth : 1 ( 1 avg)
% 0.14/0.52 % Number of predicates : 1 ( 1 usr; 0 prp; 3-3 aty)
% 0.14/0.52 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% 0.14/0.52 % Number of variables : 15 ( 0 sgn)
% 0.14/0.52 % SPC : CNF_UNS_EPR_NEQ_HRN
% 0.14/0.52
% 0.14/0.52 % Comments : In this format it is essentially a monoid problem.
% 0.14/0.52 %------------------------------------------------------------------------------
% 0.14/0.52 cnf(left_identity,axiom,
% 0.14/0.52 product(identity,X,X) ).
% 0.14/0.52
% 0.14/0.52 cnf(right_identity,axiom,
% 0.14/0.52 product(X,identity,X) ).
% 0.14/0.52
% 0.14/0.52 cnf(associativity1,axiom,
% 0.14/0.52 ( ~ product(X,Y,U)
% 0.14/0.52 | ~ product(Y,Z,V)
% 0.14/0.52 | ~ product(U,Z,W)
% 0.14/0.52 | product(X,V,W) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(associativity2,axiom,
% 0.14/0.52 ( ~ product(X,Y,U)
% 0.14/0.52 | ~ product(Y,Z,V)
% 0.14/0.52 | ~ product(X,V,W)
% 0.14/0.52 | product(U,Z,W) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(square_element,hypothesis,
% 0.14/0.52 product(X,X,identity) ).
% 0.14/0.52
% 0.14/0.52 cnf(a_times_b_is_c,hypothesis,
% 0.14/0.52 product(a,b,c) ).
% 0.14/0.52
% 0.14/0.52 cnf(prove_b_times_a_is_c,negated_conjecture,
% 0.14/0.52 ~ product(b,a,c) ).
% 0.14/0.52
% 0.14/0.52 %------------------------------------------------------------------------------
% 0.14/0.52 %-------------------------------------------
% 0.14/0.52 % Proof found
% 0.14/0.52 % SZS status Theorem for theBenchmark
% 0.14/0.52 % SZS output start Proof
% 0.14/0.52 %ClaNum:7(EqnAxiom:0)
% 0.14/0.52 %VarNum:30(SingletonVarNum:15)
% 0.14/0.52 %MaxLitNum:4
% 0.14/0.52 %MaxfuncDepth:0
% 0.14/0.52 %SharedTerms:6
% 0.14/0.52 %goalClause: 5
% 0.14/0.52 %singleGoalClaCount:1
% 0.14/0.52 [1]P1(a1,a2,a3)
% 0.14/0.52 [5]~P1(a2,a1,a3)
% 0.14/0.52 [2]P1(x21,x21,a4)
% 0.14/0.52 [3]P1(x31,a4,x31)
% 0.14/0.52 [4]P1(a4,x41,x41)
% 0.14/0.52 [6]~P1(x66,x64,x61)+P1(x61,x62,x63)+~P1(x64,x62,x65)+~P1(x66,x65,x63)
% 0.14/0.52 [7]~P1(x71,x76,x74)+P1(x71,x72,x73)+~P1(x74,x75,x73)+~P1(x76,x75,x72)
% 0.14/0.52 %EqnAxiom
% 0.14/0.52
% 0.14/0.52 %-------------------------------------------
% 0.14/0.52 cnf(15,plain,
% 0.14/0.52 (P1(x151,x151,a4)),
% 0.14/0.52 inference(rename_variables,[],[2])).
% 0.14/0.52 cnf(18,plain,
% 0.14/0.52 (~P1(a3,a1,a2)),
% 0.14/0.52 inference(scs_inference,[],[5,3,2,15,4,7,6])).
% 0.14/0.52 cnf(22,plain,
% 0.14/0.52 (P1(a3,a2,a1)),
% 0.14/0.52 inference(scs_inference,[],[1,3,2,6])).
% 0.14/0.52 cnf(35,plain,
% 0.14/0.52 ($false),
% 0.14/0.52 inference(scs_inference,[],[2,4,22,18,7]),
% 0.14/0.52 ['proof']).
% 0.14/0.52 % SZS output end Proof
% 0.14/0.52 % Total time :0.000000s
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