TSTP Solution File: GRP028-3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP028-3 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n022.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 00:10:39 EDT 2023
% Result : Unsatisfiable 0.45s 0.63s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : GRP028-3 : TPTP v8.1.2. Released v1.1.0.
% 0.11/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.11/0.32 % Computer : n022.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 19:44:39 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.56 start to proof:theBenchmark
% 0.45/0.62 %-------------------------------------------
% 0.45/0.62 % File :CSE---1.6
% 0.45/0.62 % Problem :theBenchmark
% 0.45/0.62 % Transform :cnf
% 0.45/0.62 % Format :tptp:raw
% 0.45/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.45/0.62
% 0.45/0.62 % Result :Theorem 0.010000s
% 0.45/0.62 % Output :CNFRefutation 0.010000s
% 0.45/0.63 %-------------------------------------------
% 0.45/0.63 %--------------------------------------------------------------------------
% 0.45/0.63 % File : GRP028-3 : TPTP v8.1.2. Released v1.1.0.
% 0.45/0.63 % Domain : Group Theory (Semigroups)
% 0.45/0.63 % Problem : In semigroups, left and right solutions => right id exists
% 0.45/0.63 % Version : [MOW76] axioms : Reduced > Incomplete.
% 0.45/0.63 % English : If there are left and right solutions, then there is a right
% 0.45/0.63 % identity element.
% 0.45/0.63
% 0.45/0.63 % Refs : [Luc68] Luckham (1968), Some Tree-paring Strategies for Theore
% 0.45/0.63 % : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% 0.45/0.63 % Source : [Luc68]
% 0.45/0.63 % Names : Example 1 [Luc68]
% 0.45/0.63
% 0.45/0.63 % Status : Unsatisfiable
% 0.45/0.63 % Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 v5.2.0, 0.00 v2.1.0, 0.00 v2.0.0
% 0.45/0.63 % Syntax : Number of clauses : 6 ( 4 unt; 0 nHn; 3 RR)
% 0.45/0.63 % Number of literals : 12 ( 0 equ; 7 neg)
% 0.45/0.63 % Maximal clause size : 4 ( 2 avg)
% 0.45/0.63 % Maximal term depth : 2 ( 1 avg)
% 0.45/0.63 % Number of predicates : 1 ( 1 usr; 0 prp; 3-3 aty)
% 0.45/0.63 % Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% 0.45/0.63 % Number of variables : 19 ( 0 sgn)
% 0.45/0.63 % SPC : CNF_UNS_RFO_NEQ_HRN
% 0.45/0.63
% 0.45/0.63 % Comments : [Luc68] uses less axioms than [MOW76].
% 0.45/0.63 %--------------------------------------------------------------------------
% 0.45/0.63 %----Include Semigroup axioms
% 0.45/0.63 % include('Axioms/GRP002-0.ax').
% 0.45/0.63 %--------------------------------------------------------------------------
% 0.45/0.63 %----This axiom is called closure or totality in some axiomatisations
% 0.45/0.63 cnf(total_function1,axiom,
% 0.45/0.63 product(X,Y,multiply(X,Y)) ).
% 0.45/0.63
% 0.45/0.63 %----This axiom is called well_definedness in some axiomatisations
% 0.45/0.63 %input_clause(total_function2,axiom,
% 0.45/0.63 % [--product(X,Y,Z),
% 0.45/0.63 % --product(X,Y,W),
% 0.45/0.63 % ++equal(Z,W)]).
% 0.45/0.63
% 0.45/0.63 cnf(associativity1,axiom,
% 0.45/0.63 ( ~ product(X,Y,U)
% 0.45/0.63 | ~ product(Y,Z,V)
% 0.45/0.63 | ~ product(U,Z,W)
% 0.45/0.63 | product(X,V,W) ) ).
% 0.45/0.63
% 0.45/0.63 cnf(associativity2,axiom,
% 0.45/0.63 ( ~ product(X,Y,U)
% 0.45/0.63 | ~ product(Y,Z,V)
% 0.45/0.63 | ~ product(X,V,W)
% 0.45/0.63 | product(U,Z,W) ) ).
% 0.45/0.63
% 0.45/0.63 cnf(left_soln,hypothesis,
% 0.45/0.63 product(left_solution(X,Y),X,Y) ).
% 0.45/0.63
% 0.45/0.63 cnf(right_soln,hypothesis,
% 0.45/0.63 product(X,right_solution(X,Y),Y) ).
% 0.45/0.63
% 0.45/0.63 %----There is an element for which no X is identity
% 0.45/0.63 cnf(prove_there_is_a_right_identity,negated_conjecture,
% 0.45/0.63 ~ product(not_identity(X),X,not_identity(X)) ).
% 0.45/0.63
% 0.45/0.63 %--------------------------------------------------------------------------
% 0.45/0.63 %-------------------------------------------
% 0.45/0.63 % Proof found
% 0.45/0.63 % SZS status Theorem for theBenchmark
% 0.45/0.63 % SZS output start Proof
% 0.45/0.63 %ClaNum:6(EqnAxiom:0)
% 0.45/0.63 %VarNum:39(SingletonVarNum:19)
% 0.45/0.63 %MaxLitNum:4
% 0.45/0.63 %MaxfuncDepth:1
% 0.45/0.63 %SharedTerms:0
% 0.45/0.63 %goalClause: 4
% 0.45/0.63 %singleGoalClaCount:1
% 0.45/0.63 [4]~P1(f4(x41),x41,f4(x41))
% 0.45/0.63 [1]P1(x11,x12,f1(x11,x12))
% 0.45/0.63 [2]P1(x21,f3(x21,x22),x22)
% 0.45/0.63 [3]P1(f2(x31,x32),x31,x32)
% 0.45/0.63 [5]~P1(x56,x54,x51)+P1(x51,x52,x53)+~P1(x54,x52,x55)+~P1(x56,x55,x53)
% 0.45/0.63 [6]~P1(x61,x66,x64)+P1(x61,x62,x63)+~P1(x64,x65,x63)+~P1(x66,x65,x62)
% 0.45/0.63 %EqnAxiom
% 0.45/0.63
% 0.45/0.63 %-------------------------------------------
% 0.45/0.64 cnf(43,plain,
% 0.45/0.64 (P1(x431,f3(x431,x432),x432)),
% 0.45/0.64 inference(rename_variables,[],[2])).
% 0.45/0.64 cnf(45,plain,
% 0.45/0.64 ($false),
% 0.45/0.64 inference(scs_inference,[],[2,43,3,4,1,6,5]),
% 0.45/0.64 ['proof']).
% 0.45/0.64 % SZS output end Proof
% 0.45/0.64 % Total time :0.010000s
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