%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : GRP028-3 : TPTP v8.2.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n001.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 06:38:32 EDT 2024
% Result : Unsatisfiable 0.55s 0.61s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP028-3 : TPTP v8.2.0. Released v1.1.0.
% 0.10/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.32 % Computer : n001.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
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 20 06:56:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.55/0.60 %-------------------------------------------
% 0.55/0.60 % File :CSE---1.7
% 0.55/0.60 % Problem :theBenchmark
% 0.55/0.60 % Transform :cnf
% 0.55/0.60 % Format :tptp:raw
% 0.55/0.60 % Command :java -jar mcs_scs.jar %d %s
% 0.55/0.60
% 0.55/0.60 % Result :Theorem 0.010000s
% 0.55/0.60 % Output :CNFRefutation 0.010000s
% 0.55/0.60 %-------------------------------------------
% 0.55/0.61 %--------------------------------------------------------------------------
% 0.55/0.61 % File : GRP028-3 : TPTP v8.2.0. Released v1.1.0.
% 0.55/0.61 % Domain : Group Theory (Semigroups)
% 0.55/0.61 % Problem : In semigroups, left and right solutions => right id exists
% 0.55/0.61 % Version : [MOW76] axioms : Reduced > Incomplete.
% 0.55/0.61 % English : If there are left and right solutions, then there is a right
% 0.55/0.61 % identity element.
% 0.55/0.61
% 0.55/0.61 % Refs : [Luc68] Luckham (1968), Some Tree-paring Strategies for Theore
% 0.55/0.61 % : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% 0.55/0.61 % Source : [Luc68]
% 0.55/0.61 % Names : Example 1 [Luc68]
% 0.55/0.61
% 0.55/0.61 % Status : Unsatisfiable
% 0.55/0.61 % 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
% 0.55/0.61 % Syntax : Number of clauses : 6 ( 4 unt; 0 nHn; 3 RR)
% 0.55/0.61 % Number of literals : 12 ( 0 equ; 7 neg)
% 0.55/0.61 % Maximal clause size : 4 ( 2 avg)
% 0.55/0.61 % Maximal term depth : 2 ( 1 avg)
% 0.55/0.61 % Number of predicates : 1 ( 1 usr; 0 prp; 3-3 aty)
% 0.55/0.61 % Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% 0.55/0.61 % Number of variables : 19 ( 0 sgn)
% 0.55/0.61 % SPC : CNF_UNS_RFO_NEQ_HRN
% 0.55/0.61
% 0.55/0.61 % Comments : [Luc68] uses less axioms than [MOW76].
% 0.55/0.61 %--------------------------------------------------------------------------
% 0.55/0.61 %----Include Semigroup axioms
% 0.55/0.61 % include('Axioms/GRP002-0.ax').
% 0.55/0.61 %--------------------------------------------------------------------------
% 0.55/0.61 %----This axiom is called closure or totality in some axiomatisations
% 0.55/0.61 cnf(total_function1,axiom,
% 0.55/0.61 product(X,Y,multiply(X,Y)) ).
% 0.55/0.61
% 0.55/0.61 %----This axiom is called well_definedness in some axiomatisations
% 0.55/0.61 %input_clause(total_function2,axiom,
% 0.55/0.61 % [--product(X,Y,Z),
% 0.55/0.61 % --product(X,Y,W),
% 0.55/0.61 % ++equal(Z,W)]).
% 0.55/0.61
% 0.55/0.61 cnf(associativity1,axiom,
% 0.55/0.61 ( ~ product(X,Y,U)
% 0.55/0.61 | ~ product(Y,Z,V)
% 0.55/0.61 | ~ product(U,Z,W)
% 0.55/0.61 | product(X,V,W) ) ).
% 0.55/0.61
% 0.55/0.61 cnf(associativity2,axiom,
% 0.55/0.61 ( ~ product(X,Y,U)
% 0.55/0.61 | ~ product(Y,Z,V)
% 0.55/0.61 | ~ product(X,V,W)
% 0.55/0.61 | product(U,Z,W) ) ).
% 0.55/0.61
% 0.55/0.61 cnf(left_soln,hypothesis,
% 0.55/0.61 product(left_solution(X,Y),X,Y) ).
% 0.55/0.61
% 0.55/0.61 cnf(right_soln,hypothesis,
% 0.55/0.61 product(X,right_solution(X,Y),Y) ).
% 0.55/0.61
% 0.55/0.61 %----There is an element for which no X is identity
% 0.55/0.61 cnf(prove_there_is_a_right_identity,negated_conjecture,
% 0.55/0.61 ~ product(not_identity(X),X,not_identity(X)) ).
% 0.55/0.61
% 0.55/0.61 %--------------------------------------------------------------------------
% 0.55/0.61 %-------------------------------------------
% 0.55/0.61 % Proof found
% 0.55/0.61 % SZS status Theorem for theBenchmark
% 0.55/0.61 % SZS output start Proof
% 0.55/0.61 %ClaNum:6(EqnAxiom:0)
% 0.55/0.61 %VarNum:39(SingletonVarNum:19)
% 0.55/0.61 %MaxLitNum:4
% 0.55/0.61 %MaxfuncDepth:1
% 0.55/0.61 %SharedTerms:0
% 0.55/0.61 %goalClause: 4
% 0.55/0.61 %singleGoalClaCount:1
% 0.55/0.61 [4]~P1(f4(x41),x41,f4(x41))
% 0.55/0.61 [1]P1(x11,x12,f1(x11,x12))
% 0.55/0.61 [2]P1(x21,f3(x21,x22),x22)
% 0.55/0.61 [3]P1(f2(x31,x32),x31,x32)
% 0.55/0.61 [5]~P1(x56,x54,x51)+P1(x51,x52,x53)+~P1(x54,x52,x55)+~P1(x56,x55,x53)
% 0.55/0.61 [6]~P1(x61,x66,x64)+P1(x61,x62,x63)+~P1(x64,x65,x63)+~P1(x66,x65,x62)
% 0.55/0.61 %EqnAxiom
% 0.55/0.61
% 0.55/0.61 %-------------------------------------------
% 0.55/0.61 cnf(7,plain,
% 0.55/0.61 (P1(f1(x71,x72),f3(x72,x72),f1(x71,x72))),
% 0.55/0.61 inference(scs_inference,[],[1,2,5])).
% 0.55/0.61 cnf(17,plain,
% 0.55/0.61 (~P1(f1(f4(x171),f2(x172,x171)),x172,f4(x171))),
% 0.55/0.61 inference(scs_inference,[],[4,3,1,6])).
% 0.55/0.61 cnf(24,plain,
% 0.55/0.61 (~P1(f2(x241,x242),x241,f3(f4(x242),f4(x242)))),
% 0.55/0.61 inference(scs_inference,[],[1,17,2,5])).
% 0.55/0.61 cnf(42,plain,
% 0.55/0.61 (P1(x421,x422,f1(x421,x422))),
% 0.55/0.61 inference(rename_variables,[],[1])).
% 0.55/0.61 cnf(43,plain,
% 0.55/0.61 (P1(x431,f3(x431,x432),x432)),
% 0.55/0.61 inference(rename_variables,[],[2])).
% 0.55/0.61 cnf(44,plain,
% 0.55/0.61 (P1(x441,f3(x441,x442),x442)),
% 0.55/0.61 inference(rename_variables,[],[2])).
% 0.55/0.61 cnf(46,plain,
% 0.55/0.61 (P1(x461,f3(f3(x462,x461),x463),f1(x462,x463))),
% 0.55/0.61 inference(scs_inference,[],[2,44,43,1,42,6,5])).
% 0.55/0.61 cnf(55,plain,
% 0.55/0.61 (P1(f2(x551,x552),x551,x552)),
% 0.55/0.61 inference(rename_variables,[],[3])).
% 0.55/0.61 cnf(58,plain,
% 0.55/0.61 ($false),
% 0.55/0.61 inference(scs_inference,[],[3,55,4,46,7,24,6,5]),
% 0.55/0.61 ['proof']).
% 0.55/0.61 % SZS output end Proof
% 0.55/0.61 % Total time :0.010000s
%------------------------------------------------------------------------------