TSTP Solution File: GRP004-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP004-1 : 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 : n017.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 00:10:31 EDT 2023
% Result : Unsatisfiable 1.71s 1.78s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n017.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 : Mon Aug 28 20:10:57 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 1.71/1.77 %-------------------------------------------
% 1.71/1.77 % File :CSE---1.6
% 1.71/1.77 % Problem :theBenchmark
% 1.71/1.77 % Transform :cnf
% 1.71/1.77 % Format :tptp:raw
% 1.71/1.77 % Command :java -jar mcs_scs.jar %d %s
% 1.71/1.77
% 1.71/1.77 % Result :Theorem 1.160000s
% 1.71/1.77 % Output :CNFRefutation 1.160000s
% 1.71/1.77 %-------------------------------------------
% 1.71/1.78 %--------------------------------------------------------------------------
% 1.71/1.78 % File : GRP004-1 : TPTP v8.1.2. Released v1.0.0.
% 1.71/1.78 % Domain : Group Theory
% 1.71/1.78 % Problem : Left inverse and identity => Right inverse exists
% 1.71/1.78 % Version : [Cha70] axioms : Incomplete.
% 1.71/1.78 % English : In a group with left inverses and left identity every element
% 1.71/1.78 % has a right inverse.
% 1.71/1.78
% 1.71/1.78 % Refs : [Luc68] Luckham (1968), Some Tree-paring Strategies for Theore
% 1.71/1.78 % : [Cha70] Chang (1970), The Unit Proof and the Input Proof in Th
% 1.71/1.78 % : [CL73] Chang & Lee (1973), Symbolic Logic and Mechanical Theo
% 1.71/1.78 % Source : [Cha70]
% 1.71/1.78 % Names : Example 3 [Luc68]
% 1.71/1.78 % : Example 4 [Cha70]
% 1.71/1.78 % : Example 4 [CL73]
% 1.71/1.78 % : EX4 [SPRFN]
% 1.71/1.78
% 1.71/1.78 % Status : Unsatisfiable
% 1.71/1.78 % Rating : 0.00 v7.4.0, 0.17 v7.3.0, 0.00 v5.4.0, 0.11 v5.3.0, 0.10 v5.2.0, 0.00 v2.1.0, 0.00 v2.0.0
% 1.71/1.78 % Syntax : Number of clauses : 5 ( 3 unt; 0 nHn; 3 RR)
% 1.71/1.78 % Number of literals : 11 ( 0 equ; 7 neg)
% 1.71/1.78 % Maximal clause size : 4 ( 2 avg)
% 1.71/1.78 % Maximal term depth : 2 ( 1 avg)
% 1.71/1.78 % Number of predicates : 1 ( 1 usr; 0 prp; 3-3 aty)
% 1.71/1.78 % Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% 1.71/1.78 % Number of variables : 15 ( 1 sgn)
% 1.71/1.78 % SPC : CNF_UNS_RFO_NEQ_HRN
% 1.71/1.78
% 1.71/1.78 % Comments : [Luc68] is actually the right to left version.
% 1.71/1.78 %--------------------------------------------------------------------------
% 1.71/1.78 cnf(left_inverse,axiom,
% 1.71/1.78 product(inverse(X),X,identity) ).
% 1.71/1.78
% 1.71/1.78 cnf(left_identity,axiom,
% 1.71/1.78 product(identity,X,X) ).
% 1.71/1.78
% 1.71/1.78 cnf(associativity1,axiom,
% 1.71/1.78 ( ~ product(X,Y,U)
% 1.71/1.78 | ~ product(Y,Z,V)
% 1.71/1.78 | ~ product(U,Z,W)
% 1.71/1.78 | product(X,V,W) ) ).
% 1.71/1.78
% 1.71/1.78 cnf(associativity2,axiom,
% 1.71/1.78 ( ~ product(X,Y,U)
% 1.71/1.78 | ~ product(Y,Z,V)
% 1.71/1.78 | ~ product(X,V,W)
% 1.71/1.78 | product(U,Z,W) ) ).
% 1.71/1.78
% 1.71/1.78 cnf(prove_there_is_a_right_inverse,negated_conjecture,
% 1.71/1.78 ~ product(a,X,identity) ).
% 1.71/1.78
% 1.71/1.78 %--------------------------------------------------------------------------
% 1.71/1.78 %-------------------------------------------
% 1.71/1.78 % Proof found
% 1.71/1.78 % SZS status Theorem for theBenchmark
% 1.71/1.78 % SZS output start Proof
% 1.71/1.78 %ClaNum:5(EqnAxiom:0)
% 1.71/1.78 %VarNum:29(SingletonVarNum:15)
% 1.71/1.78 %MaxLitNum:4
% 1.71/1.78 %MaxfuncDepth:1
% 1.71/1.78 %SharedTerms:2
% 1.71/1.78 %goalClause: 3
% 1.71/1.78 %singleGoalClaCount:1
% 1.71/1.78 [1]P1(a1,x11,x11)
% 1.71/1.78 [3]~P1(a2,x31,a1)
% 1.71/1.78 [2]P1(f3(x21),x21,a1)
% 1.71/1.78 [4]~P1(x46,x44,x41)+P1(x41,x42,x43)+~P1(x44,x42,x45)+~P1(x46,x45,x43)
% 1.71/1.78 [5]~P1(x51,x56,x54)+P1(x51,x52,x53)+~P1(x54,x55,x53)+~P1(x56,x55,x52)
% 1.71/1.78 %EqnAxiom
% 1.71/1.78
% 1.71/1.78 %-------------------------------------------
% 1.73/1.78 cnf(6,plain,
% 1.73/1.78 (P1(f3(a1),x61,x61)),
% 1.73/1.78 inference(scs_inference,[],[1,2,5])).
% 1.73/1.78 cnf(19,plain,
% 1.73/1.78 (~P1(a1,f3(x191),a2)),
% 1.73/1.78 inference(scs_inference,[],[1,2,3,4])).
% 1.73/1.78 cnf(27,plain,
% 1.73/1.78 (~P1(f3(a1),f3(x271),a2)),
% 1.73/1.78 inference(scs_inference,[],[1,6,19,5])).
% 1.73/1.78 cnf(31,plain,
% 1.73/1.78 (P1(a1,f3(a1),a1)),
% 1.73/1.78 inference(scs_inference,[],[2,6,4])).
% 1.73/1.78 cnf(33,plain,
% 1.73/1.78 (P1(f3(x331),x331,a1)),
% 1.73/1.78 inference(rename_variables,[],[2])).
% 1.73/1.78 cnf(36,plain,
% 1.73/1.78 (~P1(a1,a2,f3(x361))),
% 1.73/1.78 inference(scs_inference,[],[2,33,6,27,1,4,5])).
% 1.73/1.78 cnf(67,plain,
% 1.73/1.78 (P1(f3(a1),f3(a1),a1)),
% 1.73/1.78 inference(scs_inference,[],[31,6,1,5])).
% 1.73/1.78 cnf(75,plain,
% 1.73/1.78 (P1(a1,a1,f3(a1))),
% 1.73/1.78 inference(scs_inference,[],[31,67,1,5])).
% 1.73/1.78 cnf(78,plain,
% 1.73/1.78 (P1(f3(a1),a1,f3(a1))),
% 1.73/1.78 inference(scs_inference,[],[75,1,4])).
% 1.73/1.78 cnf(81,plain,
% 1.73/1.78 (P1(f3(f3(a1)),f3(a1),f3(a1))),
% 1.73/1.78 inference(scs_inference,[],[78,75,2,5])).
% 1.73/1.78 cnf(100,plain,
% 1.73/1.78 (P1(f3(f3(a1)),a1,a1)),
% 1.73/1.78 inference(scs_inference,[],[81,67,5])).
% 1.73/1.78 cnf(102,plain,
% 1.73/1.79 (P1(f3(f3(a1)),a1,f3(a1))),
% 1.73/1.79 inference(scs_inference,[],[100,78,6,4])).
% 1.73/1.79 cnf(129,plain,
% 1.73/1.79 (P1(f3(f3(a1)),x1291,x1291)),
% 1.73/1.79 inference(scs_inference,[],[1,102,6,5])).
% 1.73/1.79 cnf(252,plain,
% 1.73/1.79 (P1(f3(x2521),x2521,f3(a1))),
% 1.73/1.79 inference(scs_inference,[],[102,129,2,4])).
% 1.73/1.79 cnf(281,plain,
% 1.73/1.79 (~P1(f3(f3(a2)),f3(a1),f3(x2811))),
% 1.73/1.79 inference(scs_inference,[],[36,252,2,4])).
% 1.73/1.79 cnf(285,plain,
% 1.73/1.79 (~P1(f3(a2),f3(x2851),f3(a1))),
% 1.73/1.79 inference(scs_inference,[],[281,1,2,5])).
% 1.73/1.79 cnf(302,plain,
% 1.73/1.79 (~P1(f3(a2),f3(x3021),a1)),
% 1.73/1.79 inference(scs_inference,[],[285,102,129,4])).
% 1.73/1.79 cnf(333,plain,
% 1.73/1.79 (~P1(f3(f3(x3331)),a1,f3(a2))),
% 1.73/1.79 inference(scs_inference,[],[1,2,302,4])).
% 1.73/1.79 cnf(338,plain,
% 1.73/1.79 ($false),
% 1.73/1.79 inference(scs_inference,[],[2,6,333,252,5]),
% 1.73/1.79 ['proof']).
% 1.73/1.79 % SZS output end Proof
% 1.73/1.79 % Total time :1.160000s
%------------------------------------------------------------------------------