TSTP Solution File: GRP001+6 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 : Theorem 0.17s 0.57s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% 0.10/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Aug 28 21:47:16 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.17/0.50 start to proof:theBenchmark
% 0.17/0.57 %-------------------------------------------
% 0.17/0.57 % File :CSE---1.6
% 0.17/0.57 % Problem :theBenchmark
% 0.17/0.57 % Transform :cnf
% 0.17/0.57 % Format :tptp:raw
% 0.17/0.57 % Command :java -jar mcs_scs.jar %d %s
% 0.17/0.57
% 0.17/0.57 % Result :Theorem 0.020000s
% 0.17/0.57 % Output :CNFRefutation 0.020000s
% 0.17/0.57 %-------------------------------------------
% 0.17/0.57 %------------------------------------------------------------------------------
% 0.17/0.57 % File : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% 0.17/0.57 % Domain : Group Theory
% 0.17/0.57 % Problem : X^2 = identity => commutativity
% 0.17/0.57 % Version : Especial.
% 0.17/0.57 % English : If the square of every element is the identity, the system
% 0.17/0.57 % is commutative.
% 0.17/0.57
% 0.17/0.57 % Refs : [Shu04] Shults (2004), Email to G. Sutcliffe
% 0.17/0.57 % Source : [Shu04]
% 0.17/0.57 % Names :
% 0.17/0.57
% 0.17/0.57 % Status : Theorem
% 0.17/0.57 % Rating : 0.00 v7.5.0, 0.14 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.14 v6.4.0, 0.07 v6.3.0, 0.08 v6.2.0, 0.18 v6.1.0, 0.24 v6.0.0, 0.50 v5.5.0, 0.21 v5.4.0, 0.17 v5.3.0, 0.26 v5.2.0, 0.00 v5.0.0, 0.10 v4.1.0, 0.17 v4.0.1, 0.26 v4.0.0, 0.25 v3.7.0, 0.14 v3.5.0, 0.00 v3.2.0, 0.33 v3.1.0
% 0.17/0.57 % Syntax : Number of formulae : 1 ( 0 unt; 0 def)
% 0.17/0.57 % Number of atoms : 16 ( 0 equ)
% 0.17/0.57 % Maximal formula atoms : 16 ( 16 avg)
% 0.17/0.57 % Number of connectives : 15 ( 0 ~; 0 |; 10 &)
% 0.17/0.57 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.17/0.57 % Maximal formula depth : 15 ( 15 avg)
% 0.17/0.57 % Maximal term depth : 2 ( 1 avg)
% 0.17/0.57 % Number of predicates : 1 ( 1 usr; 0 prp; 3-3 aty)
% 0.17/0.57 % Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% 0.17/0.57 % Number of variables : 24 ( 23 !; 1 ?)
% 0.17/0.57 % SPC : FOF_THM_RFO_NEQ
% 0.17/0.57
% 0.17/0.57 % Comments :
% 0.17/0.57 %------------------------------------------------------------------------------
% 0.17/0.57 fof(commutativity,conjecture,
% 0.17/0.57 ! [E] :
% 0.17/0.57 ( ( ! [X,Y] :
% 0.17/0.57 ? [Z] : product(X,Y,Z)
% 0.17/0.57 & ! [X,Y,Z,U,V,W] :
% 0.17/0.57 ( ( product(X,Y,U)
% 0.17/0.57 & product(Y,Z,V)
% 0.17/0.57 & product(U,Z,W) )
% 0.17/0.57 => product(X,V,W) )
% 0.17/0.57 & ! [X,Y,Z,U,V,W] :
% 0.17/0.57 ( ( product(X,Y,U)
% 0.17/0.57 & product(Y,Z,V)
% 0.17/0.57 & product(X,V,W) )
% 0.17/0.57 => product(U,Z,W) )
% 0.17/0.57 & ! [X] : product(X,E,X)
% 0.17/0.57 & ! [X] : product(E,X,X)
% 0.17/0.57 & ! [X] : product(X,inverse(X),E)
% 0.17/0.57 & ! [X] : product(inverse(X),X,E) )
% 0.17/0.57 => ( ! [X] : product(X,X,E)
% 0.17/0.57 => ! [U,V,W] :
% 0.17/0.57 ( product(U,V,W)
% 0.17/0.57 => product(V,U,W) ) ) ) ).
% 0.17/0.57
% 0.17/0.57 %------------------------------------------------------------------------------
% 0.17/0.57 %-------------------------------------------
% 0.17/0.57 % Proof found
% 0.17/0.57 % SZS status Theorem for theBenchmark
% 0.17/0.57 % SZS output start Proof
% 0.17/0.57 %ClaNum:10(EqnAxiom:0)
% 0.17/0.57 %VarNum:38(SingletonVarNum:19)
% 0.17/0.57 %MaxLitNum:4
% 0.17/0.57 %MaxfuncDepth:1
% 0.17/0.57 %SharedTerms:6
% 0.17/0.57 %goalClause: 1 2 3 4 5 6 7 8 9 10
% 0.17/0.57 %singleGoalClaCount:8
% 0.17/0.57 [1]P1(a1,a4,a5)
% 0.17/0.57 [8]~P1(a4,a1,a5)
% 0.17/0.57 [2]P1(x21,x21,a2)
% 0.17/0.57 [3]P1(x31,a2,x31)
% 0.17/0.57 [4]P1(a2,x41,x41)
% 0.17/0.57 [5]P1(x51,f6(x51),a2)
% 0.17/0.57 [6]P1(f6(x61),x61,a2)
% 0.17/0.57 [7]P1(x71,x72,f3(x71,x72))
% 0.17/0.57 [9]~P1(x96,x94,x91)+P1(x91,x92,x93)+~P1(x94,x92,x95)+~P1(x96,x95,x93)
% 0.17/0.57 [10]~P1(x101,x106,x104)+P1(x101,x102,x103)+~P1(x104,x105,x103)+~P1(x106,x105,x102)
% 0.17/0.57 %EqnAxiom
% 0.17/0.57
% 0.17/0.57 %-------------------------------------------
% 0.17/0.58 cnf(11,plain,
% 0.17/0.58 (P1(a1,a5,a4)),
% 0.17/0.58 inference(scs_inference,[],[1,2,4,10])).
% 0.17/0.58 cnf(12,plain,
% 0.17/0.58 (P1(x121,x121,a2)),
% 0.17/0.58 inference(rename_variables,[],[2])).
% 0.17/0.58 cnf(14,plain,
% 0.17/0.58 (P1(a5,a4,a1)),
% 0.17/0.58 inference(scs_inference,[],[1,2,12,3,4,10,9])).
% 0.17/0.58 cnf(30,plain,
% 0.17/0.58 (~P1(a4,a5,a1)),
% 0.17/0.58 inference(scs_inference,[],[2,8,11,3,14,9,10])).
% 0.17/0.58 cnf(136,plain,
% 0.17/0.58 ($false),
% 0.17/0.58 inference(scs_inference,[],[11,30,3,2,9]),
% 0.17/0.58 ['proof']).
% 0.17/0.58 % SZS output end Proof
% 0.17/0.58 % Total time :0.020000s
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