%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP747+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:31:21 AM UTC 2026
% Result : Theorem 3.76s 0.97s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 17 unt; 0 def)
% Number of atoms : 68 ( 67 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 4 ~; 25 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('theBenchmark.p',f01) ).
fof(f02,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('theBenchmark.p',f02) ).
fof(f06,axiom,
! [A] : mult(unit,A) = A,
file('theBenchmark.p',f06) ).
fof(f08,axiom,
! [X0,X1,X2] :
( ( mult(X0,mult(X1,X2)) = mult(X0,mult(X2,X1))
& mult(mult(X0,X1),X2) = mult(mult(X0,X2),X1) )
| ( mult(mult(X0,X2),X1) = mult(X0,mult(X1,X2))
& mult(mult(X0,X1),X2) = mult(X0,mult(X2,X1)) ) ),
file('theBenchmark.p',f08) ).
fof(goals,conjecture,
mult(mult(a,b),c) = mult(a,mult(b,c)),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
mult(mult(a,b),c) != mult(a,mult(b,c)),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_10,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[f01]) ).
cnf(c_11,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[f02]) ).
cnf(c_15,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[f06]) ).
cnf(c_17,plain,
( mult(mult(A,C),B) = mult(mult(A,B),C)
| mult(mult(A,B),C) = mult(A,mult(C,B)) ),
inference(clausify,[status(thm)],[f08]) ).
cnf(c_19,plain,
( mult(mult(A,B),C) = mult(mult(A,C),B)
| mult(mult(A,B),C) = mult(A,mult(C,B)) ),
inference(clausify,[status(thm)],[f08]) ).
cnf(c_21,negated_conjecture,
mult(mult(a,b),c) != mult(a,mult(b,c)),
inference(clausify,[status(thm)],[goals_neg]) ).
cnf(c_36,plain,
( mult(mult(A,ld(mult(A,B),C)),B) = C
| mult(mult(A,ld(mult(A,B),C)),B) = mult(A,mult(B,ld(mult(A,B),C))) ),
inference(paramod,[status(thm)],[c_17,c_10]) ).
cnf(c_1200,plain,
( mult(mult(A,ld(mult(A,B),C)),B) = C
| mult(mult(A,B),ld(mult(A,B),C)) = mult(A,mult(ld(mult(A,B),C),B)) ),
inference(paramod,[status(thm)],[c_17,c_10]) ).
cnf(c_1201,plain,
( mult(mult(A,ld(mult(A,B),C)),B) = C
| C = mult(A,mult(ld(mult(A,B),C),B)) ),
inference(paramod,[status(thm)],[c_10,c_1200]) ).
cnf(c_37,plain,
( mult(mult(A,ld(mult(A,B),C)),B) = C
| mult(A,mult(ld(mult(A,B),C),B)) = C ),
inference(copy,[status(thm)],[c_1201]) ).
cnf(c_1202,plain,
( mult(A,B) = mult(mult(unit,B),A)
| mult(mult(unit,A),B) = mult(unit,mult(B,A)) ),
inference(paramod,[status(thm)],[c_15,c_19]) ).
cnf(c_1203,plain,
( mult(A,B) = mult(mult(unit,B),A)
| mult(A,B) = mult(unit,mult(B,A)) ),
inference(paramod,[status(thm)],[c_15,c_1202]) ).
cnf(c_1204,plain,
( mult(A,B) = mult(mult(unit,B),A)
| mult(A,B) = mult(B,A) ),
inference(paramod,[status(thm)],[c_15,c_1203]) ).
cnf(c_1205,plain,
( mult(A,B) = mult(B,A)
| mult(A,B) = mult(B,A) ),
inference(paramod,[status(thm)],[c_15,c_1204]) ).
cnf(c_70,plain,
mult(A,B) = mult(B,A),
inference(copy,[status(thm)],[c_1205]) ).
cnf(c_1206,plain,
( mult(mult(A,ld(mult(A,B),C)),B) = C
| mult(A,mult(B,ld(mult(A,B),C))) = C ),
inference(paramod,[status(thm)],[c_70,c_37]) ).
cnf(c_86,plain,
( mult(B,mult(A,ld(mult(A,B),C))) = C
| mult(A,mult(B,ld(mult(A,B),C))) = C ),
inference(paramod,[status(thm)],[c_70,c_1206]) ).
cnf(c_1207,plain,
( mult(mult(A,ld(mult(A,B),C)),B) = C
| mult(B,mult(A,ld(mult(A,B),C))) = mult(A,mult(B,ld(mult(A,B),C))) ),
inference(paramod,[status(thm)],[c_70,c_36]) ).
cnf(c_87,plain,
( mult(A,mult(B,ld(mult(B,A),C))) = C
| mult(A,mult(B,ld(mult(B,A),C))) = mult(B,mult(A,ld(mult(B,A),C))) ),
inference(paramod,[status(thm)],[c_70,c_1207]) ).
cnf(c_96,negated_conjecture,
mult(c,mult(a,b)) != mult(a,mult(b,c)),
inference(paramod,[status(thm)],[c_70,c_21]) ).
cnf(c_1208,plain,
( mult(mult(C,A),B) = mult(mult(A,B),C)
| mult(mult(A,B),C) = mult(A,mult(C,B)) ),
inference(paramod,[status(thm)],[c_70,c_17]) ).
cnf(c_103,plain,
( mult(mult(A,B),C) = mult(mult(C,A),B)
| mult(mult(A,B),C) = mult(A,mult(C,B)) ),
inference(copy,[status(thm)],[c_1208]) ).
cnf(c_1209,plain,
( mult(A,mult(B,ld(mult(B,A),C))) = C
| mult(A,mult(B,ld(mult(B,A),C))) = C
| mult(A,mult(B,ld(mult(B,A),C))) = C ),
inference(paramod,[status(thm)],[c_87,c_86]) ).
cnf(c_1210,plain,
( mult(A,mult(B,ld(mult(B,A),C))) = C
| mult(A,mult(B,ld(mult(B,A),C))) = C ),
inference(copy,[status(thm)],[c_1209]) ).
cnf(c_882,plain,
mult(A,mult(B,ld(mult(B,A),C))) = C,
inference(copy,[status(thm)],[c_1210]) ).
cnf(c_1211,plain,
mult(A,mult(B,C)) = mult(mult(B,A),C),
inference(paramod,[status(thm)],[c_11,c_882]) ).
cnf(c_885,plain,
mult(mult(A,B),C) = mult(B,mult(A,C)),
inference(copy,[status(thm)],[c_1211]) ).
cnf(c_1212,plain,
( mult(mult(A,B),C) = mult(mult(C,A),B)
| mult(B,mult(A,C)) = mult(A,mult(C,B)) ),
inference(paramod,[status(thm)],[c_885,c_103]) ).
cnf(c_1213,plain,
( mult(B,mult(A,C)) = mult(mult(C,A),B)
| mult(B,mult(A,C)) = mult(A,mult(C,B)) ),
inference(paramod,[status(thm)],[c_885,c_1212]) ).
cnf(c_1214,plain,
( mult(B,mult(A,C)) = mult(A,mult(C,B))
| mult(B,mult(A,C)) = mult(A,mult(C,B)) ),
inference(paramod,[status(thm)],[c_885,c_1213]) ).
cnf(c_1215,plain,
( mult(B,mult(A,C)) = mult(A,mult(C,B))
| mult(A,mult(C,B)) = mult(B,mult(A,C)) ),
inference(copy,[status(thm)],[c_1214]) ).
cnf(c_1216,plain,
( mult(A,mult(C,B)) = mult(B,mult(A,C))
| mult(A,mult(C,B)) = mult(B,mult(A,C)) ),
inference(copy,[status(thm)],[c_1215]) ).
cnf(c_1198,plain,
mult(A,mult(B,C)) = mult(C,mult(A,B)),
inference(copy,[status(thm)],[c_1216]) ).
cnf(c_1217,negated_conjecture,
mult(a,mult(b,c)) != mult(c,mult(a,b)),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_1199,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1198,c_1217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP747+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 15:42:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1962327 was started by sandbox2 on n009,
% 0.10/0.37 % Fri Sep 25 15:42:43 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.37
% 0.16/0.37 % From the command line: assign(max_seconds, 300).
% 3.76/0.97
% 3.76/0.97 % SZS status Theorem for theBenchmark
% 3.76/0.97
% 3.76/0.97 % Proof 1 at 0.43 (+ 0.11) seconds.
% 3.76/0.97 % Length of proof is 22.
% 3.76/0.97 % Level of proof is 7.
% 3.76/0.97 % Maximum clause weight is 70.000.
% 3.76/0.97 % Given clauses 60.
% 3.76/0.97
% 3.76/0.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------