%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP665+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 : n019.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 07:31:07 AM UTC 2026
% Result : Theorem 0.14s 15.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 26 unt; 0 def)
% Number of atoms : 64 ( 63 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 35 ~; 21 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 17 !; 2 ?)
% 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(f03,axiom,
! [B,A] : mult(rd(A,B),B) = A,
file('theBenchmark.p',f03) ).
fof(f07,axiom,
! [C,B,A] : mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)),
file('theBenchmark.p',f07) ).
fof(f08,axiom,
! [C,B,A] : mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))),
file('theBenchmark.p',f08) ).
fof(f09,axiom,
! [A] : mult(op_c,A) = mult(A,op_c),
file('theBenchmark.p',f09) ).
fof(goals,conjecture,
! [X0,X1] :
( mult(mult(X0,X1),op_c) = mult(X0,mult(X1,op_c))
& mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1))
& mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( mult(mult(X0,X1),op_c) = mult(X0,mult(X1,op_c))
& mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1))
& mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_11,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[f01]) ).
cnf(c_12,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[f02]) ).
cnf(c_13,plain,
mult(rd(A,B),B) = A,
inference(clausify,[status(thm)],[f03]) ).
cnf(c_17,plain,
mult(rd(mult(A,B),A),mult(A,C)) = mult(A,mult(B,C)),
inference(clausify,[status(thm)],[f07]) ).
cnf(c_18,plain,
mult(mult(A,B),ld(B,mult(C,B))) = mult(mult(A,C),B),
inference(clausify,[status(thm)],[f08]) ).
cnf(c_19,plain,
mult(op_c,A) = mult(A,op_c),
inference(clausify,[status(thm)],[f09]) ).
fof(nnf_10,plain,
? [X0,X1] :
( mult(mult(X0,X1),op_c) != mult(X0,mult(X1,op_c))
| mult(mult(X0,op_c),X1) != mult(X0,mult(op_c,X1))
| mult(mult(op_c,X0),X1) != mult(op_c,mult(X0,X1)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( mult(mult(sK0,sK1),op_c) != mult(sK0,mult(sK1,op_c))
| mult(mult(sK0,op_c),sK1) != mult(sK0,mult(op_c,sK1))
| mult(mult(op_c,sK0),sK1) != mult(op_c,mult(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_10]) ).
cnf(c_20,negated_conjecture,
( mult(mult(sK0,sK1),op_c) != mult(sK0,mult(sK1,op_c))
| mult(mult(sK0,op_c),sK1) != mult(sK0,mult(op_c,sK1))
| mult(mult(op_c,sK0),sK1) != mult(op_c,mult(sK0,sK1)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_78,negated_conjecture,
( mult(mult(sK0,sK1),op_c) != mult(sK0,mult(sK1,op_c))
| mult(mult(op_c,sK0),sK1) != mult(sK0,mult(op_c,sK1))
| mult(mult(op_c,sK0),sK1) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_19,c_20]) ).
cnf(c_79,negated_conjecture,
( mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(sK1,op_c))
| mult(mult(op_c,sK0),sK1) != mult(sK0,mult(op_c,sK1))
| mult(mult(op_c,sK0),sK1) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_19,c_78]) ).
cnf(c_80,negated_conjecture,
( mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(op_c,sK1))
| mult(mult(op_c,sK0),sK1) != mult(sK0,mult(op_c,sK1))
| mult(mult(op_c,sK0),sK1) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_19,c_79]) ).
cnf(c_21,negated_conjecture,
( mult(sK0,mult(op_c,sK1)) != mult(op_c,mult(sK0,sK1))
| mult(mult(op_c,sK0),sK1) != mult(sK0,mult(op_c,sK1))
| mult(mult(op_c,sK0),sK1) != mult(op_c,mult(sK0,sK1)) ),
inference(copy,[status(thm)],[c_80]) ).
cnf(c_28,plain,
mult(rd(A,B),mult(B,C)) = mult(B,mult(ld(B,A),C)),
inference(paramod,[status(thm)],[c_11,c_17]) ).
cnf(c_51,plain,
ld(op_c,mult(A,op_c)) = A,
inference(paramod,[status(thm)],[c_19,c_12]) ).
cnf(c_81,plain,
mult(mult(op_c,A),ld(op_c,mult(B,op_c))) = mult(mult(A,B),op_c),
inference(paramod,[status(thm)],[c_19,c_18]) ).
cnf(c_82,plain,
mult(mult(op_c,A),B) = mult(mult(A,B),op_c),
inference(paramod,[status(thm)],[c_51,c_81]) ).
cnf(c_59,plain,
mult(mult(op_c,A),B) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_19,c_82]) ).
cnf(c_83,negated_conjecture,
( mult(sK0,mult(op_c,sK1)) != mult(op_c,mult(sK0,sK1))
| mult(mult(op_c,sK0),sK1) != mult(sK0,mult(op_c,sK1))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_59,c_21]) ).
cnf(c_84,negated_conjecture,
( mult(sK0,mult(op_c,sK1)) != mult(op_c,mult(sK0,sK1))
| mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(op_c,sK1))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_59,c_83]) ).
cnf(c_85,negated_conjecture,
( mult(sK0,mult(op_c,sK1)) != mult(op_c,mult(sK0,sK1))
| mult(sK0,mult(op_c,sK1)) != mult(op_c,mult(sK0,sK1))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_86,negated_conjecture,
( mult(sK0,mult(op_c,sK1)) != mult(op_c,mult(sK0,sK1))
| mult(sK0,mult(op_c,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(copy,[status(thm)],[c_85]) ).
cnf(c_60,negated_conjecture,
mult(sK0,mult(op_c,sK1)) != mult(op_c,mult(sK0,sK1)),
inference(copy,[status(thm)],[c_86]) ).
cnf(c_87,plain,
ld(op_c,A) = rd(A,op_c),
inference(paramod,[status(thm)],[c_13,c_51]) ).
cnf(c_61,plain,
rd(A,op_c) = ld(op_c,A),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_88,plain,
mult(rd(mult(A,op_c),op_c),mult(op_c,B)) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_51,c_28]) ).
cnf(c_89,plain,
mult(ld(op_c,mult(A,op_c)),mult(op_c,B)) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_61,c_88]) ).
cnf(c_90,plain,
mult(A,mult(op_c,B)) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_51,c_89]) ).
cnf(c_76,plain,
mult(op_c,mult(A,B)) = mult(A,mult(op_c,B)),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_91,negated_conjecture,
mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(op_c,sK1)),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_77,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_76,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP665+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/15.38 % Computer : n019.cluster.edu
% 0.10/15.38 % Model : x86_64 x86_64
% 0.10/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.38 % Memory : 8046.5625MB
% 0.10/15.38 % OS : Linux 6.8.0-71-generic
% 0.10/15.38 % CPULimit : 300
% 0.10/15.38 % WCLimit : 300
% 0.10/15.38 % DateTime : Fri Sep 25 15:33:50 UTC 2026
% 0.10/15.38 % CPUTime :
% 0.10/15.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/15.38 % Process 3126874 was started by sandbox2 on n019,
% 0.10/15.38 % Fri Sep 25 15:33:50 2026
% 0.10/15.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/15.39
% 0.10/15.39 % From the command line: assign(max_seconds, 300).
% 0.14/15.40
% 0.14/15.40 % SZS status Theorem for theBenchmark
% 0.14/15.40
% 0.14/15.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/15.40 % Length of proof is 22.
% 0.14/15.40 % Level of proof is 5.
% 0.14/15.40 % Maximum clause weight is 78.000.
% 0.14/15.40 % Given clauses 20.
% 0.14/15.40
% 0.14/15.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------