%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP704+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 07:31:17 AM UTC 2026
% Result : Theorem 0.11s 5.59s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 30 unt; 0 def)
% Number of atoms : 86 ( 85 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 90 ( 53 ~; 33 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 43 ( 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(f05,axiom,
! [A] : mult(A,unit) = A,
file('theBenchmark.p',f05) ).
fof(f06,axiom,
! [A] : mult(unit,A) = A,
file('theBenchmark.p',f06) ).
fof(f08,axiom,
! [B,A] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
file('theBenchmark.p',f08) ).
fof(f10,axiom,
! [B,A] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
file('theBenchmark.p',f10) ).
fof(f11,axiom,
! [A] : op_d = ld(A,mult(op_c,A)),
file('theBenchmark.p',f11) ).
fof(f13,axiom,
! [B,A] : op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
file('theBenchmark.p',f13) ).
fof(goals,conjecture,
! [X4,X5] :
( mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5)
& mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f)
& mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X4,X5] :
( mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5)
& mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f)
& mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_15,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[f01]) ).
cnf(c_16,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[f02]) ).
cnf(c_19,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[f05]) ).
cnf(c_20,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[f06]) ).
cnf(c_22,plain,
mult(mult(op_c,A),B) = mult(op_c,mult(A,B)),
inference(clausify,[status(thm)],[f08]) ).
cnf(c_24,plain,
mult(mult(A,op_c),B) = mult(A,mult(op_c,B)),
inference(clausify,[status(thm)],[f10]) ).
cnf(c_25,plain,
ld(A,mult(op_c,A)) = op_d,
inference(clausify,[status(thm)],[f11]) ).
cnf(c_27,plain,
mult(A,mult(B,ld(mult(A,B),op_c))) = op_f,
inference(clausify,[status(thm)],[f13]) ).
fof(nnf_14,plain,
? [X4,X5] :
( mult(mult(X4,op_f),X5) != mult(X4,mult(op_f,X5))
| mult(mult(X4,X5),op_f) != mult(X4,mult(X5,op_f))
| mult(mult(op_f,X4),X5) != mult(op_f,mult(X4,X5)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( mult(mult(sK0,op_f),sK1) != mult(sK0,mult(op_f,sK1))
| mult(mult(sK0,sK1),op_f) != mult(sK0,mult(sK1,op_f))
| mult(mult(op_f,sK0),sK1) != mult(op_f,mult(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X4,sK0),skolemize(X5,sK1)],[nnf_14]) ).
cnf(c_28,negated_conjecture,
( mult(mult(sK0,op_f),sK1) != mult(sK0,mult(op_f,sK1))
| mult(mult(sK0,sK1),op_f) != mult(sK0,mult(sK1,op_f))
| mult(mult(op_f,sK0),sK1) != mult(op_f,mult(sK0,sK1)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_84,plain,
mult(A,op_d) = mult(op_c,A),
inference(paramod,[status(thm)],[c_25,c_15]) ).
cnf(c_50,plain,
mult(op_c,A) = mult(A,op_d),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_52,plain,
op_d = op_c,
inference(paramod,[status(thm)],[c_25,c_16]) ).
cnf(c_54,plain,
mult(op_c,A) = mult(A,op_c),
inference(paramod,[status(thm)],[c_52,c_50]) ).
cnf(c_85,plain,
mult(A,mult(unit,ld(A,op_c))) = op_f,
inference(paramod,[status(thm)],[c_19,c_27]) ).
cnf(c_86,plain,
mult(A,ld(A,op_c)) = op_f,
inference(paramod,[status(thm)],[c_20,c_85]) ).
cnf(c_87,plain,
op_c = op_f,
inference(paramod,[status(thm)],[c_15,c_86]) ).
cnf(c_73,plain,
op_f = op_c,
inference(copy,[status(thm)],[c_87]) ).
cnf(c_88,negated_conjecture,
( mult(mult(sK0,op_f),sK1) != mult(sK0,mult(op_f,sK1))
| mult(mult(sK0,sK1),op_f) != mult(sK0,mult(sK1,op_f))
| mult(mult(op_c,sK0),sK1) != mult(op_f,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_73,c_28]) ).
cnf(c_89,negated_conjecture,
( mult(mult(sK0,op_f),sK1) != mult(sK0,mult(op_f,sK1))
| mult(mult(sK0,sK1),op_f) != mult(sK0,mult(sK1,op_f))
| mult(op_c,mult(sK0,sK1)) != mult(op_f,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_22,c_88]) ).
cnf(c_90,negated_conjecture,
( mult(mult(sK0,op_f),sK1) != mult(sK0,mult(op_f,sK1))
| mult(mult(sK0,sK1),op_f) != mult(sK0,mult(sK1,op_f))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_73,c_89]) ).
cnf(c_91,negated_conjecture,
( mult(mult(sK0,op_f),sK1) != mult(sK0,mult(op_f,sK1))
| mult(mult(sK0,sK1),op_c) != mult(sK0,mult(sK1,op_f))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_73,c_90]) ).
cnf(c_92,negated_conjecture,
( mult(mult(sK0,op_f),sK1) != mult(sK0,mult(op_f,sK1))
| mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(sK1,op_f))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_54,c_91]) ).
cnf(c_93,negated_conjecture,
( mult(mult(sK0,op_f),sK1) != mult(sK0,mult(op_f,sK1))
| mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(sK1,op_c))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_73,c_92]) ).
cnf(c_94,negated_conjecture,
( mult(mult(sK0,op_f),sK1) != mult(sK0,mult(op_f,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_54,c_93]) ).
cnf(c_95,negated_conjecture,
( mult(mult(sK0,op_c),sK1) != mult(sK0,mult(op_f,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_73,c_94]) ).
cnf(c_96,negated_conjecture,
( mult(mult(op_c,sK0),sK1) != mult(sK0,mult(op_f,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_54,c_95]) ).
cnf(c_97,negated_conjecture,
( mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(op_f,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_22,c_96]) ).
cnf(c_98,negated_conjecture,
( mult(op_c,mult(sK0,sK1)) != 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)) ),
inference(paramod,[status(thm)],[c_73,c_97]) ).
cnf(c_99,negated_conjecture,
( mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(op_c,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_98]) ).
cnf(c_100,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_99]) ).
cnf(c_101,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_100]) ).
cnf(c_77,negated_conjecture,
mult(sK0,mult(op_c,sK1)) != mult(op_c,mult(sK0,sK1)),
inference(copy,[status(thm)],[c_101]) ).
cnf(c_102,plain,
mult(mult(A,op_c),B) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_54,c_22]) ).
cnf(c_103,plain,
mult(A,mult(op_c,B)) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_24,c_102]) ).
cnf(c_82,plain,
mult(op_c,mult(A,B)) = mult(A,mult(op_c,B)),
inference(copy,[status(thm)],[c_103]) ).
cnf(c_104,negated_conjecture,
mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(op_c,sK1)),
inference(copy,[status(thm)],[c_77]) ).
cnf(c_83,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_82,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP704+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.55 % Computer : n014.cluster.edu
% 0.11/5.55 % Model : x86_64 x86_64
% 0.11/5.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.55 % Memory : 8046.5625MB
% 0.11/5.55 % OS : Linux 6.8.0-71-generic
% 0.11/5.55 % CPULimit : 300
% 0.11/5.55 % WCLimit : 300
% 0.11/5.55 % DateTime : Fri Sep 25 15:39:08 UTC 2026
% 0.11/5.55 % CPUTime :
% 0.11/5.55 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.55 % Process 587523 was started by sandbox on n014,
% 0.11/5.55 % Fri Sep 25 15:39:08 2026
% 0.11/5.55 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.56
% 0.11/5.56 % From the command line: assign(max_seconds, 300).
% 0.11/5.59
% 0.11/5.59 % SZS status Theorem for theBenchmark
% 0.11/5.59
% 0.11/5.59 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/5.59 % Length of proof is 25.
% 0.11/5.59 % Level of proof is 5.
% 0.11/5.59 % Maximum clause weight is 51.000.
% 0.11/5.59 % Given clauses 24.
% 0.11/5.59
% 0.11/5.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------