%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP703+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 : n026.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 07:31:16 AM UTC 2026
% Result : Theorem 0.10s 0.61s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 31 unt; 0 def)
% Number of atoms : 87 ( 86 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 19 !; 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(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(f12,axiom,
! [B,A] : op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
file('theBenchmark.p',f12) ).
fof(goals,conjecture,
! [X2,X3] :
( mult(X2,mult(op_e,X3)) = mult(mult(X2,op_e),X3)
& mult(X2,mult(X3,op_e)) = mult(mult(X2,X3),op_e)
& mult(op_e,mult(X2,X3)) = mult(mult(op_e,X2),X3) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X2,X3] :
( mult(X2,mult(op_e,X3)) = mult(mult(X2,op_e),X3)
& mult(X2,mult(X3,op_e)) = mult(mult(X2,X3),op_e)
& mult(op_e,mult(X2,X3)) = mult(mult(op_e,X2),X3) ),
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_17,plain,
mult(rd(A,B),B) = A,
inference(clausify,[status(thm)],[f03]) ).
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_26,plain,
mult(mult(rd(op_c,mult(A,B)),B),A) = op_e,
inference(clausify,[status(thm)],[f12]) ).
fof(nnf_14,plain,
? [X2,X3] :
( mult(mult(X2,op_e),X3) != mult(X2,mult(op_e,X3))
| mult(mult(X2,X3),op_e) != mult(X2,mult(X3,op_e))
| mult(mult(op_e,X2),X3) != mult(op_e,mult(X2,X3)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( mult(mult(sK0,op_e),sK1) != mult(sK0,mult(op_e,sK1))
| mult(mult(sK0,sK1),op_e) != mult(sK0,mult(sK1,op_e))
| mult(mult(op_e,sK0),sK1) != mult(op_e,mult(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[nnf_14]) ).
cnf(c_28,negated_conjecture,
( mult(mult(sK0,op_e),sK1) != mult(sK0,mult(op_e,sK1))
| mult(mult(sK0,sK1),op_e) != mult(sK0,mult(sK1,op_e))
| mult(mult(op_e,sK0),sK1) != mult(op_e,mult(sK0,sK1)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_121,plain,
mult(A,op_d) = mult(op_c,A),
inference(paramod,[status(thm)],[c_25,c_15]) ).
cnf(c_68,plain,
mult(op_c,A) = mult(A,op_d),
inference(copy,[status(thm)],[c_121]) ).
cnf(c_70,plain,
op_d = op_c,
inference(paramod,[status(thm)],[c_25,c_16]) ).
cnf(c_72,plain,
mult(op_c,A) = mult(A,op_c),
inference(paramod,[status(thm)],[c_70,c_68]) ).
cnf(c_122,plain,
op_e = mult(rd(op_c,mult(unit,A)),A),
inference(paramod,[status(thm)],[c_26,c_19]) ).
cnf(c_123,plain,
op_e = mult(rd(op_c,A),A),
inference(paramod,[status(thm)],[c_20,c_122]) ).
cnf(c_81,plain,
op_e = op_c,
inference(paramod,[status(thm)],[c_17,c_123]) ).
cnf(c_124,negated_conjecture,
( mult(mult(sK0,op_e),sK1) != mult(sK0,mult(op_e,sK1))
| mult(mult(sK0,sK1),op_e) != mult(sK0,mult(sK1,op_e))
| mult(mult(op_c,sK0),sK1) != mult(op_e,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_81,c_28]) ).
cnf(c_125,negated_conjecture,
( mult(mult(sK0,op_e),sK1) != mult(sK0,mult(op_e,sK1))
| mult(mult(sK0,sK1),op_e) != mult(sK0,mult(sK1,op_e))
| mult(op_c,mult(sK0,sK1)) != mult(op_e,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_22,c_124]) ).
cnf(c_126,negated_conjecture,
( mult(mult(sK0,op_e),sK1) != mult(sK0,mult(op_e,sK1))
| mult(mult(sK0,sK1),op_e) != mult(sK0,mult(sK1,op_e))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_81,c_125]) ).
cnf(c_127,negated_conjecture,
( mult(mult(sK0,op_e),sK1) != mult(sK0,mult(op_e,sK1))
| mult(mult(sK0,sK1),op_c) != mult(sK0,mult(sK1,op_e))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_81,c_126]) ).
cnf(c_128,negated_conjecture,
( mult(mult(sK0,op_e),sK1) != mult(sK0,mult(op_e,sK1))
| mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(sK1,op_e))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_72,c_127]) ).
cnf(c_129,negated_conjecture,
( mult(mult(sK0,op_e),sK1) != mult(sK0,mult(op_e,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_81,c_128]) ).
cnf(c_130,negated_conjecture,
( mult(mult(sK0,op_e),sK1) != mult(sK0,mult(op_e,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_72,c_129]) ).
cnf(c_131,negated_conjecture,
( mult(mult(sK0,op_c),sK1) != mult(sK0,mult(op_e,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_81,c_130]) ).
cnf(c_132,negated_conjecture,
( mult(mult(op_c,sK0),sK1) != mult(sK0,mult(op_e,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_72,c_131]) ).
cnf(c_133,negated_conjecture,
( mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(op_e,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_132]) ).
cnf(c_134,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_81,c_133]) ).
cnf(c_135,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_134]) ).
cnf(c_136,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_135]) ).
cnf(c_137,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_136]) ).
cnf(c_91,negated_conjecture,
mult(sK0,mult(op_c,sK1)) != mult(op_c,mult(sK0,sK1)),
inference(copy,[status(thm)],[c_137]) ).
cnf(c_138,plain,
mult(mult(A,op_c),B) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_72,c_22]) ).
cnf(c_139,plain,
mult(A,mult(op_c,B)) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_24,c_138]) ).
cnf(c_119,plain,
mult(op_c,mult(A,B)) = mult(A,mult(op_c,B)),
inference(copy,[status(thm)],[c_139]) ).
cnf(c_140,negated_conjecture,
mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(op_c,sK1)),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_120,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_119,c_140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP703+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.58 % Computer : n026.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Fri Sep 25 15:41:25 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.58 % Process 2923133 was started by sandbox2 on n026,
% 0.10/0.58 % Fri Sep 25 15:41:25 2026
% 0.10/0.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.59
% 0.10/0.59 % From the command line: assign(max_seconds, 300).
% 0.10/0.61
% 0.10/0.61 % SZS status Theorem for theBenchmark
% 0.10/0.61
% 0.10/0.61 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.10/0.61 % Length of proof is 27.
% 0.10/0.61 % Level of proof is 5.
% 0.10/0.61 % Maximum clause weight is 33.000.
% 0.10/0.61 % Given clauses 26.
% 0.10/0.61
% 0.10/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------