%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP702+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 : n006.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 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 13 unt; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 69 ( 40 ~; 25 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 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 : 24 ( 0 sgn 13 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f02,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('theBenchmark.p',f02) ).
fof(f08,axiom,
! [B,A] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
file('theBenchmark.p',f08) ).
fof(f09,axiom,
! [B,A] : mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
file('theBenchmark.p',f09) ).
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(goals,conjecture,
! [X0,X1] :
( mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1)
& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d)
& mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1)
& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d)
& mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_16,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[f02]) ).
cnf(c_22,plain,
mult(mult(op_c,A),B) = mult(op_c,mult(A,B)),
inference(clausify,[status(thm)],[f08]) ).
cnf(c_23,plain,
mult(mult(A,B),op_c) = mult(A,mult(B,op_c)),
inference(clausify,[status(thm)],[f09]) ).
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]) ).
fof(nnf_14,plain,
? [X0,X1] :
( mult(mult(X0,op_d),X1) != mult(X0,mult(op_d,X1))
| mult(mult(X0,X1),op_d) != mult(X0,mult(X1,op_d))
| mult(mult(op_d,X0),X1) != mult(op_d,mult(X0,X1)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( mult(mult(sK0,op_d),sK1) != mult(sK0,mult(op_d,sK1))
| mult(mult(sK0,sK1),op_d) != mult(sK0,mult(sK1,op_d))
| mult(mult(op_d,sK0),sK1) != mult(op_d,mult(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_14]) ).
cnf(c_28,negated_conjecture,
( mult(mult(sK0,op_d),sK1) != mult(sK0,mult(op_d,sK1))
| mult(mult(sK0,sK1),op_d) != mult(sK0,mult(sK1,op_d))
| mult(mult(op_d,sK0),sK1) != mult(op_d,mult(sK0,sK1)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_70,plain,
op_d = op_c,
inference(paramod,[status(thm)],[c_25,c_16]) ).
cnf(c_72,negated_conjecture,
( mult(mult(sK0,op_d),sK1) != mult(sK0,mult(op_d,sK1))
| mult(mult(sK0,sK1),op_d) != mult(sK0,mult(sK1,op_d))
| mult(mult(op_c,sK0),sK1) != mult(op_d,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_70,c_28]) ).
cnf(c_73,negated_conjecture,
( mult(mult(sK0,op_d),sK1) != mult(sK0,mult(op_d,sK1))
| mult(mult(sK0,sK1),op_d) != mult(sK0,mult(sK1,op_d))
| mult(op_c,mult(sK0,sK1)) != mult(op_d,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_22,c_72]) ).
cnf(c_74,negated_conjecture,
( mult(mult(sK0,op_d),sK1) != mult(sK0,mult(op_d,sK1))
| mult(mult(sK0,sK1),op_d) != mult(sK0,mult(sK1,op_d))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_70,c_73]) ).
cnf(c_75,negated_conjecture,
( mult(mult(sK0,op_d),sK1) != mult(sK0,mult(op_d,sK1))
| mult(mult(sK0,sK1),op_c) != mult(sK0,mult(sK1,op_d))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_70,c_74]) ).
cnf(c_76,negated_conjecture,
( mult(mult(sK0,op_d),sK1) != mult(sK0,mult(op_d,sK1))
| mult(sK0,mult(sK1,op_c)) != mult(sK0,mult(sK1,op_d))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_23,c_75]) ).
cnf(c_77,negated_conjecture,
( mult(mult(sK0,op_d),sK1) != mult(sK0,mult(op_d,sK1))
| mult(sK0,mult(sK1,op_c)) != mult(sK0,mult(sK1,op_c))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_70,c_76]) ).
cnf(c_78,negated_conjecture,
( mult(mult(sK0,op_c),sK1) != mult(sK0,mult(op_d,sK1))
| mult(sK0,mult(sK1,op_c)) != mult(sK0,mult(sK1,op_c))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_70,c_77]) ).
cnf(c_79,negated_conjecture,
( mult(sK0,mult(op_c,sK1)) != mult(sK0,mult(op_d,sK1))
| mult(sK0,mult(sK1,op_c)) != mult(sK0,mult(sK1,op_c))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_24,c_78]) ).
cnf(c_80,negated_conjecture,
( mult(sK0,mult(op_c,sK1)) != mult(sK0,mult(op_c,sK1))
| mult(sK0,mult(sK1,op_c)) != mult(sK0,mult(sK1,op_c))
| mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_70,c_79]) ).
cnf(c_81,negated_conjecture,
( mult(sK0,mult(op_c,sK1)) != mult(sK0,mult(op_c,sK1))
| mult(sK0,mult(sK1,op_c)) != mult(sK0,mult(sK1,op_c)) ),
inference(copy,[status(thm)],[c_80]) ).
cnf(c_82,negated_conjecture,
mult(sK0,mult(op_c,sK1)) != mult(sK0,mult(op_c,sK1)),
inference(copy,[status(thm)],[c_81]) ).
cnf(c_71,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP702+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 : n006.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 15:38:30 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 3267789 was started by sandbox2 on n006,
% 0.10/0.37 % Fri Sep 25 15:38:30 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 14.
% 0.10/0.39 % Level of proof is 3.
% 0.10/0.39 % Maximum clause weight is 33.000.
% 0.10/0.39 % Given clauses 11.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------