%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP657+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 : n020.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 07:31:05 AM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 20 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% Number of variables : 50 ( 0 sgn 13 !; 3 ?)
% 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(f04,axiom,
! [B,A] : rd(mult(A,B),B) = A,
file('theBenchmark.p',f04) ).
fof(f05,axiom,
! [C,B,A] : mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)),
file('theBenchmark.p',f05) ).
fof(goals,conjecture,
? [X0] :
! [X1] :
( mult(X0,X1) = X1
& mult(X1,X0) = X1 ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ? [X0] :
! [X1] :
( mult(X0,X1) = X1
& mult(X1,X0) = X1 ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_7,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[f01]) ).
cnf(c_8,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[f02]) ).
cnf(c_10,plain,
rd(mult(A,B),B) = A,
inference(clausify,[status(thm)],[f04]) ).
cnf(c_11,plain,
mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)),
inference(clausify,[status(thm)],[f05]) ).
fof(nnf_6,plain,
! [X0] :
? [X1] :
( mult(X0,X1) != X1
| mult(X1,X0) != X1 ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
! [X0] :
( mult(X0,sK0(X0)) != sK0(X0)
| mult(sK0(X0),X0) != sK0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[nnf_6]) ).
cnf(c_12,negated_conjecture,
( mult(A,sK0(A)) != sK0(A)
| mult(sK0(A),A) != sK0(A) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_66,plain,
mult(A,mult(B,C)) = mult(C,mult(mult(ld(C,A),B),C)),
inference(paramod,[status(thm)],[c_7,c_11]) ).
cnf(c_15,plain,
mult(A,mult(mult(ld(A,B),C),A)) = mult(B,mult(C,A)),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_31,plain,
ld(A,mult(B,mult(C,A))) = mult(mult(ld(A,B),C),A),
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_39,plain,
mult(mult(ld(A,A),B),A) = mult(B,A),
inference(paramod,[status(thm)],[c_31,c_8]) ).
cnf(c_67,plain,
rd(mult(A,B),B) = mult(ld(B,B),A),
inference(paramod,[status(thm)],[c_39,c_10]) ).
cnf(c_68,plain,
A = mult(ld(B,B),A),
inference(paramod,[status(thm)],[c_10,c_67]) ).
cnf(c_46,plain,
mult(ld(A,A),B) = B,
inference(copy,[status(thm)],[c_68]) ).
cnf(c_49,negated_conjecture,
mult(sK0(ld(A,A)),ld(A,A)) != sK0(ld(A,A)),
inference(resolve,[status(thm)],[c_12,c_46]) ).
cnf(c_51,plain,
rd(A,A) = ld(B,B),
inference(paramod,[status(thm)],[c_46,c_10]) ).
cnf(c_62,plain,
ld(A,A) = ld(B,B),
inference(paramod,[status(thm)],[c_51,c_51]) ).
cnf(c_64,plain,
mult(A,ld(B,B)) = A,
inference(paramod,[status(thm)],[c_62,c_7]) ).
cnf(c_65,plain,
$false,
inference(resolve,[status(thm)],[c_64,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP657+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 15:32:34 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 3267148 was started by sandbox2 on n020,
% 0.10/0.37 % Fri Sep 25 15:32:34 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % 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 0.00 (+ 0.01) seconds.
% 0.10/0.39 % Length of proof is 19.
% 0.10/0.39 % Level of proof is 9.
% 0.10/0.39 % Maximum clause weight is 55.000.
% 0.10/0.39 % Given clauses 14.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------