%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP659+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 : n010.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 0.13s 0.48s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 46 unt; 0 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 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 : 101 ( 0 sgn 15 !; 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(f03,axiom,
! [B,A] : mult(rd(A,B),B) = A,
file('theBenchmark.p',f03) ).
fof(f04,axiom,
! [B,A] : rd(mult(A,B),B) = A,
file('theBenchmark.p',f04) ).
fof(f05,axiom,
! [C,B,A] : mult(mult(A,mult(B,C)),B) = mult(mult(A,B),mult(C,B)),
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_9,plain,
mult(rd(A,B),B) = A,
inference(clausify,[status(thm)],[f03]) ).
cnf(c_10,plain,
rd(mult(A,B),B) = A,
inference(clausify,[status(thm)],[f04]) ).
cnf(c_11,plain,
mult(mult(A,mult(B,C)),B) = mult(mult(A,B),mult(C,B)),
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_14,plain,
rd(A,ld(B,A)) = B,
inference(paramod,[status(thm)],[c_7,c_10]) ).
cnf(c_490,plain,
mult(mult(A,B),C) = mult(mult(A,C),mult(ld(C,B),C)),
inference(paramod,[status(thm)],[c_7,c_11]) ).
cnf(c_15,plain,
mult(mult(A,B),mult(ld(B,C),B)) = mult(mult(A,C),B),
inference(copy,[status(thm)],[c_490]) ).
cnf(c_23,plain,
ld(mult(A,B),mult(mult(A,C),B)) = mult(ld(B,C),B),
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_27,plain,
rd(mult(mult(A,B),C),mult(ld(C,B),C)) = mult(A,C),
inference(paramod,[status(thm)],[c_15,c_10]) ).
cnf(c_42,plain,
ld(mult(A,B),mult(C,B)) = mult(ld(B,ld(A,C)),B),
inference(paramod,[status(thm)],[c_7,c_23]) ).
cnf(c_44,plain,
mult(ld(A,A),A) = A,
inference(paramod,[status(thm)],[c_23,c_8]) ).
cnf(c_52,plain,
rd(A,A) = ld(A,A),
inference(paramod,[status(thm)],[c_44,c_10]) ).
cnf(c_59,plain,
rd(mult(A,B),mult(ld(B,C),B)) = mult(rd(A,C),B),
inference(paramod,[status(thm)],[c_9,c_27]) ).
cnf(c_64,plain,
rd(mult(A,B),mult(C,B)) = mult(rd(A,mult(B,C)),B),
inference(paramod,[status(thm)],[c_8,c_59]) ).
cnf(c_491,plain,
mult(rd(A,mult(B,A)),B) = ld(mult(A,B),mult(A,B)),
inference(paramod,[status(thm)],[c_64,c_52]) ).
cnf(c_126,plain,
mult(rd(A,mult(B,A)),B) = mult(ld(B,ld(A,A)),B),
inference(paramod,[status(thm)],[c_42,c_491]) ).
cnf(c_492,plain,
rd(mult(ld(A,ld(B,B)),A),A) = rd(B,mult(A,B)),
inference(paramod,[status(thm)],[c_126,c_10]) ).
cnf(c_493,plain,
ld(A,ld(B,B)) = rd(B,mult(A,B)),
inference(paramod,[status(thm)],[c_10,c_492]) ).
cnf(c_226,plain,
rd(A,mult(B,A)) = ld(B,ld(A,A)),
inference(copy,[status(thm)],[c_493]) ).
cnf(c_494,plain,
mult(rd(A,A),ld(A,A)) = mult(ld(ld(A,A),ld(A,A)),ld(A,A)),
inference(paramod,[status(thm)],[c_44,c_126]) ).
cnf(c_495,plain,
mult(ld(A,A),ld(A,A)) = mult(ld(ld(A,A),ld(A,A)),ld(A,A)),
inference(paramod,[status(thm)],[c_52,c_494]) ).
cnf(c_232,plain,
mult(ld(A,A),ld(A,A)) = ld(A,A),
inference(paramod,[status(thm)],[c_44,c_495]) ).
cnf(c_289,plain,
ld(ld(A,A),ld(A,A)) = ld(A,A),
inference(paramod,[status(thm)],[c_232,c_8]) ).
cnf(c_301,plain,
rd(A,B) = ld(rd(B,A),ld(A,A)),
inference(paramod,[status(thm)],[c_9,c_226]) ).
cnf(c_315,plain,
mult(rd(A,B),rd(B,A)) = ld(B,B),
inference(paramod,[status(thm)],[c_301,c_7]) ).
cnf(c_319,plain,
rd(ld(A,A),rd(A,B)) = rd(B,A),
inference(paramod,[status(thm)],[c_301,c_14]) ).
cnf(c_496,plain,
ld(ld(A,A),mult(B,rd(A,C))) = mult(ld(rd(A,C),ld(rd(C,A),B)),rd(A,C)),
inference(paramod,[status(thm)],[c_315,c_42]) ).
cnf(c_366,plain,
mult(ld(rd(A,B),ld(rd(B,A),C)),rd(A,B)) = ld(ld(A,A),mult(C,rd(A,B))),
inference(copy,[status(thm)],[c_496]) ).
cnf(c_370,plain,
rd(rd(A,B),ld(A,A)) = ld(rd(B,A),ld(rd(A,B),rd(A,B))),
inference(paramod,[status(thm)],[c_315,c_226]) ).
cnf(c_497,plain,
mult(rd(rd(A,B),ld(A,A)),rd(B,A)) = ld(ld(A,A),ld(A,A)),
inference(paramod,[status(thm)],[c_319,c_315]) ).
cnf(c_498,plain,
mult(ld(rd(B,A),ld(rd(A,B),rd(A,B))),rd(B,A)) = ld(ld(A,A),ld(A,A)),
inference(paramod,[status(thm)],[c_370,c_497]) ).
cnf(c_499,plain,
ld(ld(B,B),mult(rd(A,B),rd(B,A))) = ld(ld(A,A),ld(A,A)),
inference(paramod,[status(thm)],[c_366,c_498]) ).
cnf(c_500,plain,
ld(ld(B,B),ld(B,B)) = ld(ld(A,A),ld(A,A)),
inference(paramod,[status(thm)],[c_315,c_499]) ).
cnf(c_501,plain,
ld(B,B) = ld(ld(A,A),ld(A,A)),
inference(paramod,[status(thm)],[c_289,c_500]) ).
cnf(c_381,plain,
ld(A,A) = ld(B,B),
inference(paramod,[status(thm)],[c_289,c_501]) ).
cnf(c_393,plain,
mult(A,ld(B,B)) = A,
inference(paramod,[status(thm)],[c_381,c_7]) ).
cnf(c_396,plain,
mult(ld(A,A),B) = B,
inference(paramod,[status(thm)],[c_381,c_44]) ).
cnf(c_502,negated_conjecture,
mult(ld(A,A),sK0(ld(A,A))) != sK0(ld(A,A)),
inference(resolve,[status(thm)],[c_12,c_393]) ).
cnf(c_503,negated_conjecture,
sK0(ld(A,A)) != sK0(ld(A,A)),
inference(paramod,[status(thm)],[c_396,c_502]) ).
cnf(c_489,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_503]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP659+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 15:32:15 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1108891 was started by sandbox on n010,
% 0.08/0.36 % Fri Sep 25 15:32:15 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.48
% 0.13/0.48 % SZS status Theorem for theBenchmark
% 0.13/0.48
% 0.13/0.48 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.13/0.48 % Length of proof is 34.
% 0.13/0.48 % Level of proof is 13.
% 0.13/0.48 % Maximum clause weight is 58.000.
% 0.13/0.48 % Given clauses 39.
% 0.13/0.48
% 0.13/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------