%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP656-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 07:31:04 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.36s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 0 con; 1-2 aty)
% Number of variables : 42 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,ld(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',f01) ).
cnf(c_1,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[f01]) ).
fof(f02,axiom,
! [VAR_0,VAR_1] : ld(VAR_0,mult(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',f02) ).
cnf(c_2,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[f02]) ).
fof(f04,axiom,
! [VAR_0,VAR_1] : rd(mult(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',f04) ).
cnf(c_4,plain,
rd(mult(A,B),B) = A,
inference(clausify,[status(thm)],[f04]) ).
fof(f05,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,VAR_1),mult(VAR_2,VAR_0)) = mult(mult(VAR_0,mult(VAR_1,VAR_2)),VAR_0),
file('theBenchmark.p',f05) ).
cnf(c_5,plain,
mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A),
inference(clausify,[status(thm)],[f05]) ).
cnf(c_6,plain,
mult(mult(A,mult(B,C)),A) = mult(mult(A,B),mult(C,A)),
inference(copy,[status(thm)],[c_5]) ).
fof(goal,axiom,
! [VAR_0] : tuple(mult(VAR_0,x1(VAR_0)),mult(x1_2(VAR_0),VAR_0)) != tuple(x1(VAR_0),x1_2(VAR_0)),
file('theBenchmark.p',goal) ).
cnf(c_7,plain,
tuple(mult(A,x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_59,plain,
mult(mult(A,B),A) = mult(mult(A,C),mult(ld(C,B),A)),
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_10,plain,
mult(mult(A,B),mult(ld(B,C),A)) = mult(mult(A,C),A),
inference(copy,[status(thm)],[c_59]) ).
cnf(c_19,plain,
ld(mult(A,B),mult(mult(A,C),A)) = mult(ld(B,C),A),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_38,plain,
mult(ld(A,A),B) = B,
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_45,plain,
rd(A,A) = ld(B,B),
inference(paramod,[status(thm)],[c_38,c_4]) ).
cnf(c_48,plain,
tuple(x1(ld(A,A)),mult(x1_2(ld(A,A)),ld(A,A))) != tuple(x1(ld(A,A)),x1_2(ld(A,A))),
inference(paramod,[status(thm)],[c_38,c_7]) ).
cnf(c_54,plain,
ld(A,A) = ld(B,B),
inference(paramod,[status(thm)],[c_45,c_45]) ).
cnf(c_56,plain,
mult(A,ld(B,B)) = A,
inference(paramod,[status(thm)],[c_54,c_1]) ).
cnf(c_60,plain,
tuple(x1(ld(A,A)),x1_2(ld(A,A))) != tuple(x1(ld(A,A)),x1_2(ld(A,A))),
inference(paramod,[status(thm)],[c_56,c_48]) ).
cnf(c_58,plain,
$false,
inference(copy,[status(thm)],[c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP656-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n003.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 15:32:52 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 538939 was started by sandbox2 on n003,
% 0.08/0.35 % Fri Sep 25 15:32:52 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.08/0.36
% 0.08/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.36
% 0.08/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.36 % Length of proof is 14.
% 0.08/0.36 % Level of proof is 8.
% 0.08/0.36 % Maximum clause weight is 55.000.
% 0.08/0.36 % Given clauses 13.
% 0.08/0.36
% 0.08/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------