%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP657-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 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 : 45 ( 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(VAR_0,mult(mult(VAR_1,VAR_2),VAR_0)),
file('theBenchmark.p',f05) ).
cnf(c_5,plain,
mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)),
inference(clausify,[status(thm)],[f05]) ).
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_6,plain,
tuple(mult(A,x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_62,plain,
mult(A,mult(B,C)) = mult(C,mult(mult(ld(C,A),B),C)),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_9,plain,
mult(A,mult(mult(ld(A,B),C),A)) = mult(B,mult(C,A)),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_25,plain,
ld(A,mult(B,mult(C,A))) = mult(mult(ld(A,B),C),A),
inference(paramod,[status(thm)],[c_9,c_2]) ).
cnf(c_33,plain,
mult(mult(ld(A,A),B),A) = mult(B,A),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_63,plain,
rd(mult(A,B),B) = mult(ld(B,B),A),
inference(paramod,[status(thm)],[c_33,c_4]) ).
cnf(c_64,plain,
A = mult(ld(B,B),A),
inference(paramod,[status(thm)],[c_4,c_63]) ).
cnf(c_40,plain,
mult(ld(A,A),B) = B,
inference(copy,[status(thm)],[c_64]) ).
cnf(c_44,plain,
rd(A,A) = ld(B,B),
inference(paramod,[status(thm)],[c_40,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_40,c_6]) ).
cnf(c_56,plain,
ld(A,A) = ld(B,B),
inference(paramod,[status(thm)],[c_44,c_44]) ).
cnf(c_58,plain,
mult(A,ld(B,B)) = A,
inference(paramod,[status(thm)],[c_56,c_1]) ).
cnf(c_65,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_58,c_48]) ).
cnf(c_61,plain,
$false,
inference(copy,[status(thm)],[c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP657-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 15:26:47 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 2650694 was started by sandbox on n017,
% 0.08/0.35 % Fri Sep 25 15:26:47 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 14.
% 0.12/0.37 % Level of proof is 8.
% 0.12/0.37 % Maximum clause weight is 55.000.
% 0.12/0.37 % Given clauses 14.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------