%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP710-11 : 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 : n004.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 07:31:18 AM UTC 2026
% Result : Unsatisfiable 0.14s 10.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 7 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',f01) ).
cnf(c_1,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[f01]) ).
fof(f02,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',f02) ).
cnf(c_2,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[f02]) ).
fof(f03,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(VAR_0,mult(VAR_1,mult(VAR_1,VAR_2))) = mult(mult(mult(VAR_0,VAR_1),VAR_1),VAR_2),
file('theBenchmark.p',f03) ).
cnf(c_3,plain,
mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
inference(clausify,[status(thm)],[f03]) ).
cnf(c_4,plain,
mult(mult(mult(A,B),B),C) = mult(A,mult(B,mult(B,C))),
inference(copy,[status(thm)],[c_3]) ).
fof(f04,axiom,
! [VAR_0] : mult(VAR_0,i(VAR_0)) = unit,
file('theBenchmark.p',f04) ).
cnf(c_5,plain,
mult(A,i(A)) = unit,
inference(clausify,[status(thm)],[f04]) ).
fof(f05,axiom,
! [VAR_0] : mult(i(VAR_0),VAR_0) = unit,
file('theBenchmark.p',f05) ).
cnf(c_6,plain,
mult(i(A),A) = unit,
inference(clausify,[status(thm)],[f05]) ).
fof(goal,axiom,
! [VAR_0] : mult(VAR_0,x4) != x3,
file('theBenchmark.p',goal) ).
cnf(c_7,plain,
mult(A,x4) != x3,
inference(clausify,[status(thm)],[goal]) ).
cnf(c_152,plain,
mult(A,mult(B,mult(B,unit))) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_153,plain,
mult(A,mult(B,B)) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_1,c_152]) ).
cnf(c_8,plain,
mult(mult(A,B),B) = mult(A,mult(B,B)),
inference(copy,[status(thm)],[c_153]) ).
cnf(c_154,plain,
mult(mult(A,A),B) = mult(unit,mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_9,plain,
mult(mult(A,A),B) = mult(A,mult(A,B)),
inference(paramod,[status(thm)],[c_2,c_154]) ).
cnf(c_13,plain,
mult(mult(A,mult(B,B)),C) = mult(A,mult(B,mult(B,C))),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_155,plain,
mult(unit,i(A)) = mult(A,mult(i(A),i(A))),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_156,plain,
i(A) = mult(A,mult(i(A),i(A))),
inference(paramod,[status(thm)],[c_2,c_155]) ).
cnf(c_19,plain,
mult(A,mult(i(A),i(A))) = i(A),
inference(copy,[status(thm)],[c_156]) ).
cnf(c_157,plain,
mult(unit,A) = mult(i(A),mult(A,A)),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_158,plain,
A = mult(i(A),mult(A,A)),
inference(paramod,[status(thm)],[c_2,c_157]) ).
cnf(c_20,plain,
mult(i(A),mult(A,A)) = A,
inference(copy,[status(thm)],[c_158]) ).
cnf(c_21,plain,
mult(A,mult(x4,x4)) != x3,
inference(paramod,[status(thm)],[c_8,c_7]) ).
cnf(c_159,plain,
mult(unit,A) = mult(i(mult(B,B)),mult(B,mult(B,A))),
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_160,plain,
A = mult(i(mult(B,B)),mult(B,mult(B,A))),
inference(paramod,[status(thm)],[c_2,c_159]) ).
cnf(c_49,plain,
mult(i(mult(A,A)),mult(A,mult(A,B))) = B,
inference(copy,[status(thm)],[c_160]) ).
cnf(c_53,plain,
mult(A,mult(B,mult(B,mult(x4,x4)))) != x3,
inference(paramod,[status(thm)],[c_13,c_21]) ).
cnf(c_161,plain,
mult(A,B) = mult(i(A),mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_20,c_13]) ).
cnf(c_56,plain,
mult(i(A),mult(A,mult(A,B))) = mult(A,B),
inference(copy,[status(thm)],[c_161]) ).
cnf(c_162,plain,
mult(i(mult(A,A)),mult(A,i(A))) = mult(i(A),i(A)),
inference(paramod,[status(thm)],[c_19,c_49]) ).
cnf(c_163,plain,
mult(i(mult(A,A)),unit) = mult(i(A),i(A)),
inference(paramod,[status(thm)],[c_5,c_162]) ).
cnf(c_91,plain,
i(mult(A,A)) = mult(i(A),i(A)),
inference(paramod,[status(thm)],[c_1,c_163]) ).
cnf(c_164,plain,
mult(mult(i(A),i(A)),mult(A,mult(A,B))) = B,
inference(paramod,[status(thm)],[c_91,c_49]) ).
cnf(c_165,plain,
mult(i(A),mult(i(A),mult(A,mult(A,B)))) = B,
inference(paramod,[status(thm)],[c_9,c_164]) ).
cnf(c_98,plain,
mult(i(A),mult(A,B)) = B,
inference(paramod,[status(thm)],[c_56,c_165]) ).
cnf(c_166,plain,
mult(A,mult(i(x4),x4)) != x3,
inference(paramod,[status(thm)],[c_98,c_53]) ).
cnf(c_167,plain,
mult(A,unit) != x3,
inference(paramod,[status(thm)],[c_6,c_166]) ).
cnf(c_168,plain,
A != x3,
inference(paramod,[status(thm)],[c_1,c_167]) ).
cnf(c_169,plain,
x3 != A,
inference(copy,[status(thm)],[c_168]) ).
cnf(c_151,plain,
$false,
inference(copy,[status(thm)],[c_169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP710-11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/10.38 % Computer : n004.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Fri Sep 25 15:39:31 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.39 % Process 3567369 was started by sandbox on n004,
% 0.11/10.39 % Fri Sep 25 15:39:31 2026
% 0.11/10.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/10.39
% 0.11/10.39 % From the command line: assign(max_seconds, 300).
% 0.14/10.42
% 0.14/10.42 % SZS status Unsatisfiable for theBenchmark
% 0.14/10.42
% 0.14/10.42 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/10.42 % Length of proof is 19.
% 0.14/10.42 % Level of proof is 7.
% 0.14/10.42 % Maximum clause weight is 55.000.
% 0.14/10.42 % Given clauses 39.
% 0.14/10.42
% 0.14/10.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------