%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP709-1 : 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 07:31:17 AM UTC 2026
% Result : Unsatisfiable 0.12s 15.64s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% 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 : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c06,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',c06) ).
cnf(c_6,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[c06]) ).
fof(c07,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(VAR_0,mult(VAR_1,mult(VAR_0,VAR_2))) = mult(mult(VAR_0,mult(VAR_1,VAR_0)),VAR_2),
file('theBenchmark.p',c07) ).
cnf(c_7,plain,
mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C),
inference(clausify,[status(thm)],[c07]) ).
cnf(c_8,plain,
mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))),
inference(copy,[status(thm)],[c_7]) ).
fof(c08,axiom,
! [VAR_0] : mult(op_c,VAR_0) = mult(VAR_0,op_c),
file('theBenchmark.p',c08) ).
cnf(c_9,plain,
mult(op_c,A) = mult(A,op_c),
inference(clausify,[status(thm)],[c08]) ).
fof(c09,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,mult(VAR_1,op_c)) = mult(mult(VAR_0,VAR_1),op_c),
file('theBenchmark.p',c09) ).
cnf(c_10,plain,
mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
inference(clausify,[status(thm)],[c09]) ).
cnf(c_63,plain,
mult(A,mult(B,op_c)) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_9,c_10]) ).
cnf(c_11,plain,
mult(op_c,mult(A,B)) = mult(A,mult(B,op_c)),
inference(copy,[status(thm)],[c_63]) ).
fof(goals,axiom,
mult(mult(op_c,op_c),mult(a,b)) != mult(mult(mult(op_c,op_c),a),b),
file('theBenchmark.p',goals) ).
cnf(c_12,plain,
mult(mult(op_c,op_c),mult(a,b)) != mult(mult(mult(op_c,op_c),a),b),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_13,plain,
mult(mult(mult(op_c,op_c),a),b) != mult(mult(op_c,op_c),mult(a,b)),
inference(copy,[status(thm)],[c_12]) ).
cnf(c_64,plain,
mult(mult(A,A),B) = mult(A,mult(unit,mult(A,B))),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_25,plain,
mult(mult(A,A),B) = mult(A,mult(A,B)),
inference(paramod,[status(thm)],[c_6,c_64]) ).
cnf(c_65,plain,
mult(mult(op_c,mult(op_c,a)),b) != mult(mult(op_c,op_c),mult(a,b)),
inference(paramod,[status(thm)],[c_25,c_13]) ).
cnf(c_27,plain,
mult(mult(op_c,mult(op_c,a)),b) != mult(op_c,mult(op_c,mult(a,b))),
inference(paramod,[status(thm)],[c_25,c_65]) ).
cnf(c_35,plain,
mult(mult(op_c,mult(op_c,A)),B) = mult(op_c,mult(A,mult(op_c,B))),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_38,plain,
mult(op_c,mult(a,mult(op_c,b))) != mult(op_c,mult(op_c,mult(a,b))),
inference(paramod,[status(thm)],[c_35,c_27]) ).
cnf(c_57,plain,
mult(op_c,mult(A,B)) = mult(A,mult(op_c,B)),
inference(paramod,[status(thm)],[c_9,c_11]) ).
cnf(c_66,plain,
mult(op_c,mult(op_c,mult(a,b))) != mult(op_c,mult(op_c,mult(a,b))),
inference(paramod,[status(thm)],[c_57,c_38]) ).
cnf(c_62,plain,
$false,
inference(copy,[status(thm)],[c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP709-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/15.61 % Computer : n010.cluster.edu
% 0.12/15.61 % Model : x86_64 x86_64
% 0.12/15.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.61 % Memory : 8046.5625MB
% 0.12/15.61 % OS : Linux 6.8.0-71-generic
% 0.12/15.61 % CPULimit : 300
% 0.12/15.61 % WCLimit : 300
% 0.12/15.61 % DateTime : Fri Sep 25 15:40:02 UTC 2026
% 0.12/15.61 % CPUTime :
% 0.12/15.62 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/15.62 % Process 1127814 was started by sandbox on n010,
% 0.12/15.62 % Fri Sep 25 15:40:02 2026
% 0.12/15.62 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/15.62
% 0.12/15.62 % From the command line: assign(max_seconds, 300).
% 0.12/15.64
% 0.12/15.64 % SZS status Unsatisfiable for theBenchmark
% 0.12/15.64
% 0.12/15.64 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/15.64 % Length of proof is 14.
% 0.12/15.64 % Level of proof is 5.
% 0.12/15.64 % Maximum clause weight is 55.000.
% 0.12/15.64 % Given clauses 9.
% 0.12/15.64
% 0.12/15.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------