%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP715-10 : 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 : n009.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 0.15s 5.61s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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; 4 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f06,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(mult(VAR_0,VAR_1),VAR_2),VAR_1) = mult(VAR_0,mult(mult(VAR_1,VAR_2),VAR_1)),
file('theBenchmark.p',f06) ).
cnf(c_6,plain,
mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)),
inference(clausify,[status(thm)],[f06]) ).
fof(f07,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,mult(VAR_1,VAR_1)) = mult(mult(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',f07) ).
cnf(c_7,plain,
mult(A,mult(B,B)) = mult(mult(A,B),B),
inference(clausify,[status(thm)],[f07]) ).
cnf(c_8,plain,
mult(mult(A,B),B) = mult(A,mult(B,B)),
inference(copy,[status(thm)],[c_7]) ).
fof(f08,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',f08) ).
cnf(c_9,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[f08]) ).
fof(f09,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',f09) ).
cnf(c_10,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[f09]) ).
fof(f10,axiom,
mult(op_a,op_b) = unit,
file('theBenchmark.p',f10) ).
cnf(c_11,plain,
mult(op_a,op_b) = unit,
inference(clausify,[status(thm)],[f10]) ).
fof(f11,axiom,
mult(op_b,op_a) = unit,
file('theBenchmark.p',f11) ).
cnf(c_12,plain,
mult(op_b,op_a) = unit,
inference(clausify,[status(thm)],[f11]) ).
fof(goal,axiom,
mult(mult(x0,op_a),op_b) != x0,
file('theBenchmark.p',goal) ).
cnf(c_13,plain,
mult(mult(x0,op_a),op_b) != x0,
inference(clausify,[status(thm)],[goal]) ).
cnf(c_25,plain,
mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)),
inference(paramod,[status(thm)],[c_6,c_6]) ).
cnf(c_538,plain,
mult(mult(unit,A),op_b) = mult(op_a,mult(mult(op_b,A),op_b)),
inference(paramod,[status(thm)],[c_11,c_6]) ).
cnf(c_539,plain,
mult(A,op_b) = mult(op_a,mult(mult(op_b,A),op_b)),
inference(paramod,[status(thm)],[c_10,c_538]) ).
cnf(c_34,plain,
mult(op_a,mult(mult(op_b,A),op_b)) = mult(A,op_b),
inference(copy,[status(thm)],[c_539]) ).
cnf(c_540,plain,
mult(unit,op_b) = mult(op_a,mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_11,c_8]) ).
cnf(c_541,plain,
op_b = mult(op_a,mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_10,c_540]) ).
cnf(c_35,plain,
mult(op_a,mult(op_b,op_b)) = op_b,
inference(copy,[status(thm)],[c_541]) ).
cnf(c_542,plain,
mult(mult(unit,A),op_a) = mult(op_b,mult(mult(op_a,A),op_a)),
inference(paramod,[status(thm)],[c_12,c_6]) ).
cnf(c_543,plain,
mult(A,op_a) = mult(op_b,mult(mult(op_a,A),op_a)),
inference(paramod,[status(thm)],[c_10,c_542]) ).
cnf(c_36,plain,
mult(op_b,mult(mult(op_a,A),op_a)) = mult(A,op_a),
inference(copy,[status(thm)],[c_543]) ).
cnf(c_544,plain,
mult(mult(A,mult(op_b,op_a)),mult(op_b,op_b)) = mult(mult(A,op_a),mult(mult(mult(op_b,op_b),op_a),mult(op_b,op_b))),
inference(paramod,[status(thm)],[c_35,c_25]) ).
cnf(c_545,plain,
mult(mult(A,unit),mult(op_b,op_b)) = mult(mult(A,op_a),mult(mult(mult(op_b,op_b),op_a),mult(op_b,op_b))),
inference(paramod,[status(thm)],[c_12,c_544]) ).
cnf(c_546,plain,
mult(A,mult(op_b,op_b)) = mult(mult(A,op_a),mult(mult(mult(op_b,op_b),op_a),mult(op_b,op_b))),
inference(paramod,[status(thm)],[c_9,c_545]) ).
cnf(c_265,plain,
mult(mult(A,op_a),mult(mult(mult(op_b,op_b),op_a),mult(op_b,op_b))) = mult(A,mult(op_b,op_b)),
inference(copy,[status(thm)],[c_546]) ).
cnf(c_287,plain,
mult(op_a,mult(op_b,mult(op_b,op_b))) = mult(op_b,op_b),
inference(paramod,[status(thm)],[c_8,c_34]) ).
cnf(c_547,plain,
mult(op_b,mult(op_b,op_a)) = mult(mult(op_b,op_b),op_a),
inference(paramod,[status(thm)],[c_35,c_36]) ).
cnf(c_548,plain,
mult(op_b,unit) = mult(mult(op_b,op_b),op_a),
inference(paramod,[status(thm)],[c_12,c_547]) ).
cnf(c_549,plain,
op_b = mult(mult(op_b,op_b),op_a),
inference(paramod,[status(thm)],[c_9,c_548]) ).
cnf(c_317,plain,
mult(mult(op_b,op_b),op_a) = op_b,
inference(copy,[status(thm)],[c_549]) ).
cnf(c_328,plain,
mult(mult(A,op_a),mult(op_b,mult(op_b,op_b))) = mult(A,mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_317,c_265]) ).
cnf(c_550,plain,
mult(mult(mult(A,op_a),mult(op_b,mult(op_b,op_b))),op_a) = mult(A,mult(mult(op_b,op_b),op_a)),
inference(paramod,[status(thm)],[c_287,c_6]) ).
cnf(c_551,plain,
mult(mult(A,mult(op_b,op_b)),op_a) = mult(A,mult(mult(op_b,op_b),op_a)),
inference(paramod,[status(thm)],[c_328,c_550]) ).
cnf(c_453,plain,
mult(mult(A,mult(op_b,op_b)),op_a) = mult(A,op_b),
inference(paramod,[status(thm)],[c_317,c_551]) ).
cnf(c_552,plain,
mult(mult(A,op_a),op_b) = mult(A,mult(mult(op_a,mult(op_b,op_b)),op_a)),
inference(paramod,[status(thm)],[c_453,c_6]) ).
cnf(c_553,plain,
mult(mult(A,op_a),op_b) = mult(A,mult(op_b,op_a)),
inference(paramod,[status(thm)],[c_35,c_552]) ).
cnf(c_554,plain,
mult(mult(A,op_a),op_b) = mult(A,unit),
inference(paramod,[status(thm)],[c_12,c_553]) ).
cnf(c_536,plain,
mult(mult(A,op_a),op_b) = A,
inference(paramod,[status(thm)],[c_9,c_554]) ).
cnf(c_537,plain,
$false,
inference(resolve,[status(thm)],[c_536,c_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP715-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n009.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 15:40:04 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 1960062 was started by sandbox2 on n009,
% 0.10/5.38 % Fri Sep 25 15:40:04 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 0.15/5.61
% 0.15/5.61 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.61
% 0.15/5.61 % Proof 1 at 0.17 (+ 0.05) seconds.
% 0.15/5.61 % Length of proof is 19.
% 0.15/5.61 % Level of proof is 7.
% 0.15/5.61 % Maximum clause weight is 19.000.
% 0.15/5.61 % Given clauses 54.
% 0.15/5.61
% 0.15/5.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------