%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP715+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 : Theorem 0.22s 0.80s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 45 unt; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 4 |; 2 &)
% ( 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 : 42 ( 0 sgn 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f06,axiom,
! [C,B,A] : mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)),
file('theBenchmark.p',f06) ).
fof(f07,axiom,
! [B,A] : mult(A,mult(B,B)) = mult(mult(A,B),B),
file('theBenchmark.p',f07) ).
fof(f08,axiom,
! [A] : mult(A,unit) = A,
file('theBenchmark.p',f08) ).
fof(f09,axiom,
! [A] : mult(unit,A) = A,
file('theBenchmark.p',f09) ).
fof(goals,conjecture,
! [X0] :
( mult(mult(X0,op_b),op_a) = X0
& mult(mult(X0,op_a),op_b) = X0 ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( mult(mult(X0,op_b),op_a) = X0
& mult(mult(X0,op_a),op_b) = X0 ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_16,plain,
mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)),
inference(clausify,[status(thm)],[f06]) ).
cnf(c_17,plain,
mult(mult(A,B),B) = mult(A,mult(B,B)),
inference(clausify,[status(thm)],[f07]) ).
cnf(c_18,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[f08]) ).
cnf(c_19,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_20,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_21,plain,
mult(op_b,op_a) = unit,
inference(clausify,[status(thm)],[f11]) ).
fof(nnf_10,plain,
? [X0] :
( mult(mult(X0,op_b),op_a) != X0
| mult(mult(X0,op_a),op_b) != X0 ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( mult(mult(sK0,op_b),op_a) != sK0
| mult(mult(sK0,op_a),op_b) != sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_10]) ).
cnf(c_22,negated_conjecture,
( mult(mult(sK0,op_b),op_a) != sK0
| mult(mult(sK0,op_a),op_b) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_34,plain,
mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)),
inference(paramod,[status(thm)],[c_16,c_16]) ).
cnf(c_595,plain,
mult(mult(unit,A),op_b) = mult(op_a,mult(mult(op_b,A),op_b)),
inference(paramod,[status(thm)],[c_20,c_16]) ).
cnf(c_596,plain,
mult(A,op_b) = mult(op_a,mult(mult(op_b,A),op_b)),
inference(paramod,[status(thm)],[c_19,c_595]) ).
cnf(c_43,plain,
mult(op_a,mult(mult(op_b,A),op_b)) = mult(A,op_b),
inference(copy,[status(thm)],[c_596]) ).
cnf(c_597,plain,
mult(unit,op_b) = mult(op_a,mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_20,c_17]) ).
cnf(c_598,plain,
op_b = mult(op_a,mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_19,c_597]) ).
cnf(c_44,plain,
mult(op_a,mult(op_b,op_b)) = op_b,
inference(copy,[status(thm)],[c_598]) ).
cnf(c_599,plain,
mult(mult(unit,A),op_a) = mult(op_b,mult(mult(op_a,A),op_a)),
inference(paramod,[status(thm)],[c_21,c_16]) ).
cnf(c_600,plain,
mult(A,op_a) = mult(op_b,mult(mult(op_a,A),op_a)),
inference(paramod,[status(thm)],[c_19,c_599]) ).
cnf(c_45,plain,
mult(op_b,mult(mult(op_a,A),op_a)) = mult(A,op_a),
inference(copy,[status(thm)],[c_600]) ).
cnf(c_601,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_44,c_34]) ).
cnf(c_602,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_21,c_601]) ).
cnf(c_603,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_18,c_602]) ).
cnf(c_274,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_603]) ).
cnf(c_296,plain,
mult(op_a,mult(op_b,mult(op_b,op_b))) = mult(op_b,op_b),
inference(paramod,[status(thm)],[c_17,c_43]) ).
cnf(c_604,plain,
mult(op_b,mult(op_b,op_a)) = mult(mult(op_b,op_b),op_a),
inference(paramod,[status(thm)],[c_44,c_45]) ).
cnf(c_605,plain,
mult(op_b,unit) = mult(mult(op_b,op_b),op_a),
inference(paramod,[status(thm)],[c_21,c_604]) ).
cnf(c_606,plain,
op_b = mult(mult(op_b,op_b),op_a),
inference(paramod,[status(thm)],[c_18,c_605]) ).
cnf(c_326,plain,
mult(mult(op_b,op_b),op_a) = op_b,
inference(copy,[status(thm)],[c_606]) ).
cnf(c_337,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_326,c_274]) ).
cnf(c_607,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_296,c_16]) ).
cnf(c_608,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_337,c_607]) ).
cnf(c_462,plain,
mult(mult(A,mult(op_b,op_b)),op_a) = mult(A,op_b),
inference(paramod,[status(thm)],[c_326,c_608]) ).
cnf(c_609,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_462,c_16]) ).
cnf(c_610,plain,
mult(mult(A,op_a),op_b) = mult(A,mult(op_b,op_a)),
inference(paramod,[status(thm)],[c_44,c_609]) ).
cnf(c_611,plain,
mult(mult(A,op_a),op_b) = mult(A,unit),
inference(paramod,[status(thm)],[c_21,c_610]) ).
cnf(c_545,plain,
mult(mult(A,op_a),op_b) = A,
inference(paramod,[status(thm)],[c_18,c_611]) ).
cnf(c_612,negated_conjecture,
( mult(mult(sK0,op_b),op_a) != sK0
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_545,c_22]) ).
cnf(c_571,negated_conjecture,
mult(mult(sK0,op_b),op_a) != sK0,
inference(copy,[status(thm)],[c_612]) ).
cnf(c_613,plain,
mult(A,op_b) = mult(mult(A,op_a),mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_545,c_17]) ).
cnf(c_579,plain,
mult(mult(A,op_a),mult(op_b,op_b)) = mult(A,op_b),
inference(copy,[status(thm)],[c_613]) ).
cnf(c_614,plain,
mult(mult(mult(A,op_a),mult(op_b,op_b)),op_a) = A,
inference(paramod,[status(thm)],[c_545,c_462]) ).
cnf(c_593,plain,
mult(mult(A,op_b),op_a) = A,
inference(paramod,[status(thm)],[c_579,c_614]) ).
cnf(c_594,plain,
$false,
inference(resolve,[status(thm)],[c_593,c_571]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP715+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.64 % Computer : n018.cluster.edu
% 0.16/0.64 % Model : x86_64 x86_64
% 0.16/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.64 % Memory : 8046.5625MB
% 0.16/0.64 % OS : Linux 6.8.0-71-generic
% 0.16/0.64 % CPULimit : 300
% 0.16/0.64 % WCLimit : 300
% 0.16/0.64 % DateTime : Fri Sep 25 15:41:52 UTC 2026
% 0.16/0.65 % CPUTime :
% 0.16/0.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.65 % Process 2327271 was started by sandbox2 on n018,
% 0.16/0.65 % Fri Sep 25 15:41:52 2026
% 0.16/0.65 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.22/0.66
% 0.22/0.66 % From the command line: assign(max_seconds, 300).
% 0.22/0.80
% 0.22/0.80 % SZS status Theorem for theBenchmark
% 0.22/0.80
% 0.22/0.80 % Proof 1 at 0.10 (+ 0.04) seconds.
% 0.22/0.80 % Length of proof is 26.
% 0.22/0.80 % Level of proof is 9.
% 0.22/0.80 % Maximum clause weight is 19.000.
% 0.22/0.80 % Given clauses 55.
% 0.22/0.80
% 0.22/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------