%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP711+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 : 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 : Theorem 1.04s 0.58s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 48 unt; 0 def)
% Number of atoms : 89 ( 88 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 7 ~; 14 |; 7 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [A] : mult(A,unit) = A,
file('theBenchmark.p',f01) ).
fof(f02,axiom,
! [A] : mult(unit,A) = A,
file('theBenchmark.p',f02) ).
fof(f03,axiom,
! [C,B,A] : mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
file('theBenchmark.p',f03) ).
fof(f04,axiom,
! [A] : mult(A,i(A)) = unit,
file('theBenchmark.p',f04) ).
fof(f05,axiom,
! [A] : mult(i(A),A) = unit,
file('theBenchmark.p',f05) ).
fof(goals,conjecture,
! [X6,X7,X8] :
( ( mult(X7,X6) = mult(X8,X6)
=> X7 = X8 )
& ( mult(X6,X7) = mult(X6,X8)
=> X7 = X8 ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X6,X7,X8] :
( ( mult(X7,X6) = mult(X8,X6)
=> X7 = X8 )
& ( mult(X6,X7) = mult(X6,X8)
=> X7 = X8 ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_7,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[f01]) ).
cnf(c_8,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[f02]) ).
cnf(c_9,plain,
mult(mult(mult(A,B),B),C) = mult(A,mult(B,mult(B,C))),
inference(clausify,[status(thm)],[f03]) ).
cnf(c_10,plain,
mult(A,i(A)) = unit,
inference(clausify,[status(thm)],[f04]) ).
cnf(c_11,plain,
mult(i(A),A) = unit,
inference(clausify,[status(thm)],[f05]) ).
fof(nnf_6,plain,
? [X6,X7,X8] :
( ( X8 != X7
& mult(X8,X6) = mult(X7,X6) )
| ( X8 != X7
& mult(X6,X8) = mult(X6,X7) ) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ( sK1 != sK2
& mult(sK1,sK0) = mult(sK2,sK0) )
| ( sK1 != sK2
& mult(sK0,sK1) = mult(sK0,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X6,sK0),skolemize(X7,sK2),skolemize(X8,sK1)],[nnf_6]) ).
fof(sk_goals_neg,plain,
( sK1 != sK2
& ( mult(sK1,sK0) = mult(sK2,sK0)
| mult(sK0,sK1) = mult(sK0,sK2) ) ),
inference(cnf_transformation,[status(thm)],[sk_goals_neg_sk]) ).
cnf(c_12,negated_conjecture,
( mult(sK1,sK0) = mult(sK2,sK0)
| mult(sK0,sK1) = mult(sK0,sK2) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_13,negated_conjecture,
sK1 != sK2,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_254,plain,
mult(A,mult(B,mult(B,unit))) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_255,plain,
mult(A,mult(B,B)) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_7,c_254]) ).
cnf(c_14,plain,
mult(mult(A,B),B) = mult(A,mult(B,B)),
inference(copy,[status(thm)],[c_255]) ).
cnf(c_256,plain,
mult(mult(A,A),B) = mult(unit,mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_8,c_9]) ).
cnf(c_15,plain,
mult(mult(A,A),B) = mult(A,mult(A,B)),
inference(paramod,[status(thm)],[c_8,c_256]) ).
cnf(c_19,plain,
mult(mult(A,mult(B,B)),C) = mult(A,mult(B,mult(B,C))),
inference(paramod,[status(thm)],[c_14,c_9]) ).
cnf(c_257,plain,
mult(unit,i(A)) = mult(A,mult(i(A),i(A))),
inference(paramod,[status(thm)],[c_10,c_14]) ).
cnf(c_258,plain,
i(A) = mult(A,mult(i(A),i(A))),
inference(paramod,[status(thm)],[c_8,c_257]) ).
cnf(c_23,plain,
mult(A,mult(i(A),i(A))) = i(A),
inference(copy,[status(thm)],[c_258]) ).
cnf(c_259,plain,
mult(unit,A) = mult(i(A),mult(A,A)),
inference(paramod,[status(thm)],[c_11,c_14]) ).
cnf(c_260,plain,
A = mult(i(A),mult(A,A)),
inference(paramod,[status(thm)],[c_8,c_259]) ).
cnf(c_24,plain,
mult(i(A),mult(A,A)) = A,
inference(copy,[status(thm)],[c_260]) ).
cnf(c_261,plain,
( mult(mult(sK2,sK0),sK0) = mult(sK1,mult(sK0,sK0))
| mult(sK0,sK1) = mult(sK0,sK2) ),
inference(paramod,[status(thm)],[c_12,c_14]) ).
cnf(c_262,plain,
( mult(sK2,mult(sK0,sK0)) = mult(sK1,mult(sK0,sK0))
| mult(sK0,sK1) = mult(sK0,sK2) ),
inference(paramod,[status(thm)],[c_14,c_261]) ).
cnf(c_25,plain,
( mult(sK1,mult(sK0,sK0)) = mult(sK2,mult(sK0,sK0))
| mult(sK0,sK1) = mult(sK0,sK2) ),
inference(copy,[status(thm)],[c_262]) ).
cnf(c_49,plain,
mult(A,mult(B,mult(B,i(mult(A,mult(B,B)))))) = unit,
inference(paramod,[status(thm)],[c_19,c_10]) ).
cnf(c_263,plain,
mult(unit,A) = mult(i(mult(B,B)),mult(B,mult(B,A))),
inference(paramod,[status(thm)],[c_11,c_19]) ).
cnf(c_264,plain,
A = mult(i(mult(B,B)),mult(B,mult(B,A))),
inference(paramod,[status(thm)],[c_8,c_263]) ).
cnf(c_50,plain,
mult(i(mult(A,A)),mult(A,mult(A,B))) = B,
inference(copy,[status(thm)],[c_264]) ).
cnf(c_265,plain,
mult(A,B) = mult(i(A),mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_24,c_19]) ).
cnf(c_55,plain,
mult(i(A),mult(A,mult(A,B))) = mult(A,B),
inference(copy,[status(thm)],[c_265]) ).
cnf(c_266,plain,
mult(i(mult(A,A)),mult(A,unit)) = i(A),
inference(paramod,[status(thm)],[c_10,c_50]) ).
cnf(c_70,plain,
mult(i(mult(A,A)),A) = i(A),
inference(paramod,[status(thm)],[c_7,c_266]) ).
cnf(c_267,plain,
mult(i(mult(i(A),i(A))),mult(i(A),unit)) = A,
inference(paramod,[status(thm)],[c_11,c_50]) ).
cnf(c_268,plain,
mult(i(mult(i(A),i(A))),i(A)) = A,
inference(paramod,[status(thm)],[c_7,c_267]) ).
cnf(c_71,plain,
i(i(A)) = A,
inference(paramod,[status(thm)],[c_70,c_268]) ).
cnf(c_269,plain,
mult(i(mult(A,A)),mult(A,i(A))) = mult(i(A),i(A)),
inference(paramod,[status(thm)],[c_23,c_50]) ).
cnf(c_270,plain,
mult(i(mult(A,A)),unit) = mult(i(A),i(A)),
inference(paramod,[status(thm)],[c_10,c_269]) ).
cnf(c_76,plain,
i(mult(A,A)) = mult(i(A),i(A)),
inference(paramod,[status(thm)],[c_7,c_270]) ).
cnf(c_271,plain,
mult(mult(i(A),i(A)),mult(A,mult(A,B))) = B,
inference(paramod,[status(thm)],[c_76,c_50]) ).
cnf(c_272,plain,
mult(i(A),mult(i(A),mult(A,mult(A,B)))) = B,
inference(paramod,[status(thm)],[c_15,c_271]) ).
cnf(c_86,plain,
mult(i(A),mult(A,B)) = B,
inference(paramod,[status(thm)],[c_55,c_272]) ).
cnf(c_231,plain,
( mult(sK1,mult(sK0,mult(sK0,i(mult(sK2,mult(sK0,sK0)))))) = unit
| mult(sK0,sK1) = mult(sK0,sK2) ),
inference(paramod,[status(thm)],[c_25,c_49]) ).
cnf(c_273,plain,
mult(i(A),unit) = mult(B,mult(B,i(mult(A,mult(B,B))))),
inference(paramod,[status(thm)],[c_49,c_86]) ).
cnf(c_274,plain,
i(A) = mult(B,mult(B,i(mult(A,mult(B,B))))),
inference(paramod,[status(thm)],[c_7,c_273]) ).
cnf(c_232,plain,
mult(A,mult(A,i(mult(B,mult(A,A))))) = i(B),
inference(copy,[status(thm)],[c_274]) ).
cnf(c_236,plain,
( mult(sK1,i(sK2)) = unit
| mult(sK0,sK1) = mult(sK0,sK2) ),
inference(paramod,[status(thm)],[c_232,c_231]) ).
cnf(c_275,plain,
( mult(i(sK1),unit) = i(sK2)
| mult(sK0,sK1) = mult(sK0,sK2) ),
inference(paramod,[status(thm)],[c_236,c_86]) ).
cnf(c_244,plain,
( i(sK1) = i(sK2)
| mult(sK0,sK1) = mult(sK0,sK2) ),
inference(paramod,[status(thm)],[c_7,c_275]) ).
cnf(c_276,plain,
( i(i(sK2)) = sK1
| mult(sK0,sK1) = mult(sK0,sK2) ),
inference(paramod,[status(thm)],[c_244,c_71]) ).
cnf(c_277,plain,
( sK2 = sK1
| mult(sK0,sK1) = mult(sK0,sK2) ),
inference(paramod,[status(thm)],[c_71,c_276]) ).
cnf(c_278,plain,
( sK1 = sK2
| mult(sK0,sK1) = mult(sK0,sK2) ),
inference(copy,[status(thm)],[c_277]) ).
cnf(c_250,negated_conjecture,
mult(sK0,sK1) = mult(sK0,sK2),
inference(resolve,[status(thm)],[c_13,c_278]) ).
cnf(c_279,plain,
mult(i(sK0),mult(sK0,sK2)) = sK1,
inference(paramod,[status(thm)],[c_250,c_86]) ).
cnf(c_280,plain,
sK2 = sK1,
inference(paramod,[status(thm)],[c_86,c_279]) ).
cnf(c_281,plain,
sK1 = sK2,
inference(copy,[status(thm)],[c_280]) ).
cnf(c_253,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_13,c_281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP711+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n009.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 15:39:44 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 1959274 was started by sandbox on n009,
% 0.15/0.42 % Fri Sep 25 15:39:44 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 1.04/0.58
% 1.04/0.58 % SZS status Theorem for theBenchmark
% 1.04/0.58
% 1.04/0.58 % Proof 1 at 0.11 (+ 0.03) seconds.
% 1.04/0.58 % Length of proof is 32.
% 1.04/0.58 % Level of proof is 11.
% 1.04/0.58 % Maximum clause weight is 71.000.
% 1.04/0.58 % Given clauses 49.
% 1.04/0.58
% 1.04/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------