%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP710+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 : n019.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 0.14s 0.65s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 53 unt; 0 def)
% Number of atoms : 67 ( 66 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 13 ~; 5 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 121 ( 6 sgn 21 !; 8 ?)
% 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,
( ! [X3,X4] :
? [X5] : mult(X5,X4) = X3
& ! [X0,X1] :
? [X2] : mult(X0,X2) = X1 ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ( ! [X3,X4] :
? [X5] : mult(X5,X4) = X3
& ! [X0,X1] :
? [X2] : mult(X0,X2) = X1 ),
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,
( ? [X3,X4] :
! [X5] : mult(X5,X4) != X3
| ? [X0,X1] :
! [X2] : mult(X0,X2) != X1 ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ! [X5] : mult(X5,sK2) != sK3
| ! [X2] : mult(sK0,X2) != sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK3),skolemize(X4,sK2)],[nnf_6]) ).
fof(sk_goals_neg,plain,
! [VAR_0,VAR_1] :
( mult(VAR_1,sK2) != sK3
| mult(sK0,VAR_0) != sK1 ),
inference(cnf_transformation,[status(thm)],[sk_goals_neg_sk]) ).
cnf(c_12,negated_conjecture,
( mult(B,sK2) != sK3
| mult(sK0,A) != sK1 ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_218,plain,
mult(A,mult(B,mult(B,unit))) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_219,plain,
mult(A,mult(B,B)) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_7,c_218]) ).
cnf(c_13,plain,
mult(mult(A,B),B) = mult(A,mult(B,B)),
inference(copy,[status(thm)],[c_219]) ).
cnf(c_220,plain,
mult(mult(A,A),B) = mult(unit,mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_8,c_9]) ).
cnf(c_14,plain,
mult(mult(A,A),B) = mult(A,mult(A,B)),
inference(paramod,[status(thm)],[c_8,c_220]) ).
cnf(c_221,plain,
mult(mult(mult(mult(mult(A,B),B),C),C),D) = mult(A,mult(B,mult(B,mult(C,mult(C,D))))),
inference(paramod,[status(thm)],[c_9,c_9]) ).
cnf(c_222,plain,
mult(mult(mult(mult(A,mult(B,B)),C),C),D) = mult(A,mult(B,mult(B,mult(C,mult(C,D))))),
inference(paramod,[status(thm)],[c_13,c_221]) ).
cnf(c_17,plain,
mult(mult(mult(A,mult(B,B)),mult(C,C)),D) = mult(A,mult(B,mult(B,mult(C,mult(C,D))))),
inference(paramod,[status(thm)],[c_13,c_222]) ).
cnf(c_18,plain,
mult(mult(A,mult(B,B)),C) = mult(A,mult(B,mult(B,C))),
inference(paramod,[status(thm)],[c_13,c_9]) ).
cnf(c_19,plain,
mult(mult(A,mult(B,mult(B,mult(C,C)))),D) = mult(A,mult(B,mult(B,mult(C,mult(C,D))))),
inference(paramod,[status(thm)],[c_18,c_17]) ).
cnf(c_223,plain,
mult(unit,i(A)) = mult(A,mult(i(A),i(A))),
inference(paramod,[status(thm)],[c_10,c_13]) ).
cnf(c_224,plain,
i(A) = mult(A,mult(i(A),i(A))),
inference(paramod,[status(thm)],[c_8,c_223]) ).
cnf(c_26,plain,
mult(A,mult(i(A),i(A))) = i(A),
inference(copy,[status(thm)],[c_224]) ).
cnf(c_225,plain,
mult(unit,A) = mult(i(A),mult(A,A)),
inference(paramod,[status(thm)],[c_11,c_13]) ).
cnf(c_226,plain,
A = mult(i(A),mult(A,A)),
inference(paramod,[status(thm)],[c_8,c_225]) ).
cnf(c_27,plain,
mult(i(A),mult(A,A)) = A,
inference(copy,[status(thm)],[c_226]) ).
cnf(c_28,plain,
( mult(B,mult(sK2,sK2)) != sK3
| mult(sK0,A) != sK1 ),
inference(paramod,[status(thm)],[c_13,c_12]) ).
cnf(c_227,plain,
mult(unit,A) = mult(i(mult(B,B)),mult(B,mult(B,A))),
inference(paramod,[status(thm)],[c_11,c_18]) ).
cnf(c_228,plain,
A = mult(i(mult(B,B)),mult(B,mult(B,A))),
inference(paramod,[status(thm)],[c_8,c_227]) ).
cnf(c_54,plain,
mult(i(mult(A,A)),mult(A,mult(A,B))) = B,
inference(copy,[status(thm)],[c_228]) ).
cnf(c_229,plain,
mult(mult(A,mult(B,mult(B,C))),C) = mult(mult(A,mult(B,B)),mult(C,C)),
inference(paramod,[status(thm)],[c_18,c_13]) ).
cnf(c_56,plain,
mult(mult(A,mult(B,mult(B,C))),C) = mult(A,mult(B,mult(B,mult(C,C)))),
inference(paramod,[status(thm)],[c_18,c_229]) ).
cnf(c_230,plain,
mult(A,B) = mult(i(A),mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_27,c_18]) ).
cnf(c_60,plain,
mult(i(A),mult(A,mult(A,B))) = mult(A,B),
inference(copy,[status(thm)],[c_230]) ).
cnf(c_231,plain,
mult(i(mult(A,A)),mult(A,unit)) = i(A),
inference(paramod,[status(thm)],[c_10,c_54]) ).
cnf(c_82,plain,
mult(i(mult(A,A)),A) = i(A),
inference(paramod,[status(thm)],[c_7,c_231]) ).
cnf(c_232,plain,
mult(i(mult(i(A),i(A))),mult(i(A),unit)) = A,
inference(paramod,[status(thm)],[c_11,c_54]) ).
cnf(c_233,plain,
mult(i(mult(i(A),i(A))),i(A)) = A,
inference(paramod,[status(thm)],[c_7,c_232]) ).
cnf(c_83,plain,
i(i(A)) = A,
inference(paramod,[status(thm)],[c_82,c_233]) ).
cnf(c_234,plain,
mult(i(mult(A,A)),mult(A,i(A))) = mult(i(A),i(A)),
inference(paramod,[status(thm)],[c_26,c_54]) ).
cnf(c_235,plain,
mult(i(mult(A,A)),unit) = mult(i(A),i(A)),
inference(paramod,[status(thm)],[c_10,c_234]) ).
cnf(c_87,plain,
i(mult(A,A)) = mult(i(A),i(A)),
inference(paramod,[status(thm)],[c_7,c_235]) ).
cnf(c_236,plain,
mult(mult(i(A),i(A)),mult(A,mult(A,B))) = B,
inference(paramod,[status(thm)],[c_87,c_54]) ).
cnf(c_237,plain,
mult(i(A),mult(i(A),mult(A,mult(A,B)))) = B,
inference(paramod,[status(thm)],[c_14,c_236]) ).
cnf(c_93,plain,
mult(i(A),mult(A,B)) = B,
inference(paramod,[status(thm)],[c_60,c_237]) ).
cnf(c_100,plain,
mult(A,mult(i(A),B)) = B,
inference(paramod,[status(thm)],[c_83,c_93]) ).
cnf(c_134,plain,
mult(A,mult(sK2,sK2)) != sK3,
inference(resolve,[status(thm)],[c_28,c_100]) ).
cnf(c_183,plain,
mult(A,mult(B,mult(B,mult(C,mult(C,mult(sK2,sK2)))))) != sK3,
inference(paramod,[status(thm)],[c_19,c_134]) ).
cnf(c_238,plain,
mult(mult(A,mult(i(B),unit)),B) = mult(A,mult(i(B),mult(i(B),mult(B,B)))),
inference(paramod,[status(thm)],[c_11,c_56]) ).
cnf(c_239,plain,
mult(mult(A,i(B)),B) = mult(A,mult(i(B),mult(i(B),mult(B,B)))),
inference(paramod,[status(thm)],[c_7,c_238]) ).
cnf(c_240,plain,
mult(mult(A,i(B)),B) = mult(A,mult(i(B),B)),
inference(paramod,[status(thm)],[c_93,c_239]) ).
cnf(c_241,plain,
mult(mult(A,i(B)),B) = mult(A,unit),
inference(paramod,[status(thm)],[c_11,c_240]) ).
cnf(c_216,plain,
mult(mult(A,i(B)),B) = A,
inference(paramod,[status(thm)],[c_7,c_241]) ).
cnf(c_217,plain,
$false,
inference(resolve,[status(thm)],[c_216,c_183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP710+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.55 % Computer : n019.cluster.edu
% 0.11/0.55 % Model : x86_64 x86_64
% 0.11/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.55 % Memory : 8046.5625MB
% 0.11/0.55 % OS : Linux 6.8.0-71-generic
% 0.11/0.56 % CPULimit : 300
% 0.11/0.56 % WCLimit : 300
% 0.11/0.56 % DateTime : Fri Sep 25 15:39:37 UTC 2026
% 0.11/0.56 % CPUTime :
% 0.11/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.56 % Process 3143013 was started by sandbox2 on n019,
% 0.11/0.56 % Fri Sep 25 15:39:37 2026
% 0.11/0.56 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.56
% 0.11/0.56 % From the command line: assign(max_seconds, 300).
% 0.14/0.65
% 0.14/0.65 % SZS status Theorem for theBenchmark
% 0.14/0.65
% 0.14/0.65 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.14/0.65 % Length of proof is 32.
% 0.14/0.65 % Level of proof is 10.
% 0.14/0.65 % Maximum clause weight is 93.000.
% 0.14/0.65 % Given clauses 61.
% 0.14/0.65
% 0.14/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------