%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP729-1 : 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 : n020.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 07:31:20 AM UTC 2026
% Result : Unsatisfiable 5.42s 1.12s
% Output : CNFRefutation 5.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 40 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 78 ( 9 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c01,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',c01) ).
cnf(c_1,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[c01]) ).
fof(c02,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',c02) ).
cnf(c_2,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[c02]) ).
fof(c03,axiom,
! [VAR_0] : mult(VAR_0,i(VAR_0)) = unit,
file('theBenchmark.p',c03) ).
cnf(c_3,plain,
mult(A,i(A)) = unit,
inference(clausify,[status(thm)],[c03]) ).
fof(c04,axiom,
! [VAR_0] : mult(i(VAR_0),VAR_0) = unit,
file('theBenchmark.p',c04) ).
cnf(c_4,plain,
mult(i(A),A) = unit,
inference(clausify,[status(thm)],[c04]) ).
fof(c05,axiom,
! [VAR_0,VAR_1] : i(mult(VAR_0,VAR_1)) = mult(i(VAR_0),i(VAR_1)),
file('theBenchmark.p',c05) ).
cnf(c_5,plain,
i(mult(A,B)) = mult(i(A),i(B)),
inference(clausify,[status(thm)],[c05]) ).
fof(c06,axiom,
! [VAR_0,VAR_1] : mult(i(VAR_0),mult(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',c06) ).
cnf(c_6,plain,
mult(i(A),mult(A,B)) = B,
inference(clausify,[status(thm)],[c06]) ).
fof(c10,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,VAR_1),VAR_2) = mult(mult(VAR_0,mult(VAR_1,VAR_2)),asoc(VAR_0,VAR_1,VAR_2)),
file('theBenchmark.p',c10) ).
cnf(c_10,plain,
mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)),
inference(clausify,[status(thm)],[c10]) ).
cnf(c_11,plain,
mult(mult(A,mult(B,C)),asoc(A,B,C)) = mult(mult(A,B),C),
inference(copy,[status(thm)],[c_10]) ).
fof(c11,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,VAR_1) = mult(mult(VAR_1,VAR_0),op_k(VAR_0,VAR_1)),
file('theBenchmark.p',c11) ).
cnf(c_12,plain,
mult(A,B) = mult(mult(B,A),op_k(A,B)),
inference(clausify,[status(thm)],[c11]) ).
cnf(c_13,plain,
mult(mult(A,B),op_k(B,A)) = mult(B,A),
inference(copy,[status(thm)],[c_12]) ).
fof(c22,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : asoc(VAR_0,VAR_1,asoc(VAR_2,VAR_3,VAR_4)) = unit,
file('theBenchmark.p',c22) ).
cnf(c_31,plain,
asoc(A,B,asoc(C,D,E)) = unit,
inference(clausify,[status(thm)],[c22]) ).
fof(goals,axiom,
asoc(a,b,op_k(c,d)) != unit,
file('theBenchmark.p',goals) ).
cnf(c_32,plain,
asoc(a,b,op_k(c,d)) != unit,
inference(clausify,[status(thm)],[goals]) ).
cnf(c_2417,plain,
mult(i(i(A)),unit) = A,
inference(paramod,[status(thm)],[c_4,c_6]) ).
cnf(c_36,plain,
i(i(A)) = A,
inference(paramod,[status(thm)],[c_2,c_2417]) ).
cnf(c_2418,plain,
mult(i(mult(A,mult(B,C))),mult(mult(A,B),C)) = asoc(A,B,C),
inference(paramod,[status(thm)],[c_11,c_6]) ).
cnf(c_2419,plain,
mult(mult(i(A),i(mult(B,C))),mult(mult(A,B),C)) = asoc(A,B,C),
inference(paramod,[status(thm)],[c_5,c_2418]) ).
cnf(c_60,plain,
mult(mult(i(A),mult(i(B),i(C))),mult(mult(A,B),C)) = asoc(A,B,C),
inference(paramod,[status(thm)],[c_5,c_2419]) ).
cnf(c_2420,plain,
mult(i(mult(A,B)),mult(B,A)) = op_k(B,A),
inference(paramod,[status(thm)],[c_13,c_6]) ).
cnf(c_76,plain,
mult(mult(i(A),i(B)),mult(B,A)) = op_k(B,A),
inference(paramod,[status(thm)],[c_5,c_2420]) ).
cnf(c_217,plain,
mult(A,mult(i(A),B)) = B,
inference(paramod,[status(thm)],[c_36,c_6]) ).
cnf(c_2421,plain,
mult(mult(i(i(A)),mult(i(i(B)),i(mult(B,A)))),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_76,c_60]) ).
cnf(c_2422,plain,
mult(mult(A,mult(i(i(B)),i(mult(B,A)))),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_36,c_2421]) ).
cnf(c_2423,plain,
mult(mult(A,mult(B,i(mult(B,A)))),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_36,c_2422]) ).
cnf(c_2424,plain,
mult(mult(A,mult(B,mult(i(B),i(A)))),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_5,c_2423]) ).
cnf(c_2425,plain,
mult(mult(A,i(A)),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_217,c_2424]) ).
cnf(c_2426,plain,
mult(unit,op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_3,c_2425]) ).
cnf(c_2427,plain,
op_k(B,A) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_1,c_2426]) ).
cnf(c_2309,plain,
asoc(i(A),i(B),mult(B,A)) = op_k(B,A),
inference(copy,[status(thm)],[c_2427]) ).
cnf(c_2415,plain,
asoc(A,B,op_k(C,D)) = unit,
inference(paramod,[status(thm)],[c_2309,c_31]) ).
cnf(c_2416,plain,
$false,
inference(resolve,[status(thm)],[c_2415,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP729-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 15:42:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3282952 was started by sandbox2 on n020,
% 0.09/0.36 % Fri Sep 25 15:42:03 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 5.42/1.12
% 5.42/1.12 % Assigning unary symbol i kb_weight 0 and highest precedence (14).
% 5.42/1.12
% 5.42/1.12 % SZS status Unsatisfiable for theBenchmark
% 5.42/1.12
% 5.42/1.12 % Proof 1 at 0.48 (+ 0.18) seconds.
% 5.42/1.12 % Length of proof is 19.
% 5.42/1.12 % Level of proof is 5.
% 5.42/1.12 % Maximum clause weight is 64.000.
% 5.42/1.12 % Given clauses 148.
% 5.42/1.12
% 5.42/1.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------