%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP708-1 : 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 : n026.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 07:31:17 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 41 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c02,axiom,
! [VAR_0,VAR_1] : ld(VAR_0,mult(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',c02) ).
cnf(c_2,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[c02]) ).
fof(c06,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',c06) ).
cnf(c_6,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[c06]) ).
fof(c07,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(VAR_0,mult(VAR_1,mult(VAR_0,VAR_2))) = mult(mult(VAR_0,mult(VAR_1,VAR_0)),VAR_2),
file('theBenchmark.p',c07) ).
cnf(c_7,plain,
mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C),
inference(clausify,[status(thm)],[c07]) ).
cnf(c_8,plain,
mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))),
inference(copy,[status(thm)],[c_7]) ).
fof(c08,axiom,
! [VAR_0] : mult(op_c,VAR_0) = mult(VAR_0,op_c),
file('theBenchmark.p',c08) ).
cnf(c_9,plain,
mult(op_c,A) = mult(A,op_c),
inference(clausify,[status(thm)],[c08]) ).
fof(c09,axiom,
! [VAR_0,VAR_1] : mult(mult(op_c,op_c),mult(VAR_0,VAR_1)) = mult(mult(mult(op_c,op_c),VAR_0),VAR_1),
file('theBenchmark.p',c09) ).
cnf(c_10,plain,
mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B),
inference(clausify,[status(thm)],[c09]) ).
cnf(c_11,plain,
mult(mult(mult(op_c,op_c),A),B) = mult(mult(op_c,op_c),mult(A,B)),
inference(copy,[status(thm)],[c_10]) ).
fof(goals,axiom,
mult(a,mult(b,op_c)) != mult(mult(a,b),op_c),
file('theBenchmark.p',goals) ).
cnf(c_12,plain,
mult(a,mult(b,op_c)) != mult(mult(a,b),op_c),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_216,plain,
mult(a,mult(op_c,b)) != mult(mult(a,b),op_c),
inference(paramod,[status(thm)],[c_9,c_12]) ).
cnf(c_13,plain,
mult(a,mult(op_c,b)) != mult(op_c,mult(a,b)),
inference(paramod,[status(thm)],[c_9,c_216]) ).
cnf(c_217,plain,
mult(mult(A,A),B) = mult(A,mult(unit,mult(A,B))),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_25,plain,
mult(mult(A,A),B) = mult(A,mult(A,B)),
inference(paramod,[status(thm)],[c_6,c_217]) ).
cnf(c_218,plain,
mult(mult(op_c,mult(op_c,A)),B) = mult(mult(op_c,op_c),mult(A,B)),
inference(paramod,[status(thm)],[c_25,c_11]) ).
cnf(c_27,plain,
mult(mult(op_c,mult(op_c,A)),B) = mult(op_c,mult(op_c,mult(A,B))),
inference(paramod,[status(thm)],[c_25,c_218]) ).
cnf(c_219,plain,
mult(mult(op_c,mult(op_c,A)),B) = mult(op_c,mult(A,mult(op_c,B))),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_35,plain,
mult(op_c,mult(op_c,mult(A,B))) = mult(op_c,mult(A,mult(op_c,B))),
inference(paramod,[status(thm)],[c_27,c_219]) ).
cnf(c_220,plain,
ld(op_c,mult(op_c,mult(A,mult(op_c,B)))) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_35,c_2]) ).
cnf(c_221,plain,
mult(A,mult(op_c,B)) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_2,c_220]) ).
cnf(c_214,plain,
mult(op_c,mult(A,B)) = mult(A,mult(op_c,B)),
inference(copy,[status(thm)],[c_221]) ).
cnf(c_222,plain,
mult(op_c,mult(a,b)) != mult(a,mult(op_c,b)),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_215,plain,
$false,
inference(resolve,[status(thm)],[c_214,c_222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP708-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n026.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Fri Sep 25 15:42:15 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 2923947 was started by sandbox2 on n026,
% 0.11/5.38 % Fri Sep 25 15:42:15 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.45
% 0.15/5.45 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.45
% 0.15/5.45 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.15/5.45 % Length of proof is 14.
% 0.15/5.45 % Level of proof is 6.
% 0.15/5.45 % Maximum clause weight is 55.000.
% 0.15/5.45 % Given clauses 46.
% 0.15/5.45
% 0.15/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------