%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP206-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:28:22 AM UTC 2026
% Result : Unsatisfiable 0.06s 0.43s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 20 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(right_identity,axiom,
! [VAR_0] : multiply(VAR_0,identity) = VAR_0,
file('theBenchmark.p',right_identity) ).
cnf(c_2,plain,
multiply(A,identity) = A,
inference(clausify,[status(thm)],[right_identity]) ).
fof(moufang4,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,multiply(multiply(VAR_1,VAR_2),VAR_0)) = multiply(multiply(VAR_0,VAR_1),multiply(VAR_2,VAR_0)),
file('theBenchmark.p',moufang4) ).
cnf(c_9,plain,
multiply(A,multiply(multiply(B,C),A)) = multiply(multiply(A,B),multiply(C,A)),
inference(clausify,[status(thm)],[moufang4]) ).
cnf(c_10,plain,
multiply(multiply(A,B),multiply(C,A)) = multiply(A,multiply(multiply(B,C),A)),
inference(copy,[status(thm)],[c_9]) ).
fof(prove_moufang1,axiom,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
file('theBenchmark.p',prove_moufang1) ).
cnf(c_11,plain,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
inference(clausify,[status(thm)],[prove_moufang1]) ).
cnf(c_54,plain,
multiply(multiply(A,B),A) = multiply(A,multiply(multiply(B,identity),A)),
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_25,plain,
multiply(multiply(A,B),A) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_54]) ).
cnf(c_52,plain,
multiply(a,multiply(multiply(b,c),a)) != multiply(multiply(a,b),multiply(c,a)),
inference(paramod,[status(thm)],[c_25,c_11]) ).
cnf(c_55,plain,
multiply(A,multiply(multiply(B,C),A)) = multiply(multiply(A,B),multiply(C,A)),
inference(copy,[status(thm)],[c_10]) ).
cnf(c_53,plain,
$false,
inference(resolve,[status(thm)],[c_52,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP206-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n020.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.06/0.40 % CPULimit : 300
% 0.06/0.40 % WCLimit : 300
% 0.06/0.40 % DateTime : Fri Sep 25 14:38:49 UTC 2026
% 0.06/0.41 % CPUTime :
% 0.06/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.41 % Process 3146150 was started by sandbox on n020,
% 0.06/0.41 % Fri Sep 25 14:38:49 2026
% 0.06/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.06/0.42
% 0.06/0.42 % From the command line: assign(max_seconds, 300).
% 0.06/0.43
% 0.06/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.06/0.43
% 0.06/0.43 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.06/0.43 % Length of proof is 8.
% 0.06/0.43 % Level of proof is 4.
% 0.06/0.43 % Maximum clause weight is 15.000.
% 0.06/0.43 % Given clauses 9.
% 0.06/0.43
% 0.06/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------