%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP001-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 07:26:07 AM UTC 2026
% Result : Unsatisfiable 0.16s 5.40s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 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 : 29 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_1,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_2,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(squareness,axiom,
! [VAR_0] : multiply(VAR_0,VAR_0) = identity,
file('theBenchmark.p',squareness) ).
cnf(c_3,plain,
multiply(A,A) = identity,
inference(clausify,[status(thm)],[squareness]) ).
fof(a_times_b_is_c,axiom,
multiply(a,b) = c,
file('theBenchmark.p',a_times_b_is_c) ).
cnf(c_4,plain,
multiply(a,b) = c,
inference(clausify,[status(thm)],[a_times_b_is_c]) ).
cnf(c_5,plain,
c = multiply(a,b),
inference(copy,[status(thm)],[c_4]) ).
fof(prove_b_times_a_is_c,axiom,
multiply(b,a) != c,
file('theBenchmark.p',prove_b_times_a_is_c) ).
cnf(c_6,plain,
multiply(b,a) != c,
inference(clausify,[status(thm)],[prove_b_times_a_is_c]) ).
cnf(c_7,plain,
multiply(b,a) != multiply(a,b),
inference(paramod,[status(thm)],[c_5,c_6]) ).
cnf(c_19,plain,
multiply(identity,A) = multiply(B,multiply(B,A)),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_20,plain,
A = multiply(B,multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_19]) ).
cnf(c_8,plain,
multiply(A,multiply(A,B)) = B,
inference(copy,[status(thm)],[c_20]) ).
cnf(c_21,plain,
identity = multiply(A,multiply(B,multiply(A,B))),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_9,plain,
multiply(A,multiply(B,multiply(A,B))) = identity,
inference(copy,[status(thm)],[c_21]) ).
cnf(c_11,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_22,plain,
multiply(A,identity) = multiply(B,multiply(A,B)),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_23,plain,
A = multiply(B,multiply(A,B)),
inference(paramod,[status(thm)],[c_11,c_22]) ).
cnf(c_13,plain,
multiply(A,multiply(B,A)) = B,
inference(copy,[status(thm)],[c_23]) ).
cnf(c_17,plain,
multiply(A,B) = multiply(B,A),
inference(paramod,[status(thm)],[c_13,c_8]) ).
cnf(c_18,plain,
$false,
inference(resolve,[status(thm)],[c_17,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP001-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n006.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Fri Sep 25 14:15:05 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 3080714 was started by sandbox on n006,
% 0.11/5.38 % Fri Sep 25 14:15:05 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.38
% 0.11/5.38 % From the command line: assign(max_seconds, 300).
% 0.16/5.40
% 0.16/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.40
% 0.16/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/5.40 % Length of proof is 13.
% 0.16/5.40 % Level of proof is 5.
% 0.16/5.40 % Maximum clause weight is 11.000.
% 0.16/5.40 % Given clauses 9.
% 0.16/5.40
% 0.16/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------