%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP010-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 07:26:09 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.48s
% Output : CNFRefutation 0.17s
% 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 : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 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(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_3,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(c_times_b_is_e,axiom,
multiply(c,b) = identity,
file('theBenchmark.p',c_times_b_is_e) ).
cnf(c_4,plain,
multiply(c,b) = identity,
inference(clausify,[status(thm)],[c_times_b_is_e]) ).
cnf(c_5,plain,
identity = multiply(c,b),
inference(copy,[status(thm)],[c_4]) ).
fof(prove_b_times_c_is_e,axiom,
multiply(b,c) != identity,
file('theBenchmark.p',prove_b_times_c_is_e) ).
cnf(c_6,plain,
multiply(b,c) != identity,
inference(clausify,[status(thm)],[prove_b_times_c_is_e]) ).
cnf(c_19,plain,
multiply(b,c) != multiply(c,b),
inference(paramod,[status(thm)],[c_5,c_6]) ).
cnf(c_7,plain,
multiply(c,b) != multiply(b,c),
inference(copy,[status(thm)],[c_19]) ).
cnf(c_8,plain,
multiply(inverse(A),A) = multiply(c,b),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_20,plain,
multiply(multiply(c,b),A) = A,
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_9,plain,
multiply(c,multiply(b,A)) = A,
inference(paramod,[status(thm)],[c_1,c_20]) ).
cnf(c_21,plain,
multiply(multiply(c,b),A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_22,plain,
multiply(c,multiply(b,A)) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_23,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_9,c_22]) ).
cnf(c_10,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_23]) ).
cnf(c_12,plain,
multiply(inverse(A),A) != multiply(b,c),
inference(paramod,[status(thm)],[c_8,c_7]) ).
cnf(c_17,plain,
multiply(inverse(c),A) = multiply(b,A),
inference(paramod,[status(thm)],[c_9,c_10]) ).
cnf(c_18,plain,
$false,
inference(resolve,[status(thm)],[c_17,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n013.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 14:15:37 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 586826 was started by sandbox2 on n013,
% 0.17/0.45 % Fri Sep 25 14:15:37 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.48
% 0.17/0.48 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.17/0.48
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.48
% 0.17/0.48 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.48 % Length of proof is 13.
% 0.17/0.48 % Level of proof is 5.
% 0.17/0.48 % Maximum clause weight is 36.000.
% 0.17/0.48 % Given clauses 6.
% 0.17/0.48
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------