%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP171-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 07:28:12 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 3 ( 2 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 : 26 ( 0 sgn 7 !; 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(associativity_of_lub,axiom,
! [VAR_0,VAR_1,VAR_2] : least_upper_bound(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(least_upper_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_lub) ).
cnf(c_8,plain,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_lub]) ).
cnf(c_9,plain,
least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_8]) ).
fof(monotony_lub2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(least_upper_bound(VAR_0,VAR_1),VAR_2) = least_upper_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_lub2) ).
cnf(c_18,plain,
multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_lub2]) ).
cnf(c_19,plain,
least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B),
inference(copy,[status(thm)],[c_18]) ).
fof(p04a_1,axiom,
least_upper_bound(identity,a) = a,
file('theBenchmark.p',p04a_1) ).
cnf(c_22,plain,
least_upper_bound(identity,a) = a,
inference(clausify,[status(thm)],[p04a_1]) ).
fof(p04a_2,axiom,
least_upper_bound(identity,b) = b,
file('theBenchmark.p',p04a_2) ).
cnf(c_23,plain,
least_upper_bound(identity,b) = b,
inference(clausify,[status(thm)],[p04a_2]) ).
fof(prove_p04a,axiom,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
file('theBenchmark.p',prove_p04a) ).
cnf(c_24,plain,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
inference(clausify,[status(thm)],[prove_p04a]) ).
cnf(c_50,plain,
least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(identity,B),A),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_250,plain,
least_upper_bound(multiply(identity,A),multiply(a,A)) = multiply(a,A),
inference(paramod,[status(thm)],[c_22,c_19]) ).
cnf(c_67,plain,
least_upper_bound(A,multiply(a,A)) = multiply(a,A),
inference(paramod,[status(thm)],[c_1,c_250]) ).
cnf(c_251,plain,
least_upper_bound(b,A) = least_upper_bound(identity,least_upper_bound(b,A)),
inference(paramod,[status(thm)],[c_23,c_9]) ).
cnf(c_68,plain,
least_upper_bound(identity,least_upper_bound(b,A)) = least_upper_bound(b,A),
inference(copy,[status(thm)],[c_251]) ).
cnf(c_252,plain,
least_upper_bound(identity,multiply(a,b)) = least_upper_bound(b,multiply(a,b)),
inference(paramod,[status(thm)],[c_67,c_68]) ).
cnf(c_253,plain,
least_upper_bound(identity,multiply(a,b)) = multiply(least_upper_bound(identity,a),b),
inference(paramod,[status(thm)],[c_50,c_252]) ).
cnf(c_248,plain,
least_upper_bound(identity,multiply(a,b)) = multiply(a,b),
inference(paramod,[status(thm)],[c_22,c_253]) ).
cnf(c_249,plain,
$false,
inference(resolve,[status(thm)],[c_248,c_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP171-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 14:31:54 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 1217305 was started by sandbox on n007,
% 0.10/0.38 % Fri Sep 25 14:31:54 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.47
% 0.15/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.47
% 0.15/0.47 % Proof 1 at 0.05 (+ 0.03) seconds.
% 0.15/0.47 % Length of proof is 13.
% 0.15/0.47 % Level of proof is 4.
% 0.15/0.47 % Maximum clause weight is 13.000.
% 0.15/0.47 % Given clauses 52.
% 0.15/0.47
% 0.15/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------