%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP171-2 : 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 : n003.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 0.12s 0.60s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 2 sgn 9 !; 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(glb_absorbtion,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,least_upper_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',glb_absorbtion) ).
cnf(c_13,plain,
greatest_lower_bound(A,least_upper_bound(A,B)) = A,
inference(clausify,[status(thm)],[glb_absorbtion]) ).
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(p04c_1,axiom,
least_upper_bound(identity,a) = a,
file('theBenchmark.p',p04c_1) ).
cnf(c_22,plain,
least_upper_bound(identity,a) = a,
inference(clausify,[status(thm)],[p04c_1]) ).
fof(p04c_2,axiom,
least_upper_bound(identity,b) = b,
file('theBenchmark.p',p04c_2) ).
cnf(c_23,plain,
least_upper_bound(identity,b) = b,
inference(clausify,[status(thm)],[p04c_2]) ).
fof(prove_p04c,axiom,
greatest_lower_bound(identity,multiply(a,b)) != identity,
file('theBenchmark.p',prove_p04c) ).
cnf(c_24,plain,
greatest_lower_bound(identity,multiply(a,b)) != identity,
inference(clausify,[status(thm)],[prove_p04c]) ).
cnf(c_257,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_257]) ).
cnf(c_258,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_258]) ).
cnf(c_244,plain,
greatest_lower_bound(identity,least_upper_bound(b,A)) = identity,
inference(paramod,[status(thm)],[c_68,c_13]) ).
cnf(c_255,plain,
greatest_lower_bound(identity,multiply(a,b)) = identity,
inference(paramod,[status(thm)],[c_67,c_244]) ).
cnf(c_256,plain,
$false,
inference(resolve,[status(thm)],[c_255,c_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP171-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.54 % Computer : n003.cluster.edu
% 0.08/0.54 % Model : x86_64 x86_64
% 0.08/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.54 % Memory : 8046.5625MB
% 0.08/0.54 % OS : Linux 6.8.0-71-generic
% 0.08/0.54 % CPULimit : 300
% 0.08/0.54 % WCLimit : 300
% 0.08/0.54 % DateTime : Fri Sep 25 14:35:39 UTC 2026
% 0.08/0.54 % CPUTime :
% 0.08/0.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.54 % Process 392991 was started by sandbox on n003,
% 0.08/0.54 % Fri Sep 25 14:35:39 2026
% 0.08/0.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.55
% 0.08/0.55 % From the command line: assign(max_seconds, 300).
% 0.12/0.60
% 0.12/0.60 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.60
% 0.12/0.60 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.12/0.60 % Length of proof is 14.
% 0.12/0.60 % Level of proof is 5.
% 0.12/0.60 % Maximum clause weight is 13.000.
% 0.12/0.60 % Given clauses 53.
% 0.12/0.60
% 0.12/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------