%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP168-2 : 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 : 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 07:28:11 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.57s
% Output : CNFRefutation 0.12s
% 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 : 5 ( 5 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(monotony_glb1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',monotony_glb1) ).
cnf(c_16,plain,
multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[monotony_glb1]) ).
cnf(c_17,plain,
greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_16]) ).
fof(monotony_glb2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(greatest_lower_bound(VAR_0,VAR_1),VAR_2) = greatest_lower_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_glb2) ).
cnf(c_20,plain,
multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_glb2]) ).
cnf(c_21,plain,
greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B),
inference(copy,[status(thm)],[c_20]) ).
fof(p01b_1,axiom,
greatest_lower_bound(a,b) = a,
file('theBenchmark.p',p01b_1) ).
cnf(c_22,plain,
greatest_lower_bound(a,b) = a,
inference(clausify,[status(thm)],[p01b_1]) ).
fof(prove_p01b,axiom,
greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(a,c)),
file('theBenchmark.p',prove_p01b) ).
cnf(c_23,plain,
greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(a,c)),
inference(clausify,[status(thm)],[prove_p01b]) ).
cnf(c_25,plain,
multiply(inverse(c),greatest_lower_bound(multiply(a,c),multiply(b,c))) != multiply(inverse(c),multiply(a,c)),
inference(paramod,[status(thm)],[c_17,c_23]) ).
cnf(c_26,plain,
multiply(inverse(c),multiply(greatest_lower_bound(a,b),c)) != multiply(inverse(c),multiply(a,c)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_27,plain,
multiply(inverse(c),multiply(a,c)) != multiply(inverse(c),multiply(a,c)),
inference(paramod,[status(thm)],[c_22,c_26]) ).
cnf(c_24,plain,
$false,
inference(copy,[status(thm)],[c_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP168-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.55 % Computer : n020.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.09/0.55 % CPULimit : 300
% 0.09/0.55 % WCLimit : 300
% 0.09/0.55 % DateTime : Fri Sep 25 14:34:03 UTC 2026
% 0.12/0.56 % CPUTime :
% 0.12/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.56 % Process 3133704 was started by sandbox on n020,
% 0.12/0.56 % Fri Sep 25 14:34:03 2026
% 0.12/0.56 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.56
% 0.12/0.56 % From the command line: assign(max_seconds, 300).
% 0.12/0.57
% 0.12/0.57 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.57
% 0.12/0.57 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.57 % Length of proof is 7.
% 0.12/0.57 % Level of proof is 2.
% 0.12/0.57 % Maximum clause weight is 13.000.
% 0.12/0.57 % Given clauses 0.
% 0.12/0.57
% 0.12/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------