%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP166-4 : 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 : n010.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 07:28:10 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 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 : 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 : 17 ( 0 sgn 6 !; 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(symmetry_of_glb,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,VAR_1) = greatest_lower_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_glb) ).
cnf(c_4,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_glb]) ).
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(lat3b_2,axiom,
greatest_lower_bound(b,identity) = identity,
file('theBenchmark.p',lat3b_2) ).
cnf(c_24,plain,
greatest_lower_bound(b,identity) = identity,
inference(clausify,[status(thm)],[lat3b_2]) ).
cnf(c_25,plain,
greatest_lower_bound(identity,b) = identity,
inference(paramod,[status(thm)],[c_4,c_24]) ).
fof(prove_lat3b,axiom,
greatest_lower_bound(a,multiply(b,a)) != a,
file('theBenchmark.p',prove_lat3b) ).
cnf(c_26,plain,
greatest_lower_bound(a,multiply(b,a)) != a,
inference(clausify,[status(thm)],[prove_lat3b]) ).
cnf(c_59,plain,
greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(identity,B),A),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_67,plain,
multiply(greatest_lower_bound(identity,b),a) != a,
inference(paramod,[status(thm)],[c_59,c_26]) ).
cnf(c_68,plain,
multiply(identity,a) != a,
inference(paramod,[status(thm)],[c_25,c_67]) ).
cnf(c_69,plain,
a != a,
inference(paramod,[status(thm)],[c_1,c_68]) ).
cnf(c_66,plain,
$false,
inference(copy,[status(thm)],[c_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP166-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n010.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Fri Sep 25 14:33:35 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.39 % Process 966575 was started by sandbox on n010,
% 0.09/5.39 % Fri Sep 25 14:33:35 2026
% 0.09/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.39
% 0.09/5.39 % From the command line: assign(max_seconds, 300).
% 0.14/5.42
% 0.14/5.42 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.42
% 0.14/5.42 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.14/5.42 % Length of proof is 9.
% 0.14/5.42 % Level of proof is 3.
% 0.14/5.42 % Maximum clause weight is 13.000.
% 0.14/5.42 % Given clauses 15.
% 0.14/5.42
% 0.14/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------