%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP193-2 : 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 : n006.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 07:28:20 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 36 unt; 0 def)
% Number of atoms : 36 ( 35 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 : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 10 !; 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(associativity_of_glb,axiom,
! [VAR_0,VAR_1,VAR_2] : greatest_lower_bound(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(greatest_lower_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_glb) ).
cnf(c_6,plain,
greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_glb]) ).
cnf(c_7,plain,
greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_6]) ).
fof(idempotence_of_gld,axiom,
! [VAR_0] : greatest_lower_bound(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_gld) ).
cnf(c_11,plain,
greatest_lower_bound(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_gld]) ).
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(p8_9b_2,axiom,
greatest_lower_bound(identity,b) = identity,
file('theBenchmark.p',p8_9b_2) ).
cnf(c_23,plain,
greatest_lower_bound(identity,b) = identity,
inference(clausify,[status(thm)],[p8_9b_2]) ).
fof(p8_9b_4,axiom,
greatest_lower_bound(a,b) = identity,
file('theBenchmark.p',p8_9b_4) ).
cnf(c_25,plain,
greatest_lower_bound(a,b) = identity,
inference(clausify,[status(thm)],[p8_9b_4]) ).
fof(p8_9b_5,axiom,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
file('theBenchmark.p',p8_9b_5) ).
cnf(c_26,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(clausify,[status(thm)],[p8_9b_5]) ).
cnf(c_72,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(identity,greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_25,c_26]) ).
cnf(c_73,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) = greatest_lower_bound(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_1,c_72]) ).
cnf(c_74,plain,
greatest_lower_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_4,c_73]) ).
cnf(c_27,plain,
greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_7,c_74]) ).
fof(prove_p8_9b,axiom,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('theBenchmark.p',prove_p8_9b) ).
cnf(c_28,plain,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
inference(clausify,[status(thm)],[prove_p8_9b]) ).
cnf(c_75,plain,
greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(B,greatest_lower_bound(A,C)),
inference(paramod,[status(thm)],[c_4,c_7]) ).
cnf(c_31,plain,
greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(B,greatest_lower_bound(A,C)),
inference(paramod,[status(thm)],[c_7,c_75]) ).
cnf(c_32,plain,
greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_31,c_27]) ).
cnf(c_76,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(A,greatest_lower_bound(A,B)),
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_38,plain,
greatest_lower_bound(A,greatest_lower_bound(A,B)) = greatest_lower_bound(A,B),
inference(copy,[status(thm)],[c_76]) ).
cnf(c_41,plain,
greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_38,c_32]) ).
cnf(c_63,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_77,plain,
greatest_lower_bound(a,multiply(greatest_lower_bound(identity,b),c)) = greatest_lower_bound(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_63,c_41]) ).
cnf(c_78,plain,
greatest_lower_bound(a,multiply(identity,c)) = greatest_lower_bound(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_23,c_77]) ).
cnf(c_79,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_1,c_78]) ).
cnf(c_70,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(copy,[status(thm)],[c_79]) ).
cnf(c_71,plain,
$false,
inference(resolve,[status(thm)],[c_70,c_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP193-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 14:37:03 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3125889 was started by sandbox on n006,
% 0.11/0.37 % Fri Sep 25 14:37:03 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.38 % Length of proof is 19.
% 0.11/0.38 % Level of proof is 6.
% 0.11/0.38 % Maximum clause weight is 15.000.
% 0.11/0.38 % Given clauses 15.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------