%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP173-1 : 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 : n008.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 07:28:13 AM UTC 2026
% Result : Unsatisfiable 0.14s 10.61s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 45 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 2 sgn 14 !; 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(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
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(symmetry_of_lub,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,VAR_1) = least_upper_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_lub) ).
cnf(c_5,plain,
least_upper_bound(A,B) = least_upper_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_lub]) ).
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_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(p05a_1,axiom,
least_upper_bound(identity,a) = identity,
file('theBenchmark.p',p05a_1) ).
cnf(c_22,plain,
least_upper_bound(identity,a) = identity,
inference(clausify,[status(thm)],[p05a_1]) ).
fof(p05a_2,axiom,
least_upper_bound(identity,inverse(a)) = identity,
file('theBenchmark.p',p05a_2) ).
cnf(c_23,plain,
least_upper_bound(identity,inverse(a)) = identity,
inference(clausify,[status(thm)],[p05a_2]) ).
fof(prove_p05a,axiom,
identity != a,
file('theBenchmark.p',prove_p05a) ).
cnf(c_24,plain,
identity != a,
inference(clausify,[status(thm)],[prove_p05a]) ).
cnf(c_25,plain,
a != identity,
inference(copy,[status(thm)],[c_24]) ).
cnf(c_117,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_118,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_117]) ).
cnf(c_26,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_118]) ).
cnf(c_41,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_72,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_26]) ).
cnf(c_82,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_26,c_26]) ).
cnf(c_83,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_82,c_72]) ).
cnf(c_119,plain,
greatest_lower_bound(a,identity) = a,
inference(paramod,[status(thm)],[c_22,c_41]) ).
cnf(c_95,plain,
greatest_lower_bound(identity,a) = a,
inference(paramod,[status(thm)],[c_4,c_119]) ).
cnf(c_120,plain,
greatest_lower_bound(inverse(a),identity) = inverse(a),
inference(paramod,[status(thm)],[c_23,c_41]) ).
cnf(c_96,plain,
greatest_lower_bound(identity,inverse(a)) = inverse(a),
inference(paramod,[status(thm)],[c_4,c_120]) ).
cnf(c_121,plain,
greatest_lower_bound(multiply(A,identity),multiply(A,a)) = multiply(A,a),
inference(paramod,[status(thm)],[c_95,c_17]) ).
cnf(c_99,plain,
greatest_lower_bound(A,multiply(A,a)) = multiply(A,a),
inference(paramod,[status(thm)],[c_83,c_121]) ).
cnf(c_122,plain,
greatest_lower_bound(inverse(a),identity) = multiply(inverse(a),a),
inference(paramod,[status(thm)],[c_2,c_99]) ).
cnf(c_123,plain,
greatest_lower_bound(identity,inverse(a)) = multiply(inverse(a),a),
inference(paramod,[status(thm)],[c_4,c_122]) ).
cnf(c_124,plain,
inverse(a) = multiply(inverse(a),a),
inference(paramod,[status(thm)],[c_96,c_123]) ).
cnf(c_115,plain,
inverse(a) = identity,
inference(paramod,[status(thm)],[c_2,c_124]) ).
cnf(c_125,plain,
greatest_lower_bound(inverse(a),multiply(inverse(a),a)) = identity,
inference(paramod,[status(thm)],[c_2,c_99]) ).
cnf(c_126,plain,
greatest_lower_bound(identity,multiply(inverse(a),a)) = identity,
inference(paramod,[status(thm)],[c_115,c_125]) ).
cnf(c_127,plain,
greatest_lower_bound(identity,multiply(identity,a)) = identity,
inference(paramod,[status(thm)],[c_115,c_126]) ).
cnf(c_128,plain,
greatest_lower_bound(identity,a) = identity,
inference(paramod,[status(thm)],[c_1,c_127]) ).
cnf(c_129,plain,
a = identity,
inference(paramod,[status(thm)],[c_95,c_128]) ).
cnf(c_116,plain,
$false,
inference(resolve,[status(thm)],[c_25,c_129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP173-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.59 % Computer : n008.cluster.edu
% 0.09/10.59 % Model : x86_64 x86_64
% 0.09/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.59 % Memory : 8046.5625MB
% 0.09/10.59 % OS : Linux 6.8.0-71-generic
% 0.09/10.59 % CPULimit : 300
% 0.09/10.59 % WCLimit : 300
% 0.09/10.59 % DateTime : Fri Sep 25 14:34:35 UTC 2026
% 0.09/10.59 % CPUTime :
% 0.09/10.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.59 % Process 1273669 was started by sandbox on n008,
% 0.09/10.59 % Fri Sep 25 14:34:35 2026
% 0.09/10.59 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/10.59
% 0.09/10.59 % From the command line: assign(max_seconds, 300).
% 0.14/10.61
% 0.14/10.61 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.14/10.61
% 0.14/10.61 % SZS status Unsatisfiable for theBenchmark
% 0.14/10.61
% 0.14/10.61 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/10.61 % Length of proof is 22.
% 0.14/10.61 % Level of proof is 6.
% 0.14/10.61 % Maximum clause weight is 36.000.
% 0.14/10.61 % Given clauses 28.
% 0.14/10.61
% 0.14/10.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------