%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP192-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 52 unt; 0 def)
% Number of atoms : 52 ( 51 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 93 ( 11 sgn 18 !; 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(lub_absorbtion,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,greatest_lower_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',lub_absorbtion) ).
cnf(c_12,plain,
least_upper_bound(A,greatest_lower_bound(A,B)) = A,
inference(clausify,[status(thm)],[lub_absorbtion]) ).
fof(monotony_lub1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',monotony_lub1) ).
cnf(c_14,plain,
multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[monotony_lub1]) ).
cnf(c_15,plain,
least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_14]) ).
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(p40a_1,axiom,
! [VAR_0] : least_upper_bound(identity,VAR_0) = VAR_0,
file('theBenchmark.p',p40a_1) ).
cnf(c_22,plain,
least_upper_bound(identity,A) = A,
inference(clausify,[status(thm)],[p40a_1]) ).
fof(prove_p40a,axiom,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_p40a) ).
cnf(c_23,plain,
multiply(a,b) != multiply(b,a),
inference(clausify,[status(thm)],[prove_p40a]) ).
cnf(c_24,plain,
multiply(b,a) != multiply(a,b),
inference(copy,[status(thm)],[c_23]) ).
cnf(c_110,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_111,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_110]) ).
cnf(c_25,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_111]) ).
cnf(c_112,plain,
least_upper_bound(multiply(inverse(A),B),identity) = multiply(inverse(A),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_2,c_15]) ).
cnf(c_113,plain,
least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_5,c_112]) ).
cnf(c_114,plain,
multiply(inverse(A),B) = multiply(inverse(A),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_22,c_113]) ).
cnf(c_45,plain,
multiply(inverse(A),least_upper_bound(B,A)) = multiply(inverse(A),B),
inference(copy,[status(thm)],[c_114]) ).
cnf(c_57,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_115,plain,
A = least_upper_bound(A,identity),
inference(paramod,[status(thm)],[c_22,c_5]) ).
cnf(c_64,plain,
least_upper_bound(A,identity) = A,
inference(copy,[status(thm)],[c_115]) ).
cnf(c_65,plain,
greatest_lower_bound(identity,A) = identity,
inference(paramod,[status(thm)],[c_22,c_12]) ).
cnf(c_116,plain,
greatest_lower_bound(A,multiply(B,A)) = multiply(identity,A),
inference(paramod,[status(thm)],[c_65,c_57]) ).
cnf(c_68,plain,
greatest_lower_bound(A,multiply(B,A)) = A,
inference(paramod,[status(thm)],[c_1,c_116]) ).
cnf(c_73,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_25]) ).
cnf(c_83,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_25,c_25]) ).
cnf(c_84,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_83,c_73]) ).
cnf(c_117,plain,
least_upper_bound(multiply(A,B),multiply(A,identity)) = multiply(A,B),
inference(paramod,[status(thm)],[c_64,c_15]) ).
cnf(c_118,plain,
least_upper_bound(multiply(A,B),A) = multiply(A,B),
inference(paramod,[status(thm)],[c_84,c_117]) ).
cnf(c_85,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,B),
inference(paramod,[status(thm)],[c_5,c_118]) ).
cnf(c_119,plain,
greatest_lower_bound(multiply(A,B),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_25,c_68]) ).
cnf(c_120,plain,
greatest_lower_bound(B,multiply(A,B)) = multiply(A,B),
inference(paramod,[status(thm)],[c_4,c_119]) ).
cnf(c_121,plain,
B = multiply(A,B),
inference(paramod,[status(thm)],[c_68,c_120]) ).
cnf(c_105,plain,
multiply(A,B) = B,
inference(copy,[status(thm)],[c_121]) ).
cnf(c_122,plain,
least_upper_bound(A,B) = multiply(A,B),
inference(paramod,[status(thm)],[c_105,c_85]) ).
cnf(c_107,plain,
least_upper_bound(A,B) = B,
inference(paramod,[status(thm)],[c_105,c_122]) ).
cnf(c_123,plain,
multiply(inverse(A),A) = multiply(inverse(A),B),
inference(paramod,[status(thm)],[c_107,c_45]) ).
cnf(c_124,plain,
A = multiply(inverse(A),B),
inference(paramod,[status(thm)],[c_105,c_123]) ).
cnf(c_108,plain,
A = B,
inference(paramod,[status(thm)],[c_105,c_124]) ).
cnf(c_109,plain,
$false,
inference(resolve,[status(thm)],[c_108,c_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP192-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n013.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Fri Sep 25 14:36:22 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 639555 was started by sandbox2 on n013,
% 0.18/0.46 % Fri Sep 25 14:36:22 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.18/0.50
% 0.18/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.50
% 0.18/0.50 % Proof 1 at 0.01 (+ 0.02) seconds.
% 0.18/0.50 % Length of proof is 27.
% 0.18/0.50 % Level of proof is 7.
% 0.18/0.50 % Maximum clause weight is 13.000.
% 0.18/0.50 % Given clauses 27.
% 0.18/0.50
% 0.18/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------