%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP190-2 : 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 07:28:19 AM UTC 2026
% Result : Unsatisfiable 0.13s 20.69s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 1 sgn 15 !; 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_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_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_lub2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(least_upper_bound(VAR_0,VAR_1),VAR_2) = least_upper_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_lub2) ).
cnf(c_18,plain,
multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_lub2]) ).
cnf(c_19,plain,
least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B),
inference(copy,[status(thm)],[c_18]) ).
fof(p39c_1,axiom,
least_upper_bound(a,b) = a,
file('theBenchmark.p',p39c_1) ).
cnf(c_22,plain,
least_upper_bound(a,b) = a,
inference(clausify,[status(thm)],[p39c_1]) ).
fof(prove_p39c,axiom,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
file('theBenchmark.p',prove_p39c) ).
cnf(c_23,plain,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
inference(clausify,[status(thm)],[prove_p39c]) ).
cnf(c_568,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_569,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_568]) ).
cnf(c_24,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_569]) ).
cnf(c_43,plain,
least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)),
inference(paramod,[status(thm)],[c_2,c_15]) ).
cnf(c_49,plain,
least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(identity,B),A),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_66,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_24]) ).
cnf(c_76,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_24,c_24]) ).
cnf(c_77,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_76,c_66]) ).
cnf(c_147,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_76,c_2]) ).
cnf(c_570,plain,
least_upper_bound(identity,multiply(inverse(a),b)) = multiply(inverse(a),a),
inference(paramod,[status(thm)],[c_22,c_43]) ).
cnf(c_322,plain,
least_upper_bound(identity,multiply(inverse(a),b)) = identity,
inference(paramod,[status(thm)],[c_2,c_570]) ).
cnf(c_571,plain,
least_upper_bound(A,multiply(multiply(inverse(a),b),A)) = multiply(identity,A),
inference(paramod,[status(thm)],[c_322,c_49]) ).
cnf(c_572,plain,
least_upper_bound(A,multiply(inverse(a),multiply(b,A))) = multiply(identity,A),
inference(paramod,[status(thm)],[c_3,c_571]) ).
cnf(c_359,plain,
least_upper_bound(A,multiply(inverse(a),multiply(b,A))) = A,
inference(paramod,[status(thm)],[c_1,c_572]) ).
cnf(c_573,plain,
least_upper_bound(inverse(b),multiply(inverse(a),identity)) = inverse(b),
inference(paramod,[status(thm)],[c_147,c_359]) ).
cnf(c_574,plain,
least_upper_bound(inverse(b),inverse(a)) = inverse(b),
inference(paramod,[status(thm)],[c_77,c_573]) ).
cnf(c_559,plain,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
inference(paramod,[status(thm)],[c_5,c_574]) ).
cnf(c_566,plain,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
inference(paramod,[status(thm)],[c_559,c_13]) ).
cnf(c_567,plain,
$false,
inference(resolve,[status(thm)],[c_566,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP190-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/20.55 % Computer : n006.cluster.edu
% 0.08/20.55 % Model : x86_64 x86_64
% 0.08/20.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/20.55 % Memory : 8046.5625MB
% 0.08/20.55 % OS : Linux 6.8.0-71-generic
% 0.08/20.55 % CPULimit : 300
% 0.08/20.55 % WCLimit : 300
% 0.08/20.55 % DateTime : Fri Sep 25 14:36:33 UTC 2026
% 0.08/20.55 % CPUTime :
% 0.08/20.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/20.56 % Process 3125049 was started by sandbox on n006,
% 0.08/20.56 % Fri Sep 25 14:36:33 2026
% 0.08/20.56 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/20.56
% 0.08/20.56 % From the command line: assign(max_seconds, 300).
% 0.13/20.69
% 0.13/20.69 % SZS status Unsatisfiable for theBenchmark
% 0.13/20.69
% 0.13/20.69 % Proof 1 at 0.08 (+ 0.04) seconds.
% 0.13/20.69 % Length of proof is 23.
% 0.13/20.69 % Level of proof is 7.
% 0.13/20.69 % Maximum clause weight is 13.000.
% 0.13/20.69 % Given clauses 81.
% 0.13/20.69
% 0.13/20.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------