%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP166-1 : 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 : n018.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 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 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(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(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(lat2a_2,axiom,
least_upper_bound(b,identity) = b,
file('theBenchmark.p',lat2a_2) ).
cnf(c_24,plain,
least_upper_bound(b,identity) = b,
inference(clausify,[status(thm)],[lat2a_2]) ).
cnf(c_25,plain,
least_upper_bound(identity,b) = b,
inference(paramod,[status(thm)],[c_5,c_24]) ).
fof(prove_lat2a,axiom,
least_upper_bound(a,multiply(a,b)) != multiply(a,b),
file('theBenchmark.p',prove_lat2a) ).
cnf(c_26,plain,
least_upper_bound(a,multiply(a,b)) != multiply(a,b),
inference(clausify,[status(thm)],[prove_lat2a]) ).
cnf(c_113,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_114,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_113]) ).
cnf(c_27,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_114]) ).
cnf(c_75,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_27]) ).
cnf(c_85,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_27,c_27]) ).
cnf(c_86,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_85,c_75]) ).
cnf(c_108,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(identity,B)),
inference(paramod,[status(thm)],[c_86,c_15]) ).
cnf(c_115,plain,
multiply(a,least_upper_bound(identity,b)) != multiply(a,b),
inference(paramod,[status(thm)],[c_108,c_26]) ).
cnf(c_116,plain,
multiply(a,b) != multiply(a,b),
inference(paramod,[status(thm)],[c_25,c_115]) ).
cnf(c_112,plain,
$false,
inference(copy,[status(thm)],[c_116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP166-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n018.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 14:34:51 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 2175120 was started by sandbox on n018,
% 0.16/0.43 % Fri Sep 25 14:34:51 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 0.16/0.46
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.46
% 0.16/0.46 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/0.46 % Length of proof is 15.
% 0.16/0.46 % Level of proof is 5.
% 0.16/0.46 % Maximum clause weight is 36.000.
% 0.16/0.46 % Given clauses 24.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------