%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP184-2 : 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 : 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 07:28:17 AM UTC 2026
% Result : Unsatisfiable 6.37s 6.23s
% Output : CNFRefutation 6.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 64 ( 64 unt; 0 def)
% Number of atoms : 64 ( 63 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 16 ( 16 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 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 : 94 ( 0 sgn 24 !; 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(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_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(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(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(p21_2,axiom,
! [VAR_0] : inverse(inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',p21_2) ).
cnf(c_23,plain,
inverse(inverse(A)) = A,
inference(clausify,[status(thm)],[p21_2]) ).
fof(p21_3,axiom,
! [VAR_0,VAR_1] : inverse(multiply(VAR_0,VAR_1)) = multiply(inverse(VAR_1),inverse(VAR_0)),
file('theBenchmark.p',p21_3) ).
cnf(c_24,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(clausify,[status(thm)],[p21_3]) ).
fof(prove_p21,axiom,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('theBenchmark.p',prove_p21) ).
cnf(c_25,plain,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(clausify,[status(thm)],[prove_p21]) ).
cnf(c_3881,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(paramod,[status(thm)],[c_5,c_25]) ).
cnf(c_3882,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(paramod,[status(thm)],[c_4,c_3881]) ).
cnf(c_3883,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(a,identity)),
inference(paramod,[status(thm)],[c_4,c_3882]) ).
cnf(c_26,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)),
inference(paramod,[status(thm)],[c_5,c_3883]) ).
cnf(c_3884,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_3885,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_3884]) ).
cnf(c_27,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_3885]) ).
cnf(c_52,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_59,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_66,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_3886,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_27]) ).
cnf(c_68,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_23,c_3886]) ).
cnf(c_86,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(identity,B)),
inference(paramod,[status(thm)],[c_68,c_15]) ).
cnf(c_88,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(identity,B)),
inference(paramod,[status(thm)],[c_68,c_17]) ).
cnf(c_3887,plain,
least_upper_bound(inverse(A),identity) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_66,c_52]) ).
cnf(c_128,plain,
least_upper_bound(identity,inverse(A)) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_5,c_3887]) ).
cnf(c_3888,plain,
least_upper_bound(inverse(A),identity) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_2,c_86]) ).
cnf(c_3889,plain,
least_upper_bound(identity,inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_5,c_3888]) ).
cnf(c_189,plain,
multiply(least_upper_bound(identity,A),inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_128,c_3889]) ).
cnf(c_3890,plain,
multiply(inverse(A),greatest_lower_bound(A,multiply(A,B))) = greatest_lower_bound(identity,B),
inference(paramod,[status(thm)],[c_88,c_27]) ).
cnf(c_255,plain,
greatest_lower_bound(identity,A) = multiply(inverse(B),greatest_lower_bound(B,multiply(B,A))),
inference(copy,[status(thm)],[c_3890]) ).
cnf(c_3891,plain,
inverse(multiply(inverse(A),least_upper_bound(identity,A))) = multiply(inverse(inverse(A)),inverse(least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_189,c_24]) ).
cnf(c_3892,plain,
multiply(inverse(least_upper_bound(identity,A)),inverse(inverse(A))) = multiply(inverse(inverse(A)),inverse(least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_24,c_3891]) ).
cnf(c_3893,plain,
multiply(inverse(least_upper_bound(identity,A)),A) = multiply(inverse(inverse(A)),inverse(least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_23,c_3892]) ).
cnf(c_457,plain,
multiply(inverse(least_upper_bound(identity,A)),A) = multiply(A,inverse(least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_23,c_3893]) ).
cnf(c_3894,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(multiply(inverse(A),greatest_lower_bound(A,multiply(A,a)))),least_upper_bound(identity,a)),
inference(paramod,[status(thm)],[c_255,c_26]) ).
cnf(c_3895,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != multiply(multiply(inverse(greatest_lower_bound(A,multiply(A,a))),inverse(inverse(A))),least_upper_bound(identity,a)),
inference(paramod,[status(thm)],[c_24,c_3894]) ).
cnf(c_3896,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != multiply(multiply(inverse(greatest_lower_bound(A,multiply(A,a))),A),least_upper_bound(identity,a)),
inference(paramod,[status(thm)],[c_23,c_3895]) ).
cnf(c_3472,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(A,multiply(A,a))),multiply(A,least_upper_bound(identity,a))),
inference(paramod,[status(thm)],[c_3,c_3896]) ).
cnf(c_3897,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,a)),multiply(inverse(least_upper_bound(identity,a)),a))),identity),
inference(paramod,[status(thm)],[c_2,c_3472]) ).
cnf(c_3898,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,a)),multiply(a,inverse(least_upper_bound(identity,a))))),identity),
inference(paramod,[status(thm)],[c_457,c_3897]) ).
cnf(c_3899,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(multiply(greatest_lower_bound(identity,a),inverse(least_upper_bound(identity,a)))),identity),
inference(paramod,[status(thm)],[c_59,c_3898]) ).
cnf(c_3900,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != multiply(multiply(inverse(inverse(least_upper_bound(identity,a))),inverse(greatest_lower_bound(identity,a))),identity),
inference(paramod,[status(thm)],[c_24,c_3899]) ).
cnf(c_3901,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != multiply(multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))),identity),
inference(paramod,[status(thm)],[c_23,c_3900]) ).
cnf(c_3902,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))),
inference(paramod,[status(thm)],[c_68,c_3901]) ).
cnf(c_3880,plain,
$false,
inference(copy,[status(thm)],[c_3902]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP184-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n008.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Fri Sep 25 14:36:29 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 1276410 was started by sandbox on n008,
% 0.10/5.37 % Fri Sep 25 14:36:29 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.37
% 0.10/5.37 % From the command line: assign(max_seconds, 300).
% 6.37/6.23
% 6.37/6.23 % SZS status Unsatisfiable for theBenchmark
% 6.37/6.23
% 6.37/6.23 % Proof 1 at 0.64 (+ 0.20) seconds.
% 6.37/6.23 % Length of proof is 30.
% 6.37/6.23 % Level of proof is 6.
% 6.37/6.23 % Maximum clause weight is 51.000.
% 6.37/6.23 % Given clauses 149.
% 6.37/6.23
% 6.37/6.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------