%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP184-4 : 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 : n010.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 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 12
% Syntax : Number of formulae : 87 ( 87 unt; 0 def)
% Number of atoms : 87 ( 86 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 41 ( 41 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 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 : 82 ( 0 sgn 20 !; 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_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_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(p21x_1,axiom,
inverse(identity) = identity,
file('theBenchmark.p',p21x_1) ).
cnf(c_22,plain,
inverse(identity) = identity,
inference(clausify,[status(thm)],[p21x_1]) ).
fof(p21x_2,axiom,
! [VAR_0] : inverse(inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',p21x_2) ).
cnf(c_23,plain,
inverse(inverse(A)) = A,
inference(clausify,[status(thm)],[p21x_2]) ).
fof(p21x_3,axiom,
! [VAR_0,VAR_1] : inverse(multiply(VAR_0,VAR_1)) = multiply(inverse(VAR_1),inverse(VAR_0)),
file('theBenchmark.p',p21x_3) ).
cnf(c_24,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(clausify,[status(thm)],[p21x_3]) ).
fof(p21x_5,axiom,
! [VAR_0,VAR_1] : inverse(least_upper_bound(VAR_0,VAR_1)) = greatest_lower_bound(inverse(VAR_0),inverse(VAR_1)),
file('theBenchmark.p',p21x_5) ).
cnf(c_27,plain,
inverse(least_upper_bound(A,B)) = greatest_lower_bound(inverse(A),inverse(B)),
inference(clausify,[status(thm)],[p21x_5]) ).
fof(prove_p21x,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_p21x) ).
cnf(c_28,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_p21x]) ).
cnf(c_677,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_28]) ).
cnf(c_678,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_677]) ).
cnf(c_679,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_678]) ).
cnf(c_29,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_679]) ).
cnf(c_680,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_681,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_680]) ).
cnf(c_30,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_681]) ).
cnf(c_53,plain,
greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)),
inference(paramod,[status(thm)],[c_2,c_17]) ).
cnf(c_682,plain,
greatest_lower_bound(multiply(inverse(A),B),identity) = multiply(inverse(A),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_2,c_17]) ).
cnf(c_54,plain,
greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_4,c_682]) ).
cnf(c_63,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_70,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_683,plain,
inverse(greatest_lower_bound(inverse(A),inverse(B))) = least_upper_bound(A,B),
inference(paramod,[status(thm)],[c_27,c_23]) ).
cnf(c_80,plain,
least_upper_bound(A,B) = inverse(greatest_lower_bound(inverse(A),inverse(B))),
inference(copy,[status(thm)],[c_683]) ).
cnf(c_684,plain,
multiply(inverse(greatest_lower_bound(inverse(identity),inverse(a))),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)),
inference(paramod,[status(thm)],[c_80,c_29]) ).
cnf(c_685,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(a))),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)),
inference(paramod,[status(thm)],[c_22,c_684]) ).
cnf(c_686,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(a))),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(inverse(identity),inverse(a)))),
inference(paramod,[status(thm)],[c_80,c_685]) ).
cnf(c_93,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(a))),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(identity,inverse(a)))),
inference(paramod,[status(thm)],[c_22,c_686]) ).
cnf(c_687,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_30]) ).
cnf(c_95,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_23,c_687]) ).
cnf(c_101,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(identity,B)),
inference(paramod,[status(thm)],[c_95,c_17]) ).
cnf(c_140,plain,
greatest_lower_bound(identity,A) = multiply(inverse(B),greatest_lower_bound(B,multiply(B,A))),
inference(paramod,[status(thm)],[c_30,c_53]) ).
cnf(c_174,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_95,c_54]) ).
cnf(c_688,plain,
multiply(inverse(multiply(inverse(a),greatest_lower_bound(identity,a))),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(identity,inverse(a)))),
inference(paramod,[status(thm)],[c_174,c_93]) ).
cnf(c_689,plain,
multiply(multiply(inverse(greatest_lower_bound(identity,a)),inverse(inverse(a))),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(identity,inverse(a)))),
inference(paramod,[status(thm)],[c_24,c_688]) ).
cnf(c_690,plain,
multiply(multiply(inverse(greatest_lower_bound(identity,a)),a),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(identity,inverse(a)))),
inference(paramod,[status(thm)],[c_23,c_689]) ).
cnf(c_691,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a)))) != multiply(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(identity,inverse(a)))),
inference(paramod,[status(thm)],[c_3,c_690]) ).
cnf(c_692,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a)))) != multiply(inverse(greatest_lower_bound(identity,a)),inverse(multiply(inverse(a),greatest_lower_bound(identity,a)))),
inference(paramod,[status(thm)],[c_174,c_691]) ).
cnf(c_693,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a)))) != multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),inverse(inverse(a)))),
inference(paramod,[status(thm)],[c_24,c_692]) ).
cnf(c_694,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a)))) != multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)),
inference(paramod,[status(thm)],[c_23,c_693]) ).
cnf(c_182,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a)))),
inference(copy,[status(thm)],[c_694]) ).
cnf(c_695,plain,
greatest_lower_bound(inverse(A),identity) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_70,c_63]) ).
cnf(c_696,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_4,c_695]) ).
cnf(c_697,plain,
multiply(inverse(A),greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_174,c_696]) ).
cnf(c_213,plain,
multiply(greatest_lower_bound(identity,A),inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_697]) ).
cnf(c_698,plain,
multiply(A,greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),A),
inference(paramod,[status(thm)],[c_101,c_63]) ).
cnf(c_300,plain,
multiply(greatest_lower_bound(identity,A),A) = multiply(A,greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_698]) ).
cnf(c_699,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(multiply(inverse(A),greatest_lower_bound(A,multiply(A,a)))),multiply(a,inverse(greatest_lower_bound(identity,a)))),
inference(paramod,[status(thm)],[c_140,c_182]) ).
cnf(c_700,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(multiply(inverse(greatest_lower_bound(A,multiply(A,a))),inverse(inverse(A))),multiply(a,inverse(greatest_lower_bound(identity,a)))),
inference(paramod,[status(thm)],[c_24,c_699]) ).
cnf(c_701,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(multiply(inverse(greatest_lower_bound(A,multiply(A,a))),A),multiply(a,inverse(greatest_lower_bound(identity,a)))),
inference(paramod,[status(thm)],[c_23,c_700]) ).
cnf(c_574,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(greatest_lower_bound(A,multiply(A,a))),multiply(A,multiply(a,inverse(greatest_lower_bound(identity,a))))),
inference(paramod,[status(thm)],[c_3,c_701]) ).
cnf(c_702,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(greatest_lower_bound(inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))),multiply(inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))),a))),identity),
inference(paramod,[status(thm)],[c_2,c_574]) ).
cnf(c_703,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(greatest_lower_bound(multiply(inverse(inverse(greatest_lower_bound(identity,a))),inverse(a)),multiply(inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))),a))),identity),
inference(paramod,[status(thm)],[c_24,c_702]) ).
cnf(c_704,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(greatest_lower_bound(multiply(greatest_lower_bound(identity,a),inverse(a)),multiply(inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))),a))),identity),
inference(paramod,[status(thm)],[c_23,c_703]) ).
cnf(c_705,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(greatest_lower_bound(multiply(inverse(a),greatest_lower_bound(identity,a)),multiply(inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))),a))),identity),
inference(paramod,[status(thm)],[c_213,c_704]) ).
cnf(c_706,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(greatest_lower_bound(multiply(inverse(a),greatest_lower_bound(identity,a)),multiply(multiply(inverse(inverse(greatest_lower_bound(identity,a))),inverse(a)),a))),identity),
inference(paramod,[status(thm)],[c_24,c_705]) ).
cnf(c_707,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(greatest_lower_bound(multiply(inverse(a),greatest_lower_bound(identity,a)),multiply(multiply(greatest_lower_bound(identity,a),inverse(a)),a))),identity),
inference(paramod,[status(thm)],[c_23,c_706]) ).
cnf(c_708,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(greatest_lower_bound(multiply(inverse(a),greatest_lower_bound(identity,a)),multiply(multiply(inverse(a),greatest_lower_bound(identity,a)),a))),identity),
inference(paramod,[status(thm)],[c_213,c_707]) ).
cnf(c_709,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(greatest_lower_bound(multiply(inverse(a),greatest_lower_bound(identity,a)),multiply(inverse(a),multiply(greatest_lower_bound(identity,a),a)))),identity),
inference(paramod,[status(thm)],[c_3,c_708]) ).
cnf(c_710,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(greatest_lower_bound(multiply(inverse(a),greatest_lower_bound(identity,a)),multiply(inverse(a),multiply(a,greatest_lower_bound(identity,a))))),identity),
inference(paramod,[status(thm)],[c_300,c_709]) ).
cnf(c_711,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(greatest_lower_bound(multiply(inverse(a),greatest_lower_bound(identity,a)),greatest_lower_bound(identity,a))),identity),
inference(paramod,[status(thm)],[c_30,c_710]) ).
cnf(c_712,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,a),multiply(inverse(a),greatest_lower_bound(identity,a)))),identity),
inference(paramod,[status(thm)],[c_4,c_711]) ).
cnf(c_713,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(multiply(greatest_lower_bound(identity,inverse(a)),greatest_lower_bound(identity,a))),identity),
inference(paramod,[status(thm)],[c_63,c_712]) ).
cnf(c_714,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(multiply(multiply(inverse(a),greatest_lower_bound(identity,a)),greatest_lower_bound(identity,a))),identity),
inference(paramod,[status(thm)],[c_174,c_713]) ).
cnf(c_715,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(multiply(inverse(a),multiply(greatest_lower_bound(identity,a),greatest_lower_bound(identity,a)))),identity),
inference(paramod,[status(thm)],[c_3,c_714]) ).
cnf(c_716,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(multiply(inverse(multiply(greatest_lower_bound(identity,a),greatest_lower_bound(identity,a))),inverse(inverse(a))),identity),
inference(paramod,[status(thm)],[c_24,c_715]) ).
cnf(c_717,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(multiply(multiply(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(identity,a))),inverse(inverse(a))),identity),
inference(paramod,[status(thm)],[c_24,c_716]) ).
cnf(c_718,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(multiply(multiply(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(identity,a))),a),identity),
inference(paramod,[status(thm)],[c_23,c_717]) ).
cnf(c_719,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)),identity),
inference(paramod,[status(thm)],[c_3,c_718]) ).
cnf(c_720,plain,
multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != multiply(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)),
inference(paramod,[status(thm)],[c_95,c_719]) ).
cnf(c_676,plain,
$false,
inference(copy,[status(thm)],[c_720]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP184-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:35:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 975430 was started by sandbox2 on n010,
% 0.09/0.36 % Fri Sep 25 14:35:44 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.45
% 0.13/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.45
% 0.13/0.45 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.13/0.45 % Length of proof is 31.
% 0.13/0.45 % Level of proof is 6.
% 0.13/0.45 % Maximum clause weight is 27.000.
% 0.13/0.45 % Given clauses 71.
% 0.13/0.45
% 0.13/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
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