%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP184-3 : 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 : n009.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 9.24s 1.62s
% Output : CNFRefutation 9.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 51 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 14 ( 14 ~; 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 : 80 ( 0 sgn 21 !; 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(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_22,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_5458,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_22]) ).
cnf(c_5459,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_5458]) ).
cnf(c_5460,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_5459]) ).
cnf(c_23,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_5460]) ).
cnf(c_5461,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_5462,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_5461]) ).
cnf(c_24,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_5462]) ).
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_56,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_64,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_24]) ).
cnf(c_74,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_24,c_24]) ).
cnf(c_75,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_74,c_64]) ).
cnf(c_79,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(identity,B)),
inference(paramod,[status(thm)],[c_75,c_17]) ).
cnf(c_107,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_74,c_2]) ).
cnf(c_119,plain,
least_upper_bound(identity,multiply(A,inverse(B))) = multiply(least_upper_bound(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_107,c_19]) ).
cnf(c_363,plain,
least_upper_bound(identity,A) = multiply(inverse(B),least_upper_bound(B,multiply(B,A))),
inference(paramod,[status(thm)],[c_24,c_43]) ).
cnf(c_5463,plain,
multiply(A,greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),A),
inference(paramod,[status(thm)],[c_79,c_56]) ).
cnf(c_1023,plain,
multiply(greatest_lower_bound(identity,A),A) = multiply(A,greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_5463]) ).
cnf(c_5464,plain,
multiply(multiply(inverse(A),least_upper_bound(A,multiply(A,a))),inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)),
inference(paramod,[status(thm)],[c_363,c_23]) ).
cnf(c_5465,plain,
multiply(inverse(A),multiply(least_upper_bound(A,multiply(A,a)),inverse(greatest_lower_bound(identity,a)))) != multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)),
inference(paramod,[status(thm)],[c_3,c_5464]) ).
cnf(c_5179,plain,
multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != multiply(inverse(A),multiply(least_upper_bound(A,multiply(A,a)),inverse(greatest_lower_bound(identity,a)))),
inference(copy,[status(thm)],[c_5465]) ).
cnf(c_5466,plain,
multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,a),a),inverse(greatest_lower_bound(identity,a))))),
inference(paramod,[status(thm)],[c_119,c_5179]) ).
cnf(c_5467,plain,
multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,multiply(multiply(a,greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(identity,a))))),
inference(paramod,[status(thm)],[c_1023,c_5466]) ).
cnf(c_5468,plain,
multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,multiply(a,multiply(greatest_lower_bound(identity,a),inverse(greatest_lower_bound(identity,a)))))),
inference(paramod,[status(thm)],[c_3,c_5467]) ).
cnf(c_5469,plain,
multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,multiply(a,identity))),
inference(paramod,[status(thm)],[c_107,c_5468]) ).
cnf(c_5470,plain,
multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)),
inference(paramod,[status(thm)],[c_75,c_5469]) ).
cnf(c_5457,plain,
$false,
inference(copy,[status(thm)],[c_5470]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP184-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n009.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 14:35:29 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 1825829 was started by sandbox2 on n009,
% 0.18/0.44 % Fri Sep 25 14:35:29 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 9.24/1.62
% 9.24/1.62 % SZS status Unsatisfiable for theBenchmark
% 9.24/1.62
% 9.24/1.62 % Proof 1 at 0.87 (+ 0.29) seconds.
% 9.24/1.62 % Length of proof is 28.
% 9.24/1.62 % Level of proof is 6.
% 9.24/1.62 % Maximum clause weight is 22.000.
% 9.24/1.62 % Given clauses 208.
% 9.24/1.62
% 9.24/1.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------