%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP185-2 : 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 : n019.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 07:28:18 AM UTC 2026
% Result : Unsatisfiable 12.44s 2.16s
% Output : CNFRefutation 12.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 90 ( 90 unt; 0 def)
% Number of atoms : 90 ( 89 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 23 ( 23 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 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 : 144 ( 11 sgn 27 !; 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(associativity_of_glb,axiom,
! [VAR_0,VAR_1,VAR_2] : greatest_lower_bound(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(greatest_lower_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_glb) ).
cnf(c_6,plain,
greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_glb]) ).
cnf(c_7,plain,
greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_6]) ).
fof(associativity_of_lub,axiom,
! [VAR_0,VAR_1,VAR_2] : least_upper_bound(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(least_upper_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_lub) ).
cnf(c_8,plain,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_lub]) ).
cnf(c_9,plain,
least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_8]) ).
fof(idempotence_of_lub,axiom,
! [VAR_0] : least_upper_bound(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_lub) ).
cnf(c_10,plain,
least_upper_bound(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_lub]) ).
fof(lub_absorbtion,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,greatest_lower_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',lub_absorbtion) ).
cnf(c_12,plain,
least_upper_bound(A,greatest_lower_bound(A,B)) = A,
inference(clausify,[status(thm)],[lub_absorbtion]) ).
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(p22a_2,axiom,
! [VAR_0] : inverse(inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',p22a_2) ).
cnf(c_23,plain,
inverse(inverse(A)) = A,
inference(clausify,[status(thm)],[p22a_2]) ).
fof(prove_p22a,axiom,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
file('theBenchmark.p',prove_p22a) ).
cnf(c_25,plain,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(clausify,[status(thm)],[prove_p22a]) ).
cnf(c_6762,plain,
least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(paramod,[status(thm)],[c_5,c_25]) ).
cnf(c_6763,plain,
least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(identity,a),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(paramod,[status(thm)],[c_5,c_6762]) ).
cnf(c_6764,plain,
least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(identity,a),least_upper_bound(identity,b))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(paramod,[status(thm)],[c_5,c_6763]) ).
cnf(c_6765,plain,
least_upper_bound(multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),least_upper_bound(identity,multiply(a,b))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(paramod,[status(thm)],[c_5,c_6764]) ).
cnf(c_6766,plain,
least_upper_bound(multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),least_upper_bound(identity,multiply(a,b))) != multiply(least_upper_bound(identity,a),least_upper_bound(b,identity)),
inference(paramod,[status(thm)],[c_5,c_6765]) ).
cnf(c_26,plain,
least_upper_bound(multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),least_upper_bound(identity,multiply(a,b))) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_5,c_6766]) ).
cnf(c_6767,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_6768,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_6767]) ).
cnf(c_27,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_6768]) ).
cnf(c_30,plain,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)),
inference(paramod,[status(thm)],[c_9,c_5]) ).
cnf(c_6769,plain,
least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(B,least_upper_bound(A,C)),
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_31,plain,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(B,least_upper_bound(A,C)),
inference(paramod,[status(thm)],[c_9,c_6769]) ).
cnf(c_6770,plain,
least_upper_bound(multiply(a,b),least_upper_bound(multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),identity)) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_30,c_26]) ).
cnf(c_6771,plain,
least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)))) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_5,c_6770]) ).
cnf(c_32,plain,
least_upper_bound(identity,least_upper_bound(multiply(a,b),multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)))) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_31,c_6771]) ).
cnf(c_6772,plain,
least_upper_bound(least_upper_bound(A,B),B) = least_upper_bound(A,B),
inference(paramod,[status(thm)],[c_10,c_9]) ).
cnf(c_35,plain,
least_upper_bound(A,least_upper_bound(B,A)) = least_upper_bound(B,A),
inference(paramod,[status(thm)],[c_5,c_6772]) ).
cnf(c_39,plain,
least_upper_bound(A,greatest_lower_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_4,c_12]) ).
cnf(c_6773,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(A,greatest_lower_bound(least_upper_bound(A,C),B)),
inference(paramod,[status(thm)],[c_13,c_7]) ).
cnf(c_44,plain,
greatest_lower_bound(A,greatest_lower_bound(least_upper_bound(A,B),C)) = greatest_lower_bound(A,C),
inference(copy,[status(thm)],[c_6773]) ).
cnf(c_47,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_53,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_58,plain,
least_upper_bound(multiply(A,B),multiply(C,multiply(D,B))) = multiply(least_upper_bound(A,multiply(C,D)),B),
inference(paramod,[status(thm)],[c_3,c_19]) ).
cnf(c_67,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_6774,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_27]) ).
cnf(c_69,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_23,c_6774]) ).
cnf(c_87,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(identity,B)),
inference(paramod,[status(thm)],[c_69,c_15]) ).
cnf(c_6775,plain,
least_upper_bound(A,multiply(least_upper_bound(identity,B),C)) = least_upper_bound(C,least_upper_bound(A,multiply(B,C))),
inference(paramod,[status(thm)],[c_53,c_31]) ).
cnf(c_128,plain,
least_upper_bound(A,least_upper_bound(B,multiply(C,A))) = least_upper_bound(B,multiply(least_upper_bound(identity,C),A)),
inference(copy,[status(thm)],[c_6775]) ).
cnf(c_6776,plain,
least_upper_bound(inverse(A),identity) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_67,c_53]) ).
cnf(c_129,plain,
least_upper_bound(identity,inverse(A)) = multiply(least_upper_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_5,c_6776]) ).
cnf(c_6777,plain,
least_upper_bound(inverse(A),identity) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_2,c_87]) ).
cnf(c_6778,plain,
least_upper_bound(identity,inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_5,c_6777]) ).
cnf(c_190,plain,
multiply(least_upper_bound(identity,A),inverse(A)) = multiply(inverse(A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_129,c_6778]) ).
cnf(c_196,plain,
greatest_lower_bound(A,multiply(A,least_upper_bound(identity,B))) = A,
inference(paramod,[status(thm)],[c_87,c_13]) ).
cnf(c_6779,plain,
multiply(A,least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),A),
inference(paramod,[status(thm)],[c_87,c_53]) ).
cnf(c_210,plain,
multiply(least_upper_bound(identity,A),A) = multiply(A,least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_6779]) ).
cnf(c_571,plain,
least_upper_bound(identity,multiply(inverse(A),least_upper_bound(B,A))) = multiply(inverse(A),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_35,c_47]) ).
cnf(c_6780,plain,
greatest_lower_bound(A,least_upper_bound(A,B)) = greatest_lower_bound(A,multiply(least_upper_bound(A,B),least_upper_bound(identity,C))),
inference(paramod,[status(thm)],[c_196,c_44]) ).
cnf(c_6781,plain,
A = greatest_lower_bound(A,multiply(least_upper_bound(A,B),least_upper_bound(identity,C))),
inference(paramod,[status(thm)],[c_13,c_6780]) ).
cnf(c_795,plain,
greatest_lower_bound(A,multiply(least_upper_bound(A,B),least_upper_bound(identity,C))) = A,
inference(copy,[status(thm)],[c_6781]) ).
cnf(c_6782,plain,
least_upper_bound(multiply(A,B),multiply(C,identity)) = multiply(least_upper_bound(A,multiply(C,inverse(B))),B),
inference(paramod,[status(thm)],[c_2,c_58]) ).
cnf(c_1047,plain,
least_upper_bound(multiply(A,B),C) = multiply(least_upper_bound(A,multiply(C,inverse(B))),B),
inference(paramod,[status(thm)],[c_69,c_6782]) ).
cnf(c_6783,plain,
least_upper_bound(identity,multiply(least_upper_bound(a,multiply(multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),inverse(b))),b)) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_1047,c_32]) ).
cnf(c_6784,plain,
least_upper_bound(identity,multiply(least_upper_bound(a,multiply(least_upper_bound(identity,a),multiply(least_upper_bound(identity,b),inverse(b)))),b)) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_3,c_6783]) ).
cnf(c_1233,plain,
least_upper_bound(identity,multiply(least_upper_bound(a,multiply(least_upper_bound(identity,a),multiply(inverse(b),least_upper_bound(identity,b)))),b)) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_190,c_6784]) ).
cnf(c_6785,plain,
least_upper_bound(multiply(least_upper_bound(A,B),least_upper_bound(identity,C)),A) = multiply(least_upper_bound(A,B),least_upper_bound(identity,C)),
inference(paramod,[status(thm)],[c_795,c_39]) ).
cnf(c_2084,plain,
least_upper_bound(A,multiply(least_upper_bound(A,B),least_upper_bound(identity,C))) = multiply(least_upper_bound(A,B),least_upper_bound(identity,C)),
inference(paramod,[status(thm)],[c_5,c_6785]) ).
cnf(c_6786,plain,
least_upper_bound(identity,multiply(least_upper_bound(multiply(inverse(b),least_upper_bound(identity,b)),least_upper_bound(a,multiply(a,multiply(inverse(b),least_upper_bound(identity,b))))),b)) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_128,c_1233]) ).
cnf(c_6787,plain,
least_upper_bound(identity,multiply(least_upper_bound(multiply(inverse(b),least_upper_bound(identity,b)),multiply(a,least_upper_bound(identity,multiply(inverse(b),least_upper_bound(identity,b))))),b)) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_87,c_6786]) ).
cnf(c_6788,plain,
least_upper_bound(identity,multiply(least_upper_bound(multiply(inverse(b),least_upper_bound(identity,b)),multiply(a,multiply(inverse(b),least_upper_bound(identity,b)))),b)) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_571,c_6787]) ).
cnf(c_6789,plain,
least_upper_bound(identity,multiply(multiply(least_upper_bound(identity,a),multiply(inverse(b),least_upper_bound(identity,b))),b)) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_53,c_6788]) ).
cnf(c_6790,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,a),multiply(multiply(inverse(b),least_upper_bound(identity,b)),b))) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_3,c_6789]) ).
cnf(c_6791,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,a),multiply(inverse(b),multiply(least_upper_bound(identity,b),b)))) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_3,c_6790]) ).
cnf(c_6792,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,a),multiply(inverse(b),multiply(b,least_upper_bound(identity,b))))) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_210,c_6791]) ).
cnf(c_6793,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,a),least_upper_bound(identity,b))) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_27,c_6792]) ).
cnf(c_6794,plain,
multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)),
inference(paramod,[status(thm)],[c_2084,c_6793]) ).
cnf(c_6761,plain,
$false,
inference(copy,[status(thm)],[c_6794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP185-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 14:36:05 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2982869 was started by sandbox on n019,
% 0.08/0.36 % Fri Sep 25 14:36:05 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 12.44/2.16
% 12.44/2.16 % SZS status Unsatisfiable for theBenchmark
% 12.44/2.16
% 12.44/2.16 % Proof 1 at 1.43 (+ 0.35) seconds.
% 12.44/2.16 % Length of proof is 43.
% 12.44/2.16 % Level of proof is 7.
% 12.44/2.16 % Maximum clause weight is 64.000.
% 12.44/2.16 % Given clauses 217.
% 12.44/2.16
% 12.44/2.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------