%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP181-4 : 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 07:28:16 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.92s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 65 unt; 0 def)
% Number of atoms : 65 ( 64 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 18 !; 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(p12x_2,axiom,
! [VAR_0] : inverse(inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',p12x_2) ).
cnf(c_23,plain,
inverse(inverse(A)) = A,
inference(clausify,[status(thm)],[p12x_2]) ).
fof(p12x_4,axiom,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('theBenchmark.p',p12x_4) ).
cnf(c_25,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
inference(clausify,[status(thm)],[p12x_4]) ).
cnf(c_685,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(b,c),
inference(paramod,[status(thm)],[c_4,c_25]) ).
cnf(c_686,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(c,b),
inference(paramod,[status(thm)],[c_4,c_685]) ).
cnf(c_26,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(c,a),
inference(copy,[status(thm)],[c_686]) ).
fof(p12x_5,axiom,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('theBenchmark.p',p12x_5) ).
cnf(c_27,plain,
least_upper_bound(a,c) = least_upper_bound(b,c),
inference(clausify,[status(thm)],[p12x_5]) ).
cnf(c_687,plain,
least_upper_bound(c,a) = least_upper_bound(b,c),
inference(paramod,[status(thm)],[c_5,c_27]) ).
cnf(c_688,plain,
least_upper_bound(c,a) = least_upper_bound(c,b),
inference(paramod,[status(thm)],[c_5,c_687]) ).
cnf(c_28,plain,
least_upper_bound(c,b) = least_upper_bound(c,a),
inference(copy,[status(thm)],[c_688]) ).
fof(p12x_7,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',p12x_7) ).
cnf(c_31,plain,
inverse(least_upper_bound(A,B)) = greatest_lower_bound(inverse(A),inverse(B)),
inference(clausify,[status(thm)],[p12x_7]) ).
fof(prove_p12x,axiom,
a != b,
file('theBenchmark.p',prove_p12x) ).
cnf(c_32,plain,
a != b,
inference(clausify,[status(thm)],[prove_p12x]) ).
cnf(c_33,plain,
b != a,
inference(copy,[status(thm)],[c_32]) ).
cnf(c_689,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_690,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_689]) ).
cnf(c_34,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_690]) ).
cnf(c_57,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_691,plain,
greatest_lower_bound(multiply(A,B),identity) = multiply(greatest_lower_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_2,c_21]) ).
cnf(c_70,plain,
greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_4,c_691]) ).
cnf(c_74,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_692,plain,
inverse(greatest_lower_bound(inverse(A),inverse(B))) = least_upper_bound(A,B),
inference(paramod,[status(thm)],[c_31,c_23]) ).
cnf(c_88,plain,
least_upper_bound(A,B) = inverse(greatest_lower_bound(inverse(A),inverse(B))),
inference(copy,[status(thm)],[c_692]) ).
cnf(c_693,plain,
inverse(least_upper_bound(c,a)) = greatest_lower_bound(inverse(c),inverse(b)),
inference(paramod,[status(thm)],[c_28,c_31]) ).
cnf(c_694,plain,
inverse(inverse(greatest_lower_bound(inverse(c),inverse(a)))) = greatest_lower_bound(inverse(c),inverse(b)),
inference(paramod,[status(thm)],[c_88,c_693]) ).
cnf(c_695,plain,
greatest_lower_bound(inverse(c),inverse(a)) = greatest_lower_bound(inverse(c),inverse(b)),
inference(paramod,[status(thm)],[c_23,c_694]) ).
cnf(c_89,plain,
greatest_lower_bound(inverse(c),inverse(b)) = greatest_lower_bound(inverse(c),inverse(a)),
inference(copy,[status(thm)],[c_695]) ).
cnf(c_696,plain,
greatest_lower_bound(identity,multiply(A,B)) = multiply(A,greatest_lower_bound(inverse(A),B)),
inference(paramod,[status(thm)],[c_74,c_17]) ).
cnf(c_110,plain,
multiply(A,greatest_lower_bound(inverse(A),B)) = greatest_lower_bound(identity,multiply(A,B)),
inference(copy,[status(thm)],[c_696]) ).
cnf(c_697,plain,
greatest_lower_bound(multiply(A,inverse(B)),identity) = multiply(greatest_lower_bound(A,B),inverse(B)),
inference(paramod,[status(thm)],[c_74,c_21]) ).
cnf(c_113,plain,
greatest_lower_bound(identity,multiply(A,inverse(B))) = multiply(greatest_lower_bound(A,B),inverse(B)),
inference(paramod,[status(thm)],[c_4,c_697]) ).
cnf(c_698,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(c)),inverse(b))) = multiply(inverse(inverse(c)),greatest_lower_bound(inverse(c),inverse(a))),
inference(paramod,[status(thm)],[c_89,c_57]) ).
cnf(c_699,plain,
greatest_lower_bound(identity,multiply(c,inverse(b))) = multiply(inverse(inverse(c)),greatest_lower_bound(inverse(c),inverse(a))),
inference(paramod,[status(thm)],[c_23,c_698]) ).
cnf(c_700,plain,
greatest_lower_bound(identity,multiply(c,inverse(b))) = multiply(c,greatest_lower_bound(inverse(c),inverse(a))),
inference(paramod,[status(thm)],[c_23,c_699]) ).
cnf(c_176,plain,
greatest_lower_bound(identity,multiply(c,inverse(b))) = greatest_lower_bound(identity,multiply(c,inverse(a))),
inference(paramod,[status(thm)],[c_110,c_700]) ).
cnf(c_701,plain,
greatest_lower_bound(identity,multiply(c,inverse(b))) = multiply(greatest_lower_bound(c,a),inverse(b)),
inference(paramod,[status(thm)],[c_26,c_113]) ).
cnf(c_404,plain,
greatest_lower_bound(identity,multiply(c,inverse(a))) = multiply(greatest_lower_bound(c,a),inverse(b)),
inference(paramod,[status(thm)],[c_176,c_701]) ).
cnf(c_702,plain,
multiply(greatest_lower_bound(c,a),inverse(b)) = multiply(greatest_lower_bound(c,inverse(inverse(a))),inverse(a)),
inference(paramod,[status(thm)],[c_404,c_70]) ).
cnf(c_668,plain,
multiply(greatest_lower_bound(c,a),inverse(b)) = multiply(greatest_lower_bound(c,a),inverse(a)),
inference(paramod,[status(thm)],[c_23,c_702]) ).
cnf(c_703,plain,
multiply(inverse(greatest_lower_bound(c,a)),multiply(greatest_lower_bound(c,a),inverse(a))) = inverse(b),
inference(paramod,[status(thm)],[c_668,c_34]) ).
cnf(c_704,plain,
inverse(a) = inverse(b),
inference(paramod,[status(thm)],[c_34,c_703]) ).
cnf(c_677,plain,
inverse(b) = inverse(a),
inference(copy,[status(thm)],[c_704]) ).
cnf(c_705,plain,
inverse(inverse(a)) = b,
inference(paramod,[status(thm)],[c_677,c_23]) ).
cnf(c_706,plain,
a = b,
inference(paramod,[status(thm)],[c_23,c_705]) ).
cnf(c_683,plain,
b = a,
inference(copy,[status(thm)],[c_706]) ).
cnf(c_684,plain,
$false,
inference(resolve,[status(thm)],[c_683,c_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP181-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % 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
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 14:36:14 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 1276009 was started by sandbox on n008,
% 0.10/5.37 % Fri Sep 25 14:36:14 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).
% 0.14/5.92
% 0.14/5.92 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.92
% 0.14/5.92 % Proof 1 at 0.40 (+ 0.12) seconds.
% 0.14/5.92 % Length of proof is 31.
% 0.14/5.92 % Level of proof is 8.
% 0.14/5.92 % Maximum clause weight is 21.000.
% 0.14/5.92 % Given clauses 104.
% 0.14/5.92
% 0.14/5.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------