%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP170-3 : 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 : n003.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 07:28:12 AM UTC 2026
% Result : Unsatisfiable 5.40s 1.14s
% Output : CNFRefutation 5.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 58 ( 58 unt; 0 def)
% Number of atoms : 58 ( 57 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 82 ( 2 sgn 23 !; 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_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(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_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(p03c_1,axiom,
least_upper_bound(a,b) = b,
file('theBenchmark.p',p03c_1) ).
cnf(c_22,plain,
least_upper_bound(a,b) = b,
inference(clausify,[status(thm)],[p03c_1]) ).
cnf(c_23,plain,
least_upper_bound(b,a) = b,
inference(paramod,[status(thm)],[c_5,c_22]) ).
fof(p03c_2,axiom,
least_upper_bound(c,d) = d,
file('theBenchmark.p',p03c_2) ).
cnf(c_24,plain,
least_upper_bound(c,d) = d,
inference(clausify,[status(thm)],[p03c_2]) ).
cnf(c_25,plain,
least_upper_bound(d,c) = d,
inference(paramod,[status(thm)],[c_5,c_24]) ).
fof(prove_p03c,axiom,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
file('theBenchmark.p',prove_p03c) ).
cnf(c_26,plain,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
inference(clausify,[status(thm)],[prove_p03c]) ).
cnf(c_27,plain,
greatest_lower_bound(multiply(b,d),multiply(a,c)) != multiply(a,c),
inference(paramod,[status(thm)],[c_4,c_26]) ).
cnf(c_2009,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_2010,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_2009]) ).
cnf(c_28,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_2010]) ).
cnf(c_43,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
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_2011,plain,
least_upper_bound(d,A) = least_upper_bound(d,least_upper_bound(c,A)),
inference(paramod,[status(thm)],[c_25,c_9]) ).
cnf(c_69,plain,
least_upper_bound(d,least_upper_bound(c,A)) = least_upper_bound(d,A),
inference(copy,[status(thm)],[c_2011]) ).
cnf(c_82,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_28,c_28]) ).
cnf(c_202,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_82,c_28]) ).
cnf(c_223,plain,
greatest_lower_bound(multiply(A,B),C) = multiply(A,greatest_lower_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_202,c_17]) ).
cnf(c_245,plain,
multiply(b,greatest_lower_bound(d,multiply(inverse(b),multiply(a,c)))) != multiply(a,c),
inference(paramod,[status(thm)],[c_223,c_27]) ).
cnf(c_2012,plain,
least_upper_bound(identity,multiply(inverse(b),a)) = multiply(inverse(b),b),
inference(paramod,[status(thm)],[c_23,c_47]) ).
cnf(c_319,plain,
least_upper_bound(identity,multiply(inverse(b),a)) = identity,
inference(paramod,[status(thm)],[c_2,c_2012]) ).
cnf(c_2013,plain,
least_upper_bound(A,multiply(multiply(inverse(b),a),A)) = multiply(identity,A),
inference(paramod,[status(thm)],[c_319,c_53]) ).
cnf(c_2014,plain,
least_upper_bound(A,multiply(inverse(b),multiply(a,A))) = multiply(identity,A),
inference(paramod,[status(thm)],[c_3,c_2013]) ).
cnf(c_563,plain,
least_upper_bound(A,multiply(inverse(b),multiply(a,A))) = A,
inference(paramod,[status(thm)],[c_1,c_2014]) ).
cnf(c_2015,plain,
least_upper_bound(d,c) = least_upper_bound(d,multiply(inverse(b),multiply(a,c))),
inference(paramod,[status(thm)],[c_563,c_69]) ).
cnf(c_2016,plain,
d = least_upper_bound(d,multiply(inverse(b),multiply(a,c))),
inference(paramod,[status(thm)],[c_25,c_2015]) ).
cnf(c_1506,plain,
least_upper_bound(d,multiply(inverse(b),multiply(a,c))) = d,
inference(copy,[status(thm)],[c_2016]) ).
cnf(c_2017,plain,
greatest_lower_bound(multiply(inverse(b),multiply(a,c)),d) = multiply(inverse(b),multiply(a,c)),
inference(paramod,[status(thm)],[c_1506,c_43]) ).
cnf(c_2001,plain,
greatest_lower_bound(d,multiply(inverse(b),multiply(a,c))) = multiply(inverse(b),multiply(a,c)),
inference(paramod,[status(thm)],[c_4,c_2017]) ).
cnf(c_2018,plain,
multiply(b,multiply(inverse(b),multiply(a,c))) != multiply(a,c),
inference(paramod,[status(thm)],[c_2001,c_245]) ).
cnf(c_2019,plain,
multiply(a,c) != multiply(a,c),
inference(paramod,[status(thm)],[c_202,c_2018]) ).
cnf(c_2008,plain,
$false,
inference(copy,[status(thm)],[c_2019]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP170-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n003.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 14:35:08 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 391864 was started by sandbox on n003,
% 0.15/0.42 % Fri Sep 25 14:35:08 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 5.40/1.14
% 5.40/1.14 % SZS status Unsatisfiable for theBenchmark
% 5.40/1.14
% 5.40/1.14 % Proof 1 at 0.51 (+ 0.19) seconds.
% 5.40/1.14 % Length of proof is 34.
% 5.40/1.14 % Level of proof is 7.
% 5.40/1.14 % Maximum clause weight is 15.000.
% 5.40/1.14 % Given clauses 177.
% 5.40/1.14
% 5.40/1.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------