%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP170-1 : 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 : n001.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 3.57s 0.96s
% Output : CNFRefutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 47 unt; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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; 5 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 16 !; 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_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(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(p03a_1,axiom,
least_upper_bound(a,b) = b,
file('theBenchmark.p',p03a_1) ).
cnf(c_22,plain,
least_upper_bound(a,b) = b,
inference(clausify,[status(thm)],[p03a_1]) ).
cnf(c_23,plain,
least_upper_bound(b,a) = b,
inference(paramod,[status(thm)],[c_5,c_22]) ).
fof(p03a_2,axiom,
least_upper_bound(c,d) = d,
file('theBenchmark.p',p03a_2) ).
cnf(c_24,plain,
least_upper_bound(c,d) = d,
inference(clausify,[status(thm)],[p03a_2]) ).
cnf(c_25,plain,
least_upper_bound(d,c) = d,
inference(paramod,[status(thm)],[c_5,c_24]) ).
fof(prove_p03a,axiom,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
file('theBenchmark.p',prove_p03a) ).
cnf(c_26,plain,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
inference(clausify,[status(thm)],[prove_p03a]) ).
cnf(c_27,plain,
least_upper_bound(multiply(b,d),multiply(a,c)) != multiply(b,d),
inference(paramod,[status(thm)],[c_5,c_26]) ).
cnf(c_1514,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_1515,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_1514]) ).
cnf(c_28,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_1515]) ).
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_1516,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_1516]) ).
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_222,plain,
least_upper_bound(multiply(A,B),C) = multiply(A,least_upper_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_202,c_15]) ).
cnf(c_238,plain,
multiply(b,least_upper_bound(d,multiply(inverse(b),multiply(a,c)))) != multiply(b,d),
inference(paramod,[status(thm)],[c_222,c_27]) ).
cnf(c_1517,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_1517]) ).
cnf(c_1518,plain,
least_upper_bound(A,multiply(multiply(inverse(b),a),A)) = multiply(identity,A),
inference(paramod,[status(thm)],[c_319,c_53]) ).
cnf(c_1519,plain,
least_upper_bound(A,multiply(inverse(b),multiply(a,A))) = multiply(identity,A),
inference(paramod,[status(thm)],[c_3,c_1518]) ).
cnf(c_563,plain,
least_upper_bound(A,multiply(inverse(b),multiply(a,A))) = A,
inference(paramod,[status(thm)],[c_1,c_1519]) ).
cnf(c_1520,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_1521,plain,
d = least_upper_bound(d,multiply(inverse(b),multiply(a,c))),
inference(paramod,[status(thm)],[c_25,c_1520]) ).
cnf(c_1506,plain,
least_upper_bound(d,multiply(inverse(b),multiply(a,c))) = d,
inference(copy,[status(thm)],[c_1521]) ).
cnf(c_1522,plain,
multiply(b,d) != multiply(b,d),
inference(paramod,[status(thm)],[c_1506,c_238]) ).
cnf(c_1513,plain,
$false,
inference(copy,[status(thm)],[c_1522]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP170-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n001.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 14:39:10 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 3541736 was started by sandbox2 on n001,
% 0.16/0.44 % Fri Sep 25 14:39:10 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 3.57/0.96
% 3.57/0.96 % SZS status Unsatisfiable for theBenchmark
% 3.57/0.96
% 3.57/0.96 % Proof 1 at 0.37 (+ 0.13) seconds.
% 3.57/0.96 % Length of proof is 28.
% 3.57/0.96 % Level of proof is 6.
% 3.57/0.96 % Maximum clause weight is 14.000.
% 3.57/0.96 % Given clauses 148.
% 3.57/0.96
% 3.57/0.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------