%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM017-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 : Thu Sep 24 01:38:32 PM UTC 2026
% Result : Unsatisfiable 1.29s 0.59s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 27 unt; 0 def)
% Number of atoms : 103 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 99 ( 51 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 133 ( 133 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : product(A,B,multiply(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C,D,E,F] :
( product(F,E,C)
| ~ product(A,D,F)
| ~ product(D,E,B)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( product(B,A,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C,D] :
( B = D
| ~ product(A,D,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C,D] :
( D = C
| ~ product(A,B,D)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( product(A,second_divided_by_1st(A,B),B)
| ~ divides(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] :
( divides(A,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C] :
( divides(A,C)
| ~ prime(A)
| ~ product(C,C,B)
| ~ divides(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
prime(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
! [A] :
( ~ divides(A,b)
| ~ divides(A,c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
! [C,E,F] :
( product(F,E,C)
| ! [A,D] :
( ~ product(A,D,F)
| ! [B] :
( ~ product(D,E,B)
| ~ product(A,B,C) ) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X5,X4,X2)
| ~ product(X0,X3,X5)
| ~ product(X3,X4,X1)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [X0,X1,X2] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
! [B,D] :
( B = D
| ! [A,C] :
( ~ product(A,D,C)
| ~ product(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f26,plain,
! [C,D] :
( D = C
| ! [A,B] :
( ~ product(A,B,D)
| ~ product(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( product(X0,second_divided_by_1st(X0,X1),X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f29,plain,
! [A,C] :
( divides(A,C)
| ! [B] : ~ product(A,B,C) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f30,plain,
! [X0,X1,X2] :
( divides(X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [A,C] :
( divides(A,C)
| ~ prime(A)
| ! [B] :
( ~ product(C,C,B)
| ~ divides(A,B) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f32,plain,
! [X0,X1,X2] :
( divides(X0,X2)
| ~ prime(X0)
| ~ product(X2,X2,X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
prime(a),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f37,plain,
! [X0] :
( ~ divides(X0,b)
| ~ divides(X0,c) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f38,plain,
! [X0,X1] : divides(X0,multiply(X0,X1)),
inference(resolution,[status(thm)],[f16,f30]) ).
fof(f83,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f21,f16]) ).
fof(f85,plain,
! [X0,X1] : divides(X0,multiply(X1,X0)),
inference(resolution,[status(thm)],[f83,f30]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4] :
( product(X4,X1,multiply(X3,X2))
| ~ product(X3,X0,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f18,f16]) ).
fof(f101,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ product(X0,X1,multiply(X0,X2)) ),
inference(resolution,[status(thm)],[f23,f16]) ).
fof(f171,plain,
! [X0,X1,X2] :
( X2 = multiply(X1,X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f27,f83]) ).
fof(f172,plain,
! [X0,X1,X2] :
( X2 = multiply(X0,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f27,f16]) ).
fof(f210,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[f171,f16]) ).
fof(f231,plain,
! [X0,X1] : product(X0,second_divided_by_1st(X0,multiply(X0,X1)),multiply(X0,X1)),
inference(resolution,[status(thm)],[f28,f38]) ).
fof(f252,plain,
! [X0,X1,X2] :
( divides(X1,X0)
| ~ prime(X1)
| ~ product(X0,X0,multiply(X1,X2)) ),
inference(resolution,[status(thm)],[f32,f38]) ).
fof(f305,plain,
! [X0,X1] : X0 = second_divided_by_1st(X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f231,f101]) ).
fof(f448,plain,
! [X0,X1] : X0 = second_divided_by_1st(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f210,f305]) ).
fof(f507,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,multiply(X0,multiply(X3,X1)))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f93,f83]) ).
fof(f558,plain,
! [X0] :
( divides(X0,X0)
| ~ prime(X0) ),
inference(resolution,[status(thm)],[f252,f83]) ).
fof(f565,plain,
divides(a,a),
inference(resolution,[status(thm)],[f558,f33]) ).
fof(f567,plain,
product(a,second_divided_by_1st(a,a),a),
inference(resolution,[status(thm)],[f565,f28]) ).
fof(f575,plain,
a = multiply(a,second_divided_by_1st(a,a)),
inference(resolution,[status(thm)],[f567,f172]) ).
fof(f897,plain,
! [X0,X1,X2] : product(multiply(X0,X1),X2,multiply(X1,multiply(X2,X0))),
inference(resolution,[status(thm)],[f507,f83]) ).
fof(f1769,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X2,X0),X1),
inference(resolution,[status(thm)],[f897,f172]) ).
fof(f3768,plain,
! [X0,X1,X2] : multiply(X0,X1) = second_divided_by_1st(X2,multiply(X1,multiply(X2,X0))),
inference(paramodulation,[status(thm)],[f1769,f448]) ).
fof(f4669,plain,
! [X0] : multiply(second_divided_by_1st(a,a),X0) = second_divided_by_1st(a,multiply(X0,a)),
inference(paramodulation,[status(thm)],[f575,f3768]) ).
fof(f4690,plain,
! [X0] : multiply(second_divided_by_1st(a,a),X0) = X0,
inference(forward_demodulation,[status(thm)],[f448,f4669]) ).
fof(f4828,plain,
! [X0] : divides(X0,X0),
inference(paramodulation,[status(thm)],[f4690,f85]) ).
fof(f4898,plain,
! [X0] : product(X0,second_divided_by_1st(X0,X0),X0),
inference(resolution,[status(thm)],[f4828,f28]) ).
fof(f4954,plain,
! [X0] : X0 = multiply(X0,second_divided_by_1st(X0,X0)),
inference(resolution,[status(thm)],[f4898,f172]) ).
fof(f5021,plain,
! [X0,X1] : multiply(second_divided_by_1st(X0,X0),X1) = second_divided_by_1st(X0,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f4954,f3768]) ).
fof(f5092,plain,
! [X0,X1] : multiply(second_divided_by_1st(X0,X0),X1) = X1,
inference(forward_demodulation,[status(thm)],[f448,f5021]) ).
fof(f5316,plain,
! [X0,X1] : divides(second_divided_by_1st(X0,X0),X1),
inference(paramodulation,[status(thm)],[f5092,f38]) ).
fof(f5376,plain,
! [X0] : ~ divides(second_divided_by_1st(X0,X0),b),
inference(resolution,[status(thm)],[f5316,f37]) ).
fof(f5384,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5376,f5316]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM017-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n018.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:00:59 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 1.29/0.59 % Refutation found
% 1.29/0.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.29/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.29/0.60 % Elapsed time: 0.246812 seconds
% 1.29/0.60 % CPU time: 1.696415 seconds
% 1.29/0.60 % Total memory used: 59.264 MB
% 1.29/0.60 % Net memory used: 56.349 MB
%------------------------------------------------------------------------------