%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM017-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 136.52s 17.78s
% Output : CNFRefutation 136.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 15 unt; 0 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 155 ( 79 ~; 76 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 162 ( 162 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( equalish(Y,X)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [D,B,C,A] :
( product(C,A,B)
| ~ product(C,A,D)
| ~ equalish(D,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A,C] :
( divides(C,A)
| ~ divides(C,B)
| ~ equalish(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] : product(A,B,multiply(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B,C] :
( product(B,A,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C,D] :
( equalish(B,D)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C,D] :
( equalish(D,C)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B] :
( product(A,second_divided_by_1st(A,B),B)
| ~ divides(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B,C] :
( divides(A,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,B,C] :
( divides(A,C)
| ~ prime(A)
| ~ product(C,C,B)
| ~ divides(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
prime(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
! [A] :
( ~ divides(A,b)
| ~ divides(A,c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f29,plain,
! [B,C,A] :
( product(C,A,B)
| ! [D] :
( ~ product(C,A,D)
| ~ equalish(D,B) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f35,plain,
! [A,C] :
( divides(C,A)
| ! [B] :
( ~ divides(C,B)
| ~ equalish(B,A) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f36,plain,
! [X0,X1,X2] :
( divides(X2,X1)
| ~ divides(X2,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f41,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f42,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)],[f11]) ).
fof(f43,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)],[f42]) ).
fof(f46,plain,
! [X0,X1,X2] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f47,plain,
! [B,D] :
( equalish(B,D)
| ! [A,C] :
( ~ product(A,D,C)
| ~ product(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
! [C,D] :
( equalish(D,C)
| ! [A,B] :
( ~ product(A,B,D)
| ~ product(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( equalish(X3,X2)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( product(X0,second_divided_by_1st(X0,X1),X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f54,plain,
! [A,C] :
( divides(A,C)
| ! [B] : ~ product(A,B,C) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f55,plain,
! [X0,X1,X2] :
( divides(X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [A,C] :
( divides(A,C)
| ~ prime(A)
| ! [B] :
( ~ product(C,C,B)
| ~ divides(A,B) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f57,plain,
! [X0,X1,X2] :
( divides(X0,X2)
| ~ prime(X0)
| ~ product(X2,X2,X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
prime(a),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f62,plain,
! [X0] :
( ~ divides(X0,b)
| ~ divides(X0,c) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f92,plain,
! [X0,X1,X2] :
( divides(X1,X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f46,f55]) ).
fof(f96,plain,
! [X0,X1] : divides(X0,multiply(X1,X0)),
inference(resolution,[status(thm)],[f92,f41]) ).
fof(f101,plain,
! [X0,X1,X2] :
( divides(X1,X2)
| ~ equalish(multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f96,f36]) ).
fof(f104,plain,
! [X0,X1,X2,X3] :
( ~ equalish(X3,X2)
| product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f30,f26]) ).
fof(f170,plain,
! [X0,X1,X2] :
( ~ equalish(X1,multiply(X2,X0))
| divides(X0,X1) ),
inference(resolution,[status(thm)],[f101,f26]) ).
fof(f368,plain,
! [X0,X1,X2] :
( equalish(X1,X2)
| ~ product(X0,X1,multiply(X0,X2)) ),
inference(resolution,[status(thm)],[f48,f41]) ).
fof(f376,plain,
! [X0,X1,X2] :
( equalish(multiply(X0,X1),X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f52,f41]) ).
fof(f380,plain,
! [X0,X1] :
( divides(a,X1)
| ~ product(X1,X1,X0)
| ~ divides(a,X0) ),
inference(resolution,[status(thm)],[f57,f58]) ).
fof(f547,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X2,X5,X4)
| ~ product(X5,X0,X3)
| ~ product(X2,X3,multiply(X4,X1))
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f368,f43]) ).
fof(f602,plain,
! [X0,X1] :
( ~ divides(X0,X1)
| equalish(multiply(X0,second_divided_by_1st(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f376,f53]) ).
fof(f606,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| equalish(multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f376,f46]) ).
fof(f622,plain,
! [X0,X1,X2] :
( ~ equalish(X2,multiply(X0,X1))
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f104,f41]) ).
fof(f789,plain,
! [X0,X1] : equalish(multiply(X0,X1),multiply(X1,X0)),
inference(resolution,[status(thm)],[f606,f41]) ).
fof(f818,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f622,f789]) ).
fof(f822,plain,
! [X0,X1,X2] :
( ~ equalish(multiply(X0,X1),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f622,f26]) ).
fof(f843,plain,
! [X0,X1,X2] :
( ~ equalish(X2,multiply(X1,X0))
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f818,f104]) ).
fof(f1221,plain,
! [X0,X1,X2] :
( ~ equalish(multiply(X1,X0),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f843,f26]) ).
fof(f1985,plain,
! [X0] :
( divides(a,X0)
| ~ divides(a,multiply(X0,X0)) ),
inference(resolution,[status(thm)],[f380,f818]) ).
fof(f2257,plain,
divides(a,a),
inference(resolution,[status(thm)],[f1985,f96]) ).
fof(f2891,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,X2,X3)
| ~ product(X2,X0,X1)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f547,f41]) ).
fof(f3217,plain,
! [X0,X1] :
( product(second_divided_by_1st(X0,X1),X0,X1)
| ~ divides(X0,X1) ),
inference(resolution,[status(thm)],[f602,f1221]) ).
fof(f3279,plain,
product(second_divided_by_1st(a,a),a,a),
inference(resolution,[status(thm)],[f3217,f2257]) ).
fof(f3461,plain,
equalish(multiply(a,second_divided_by_1st(a,a)),a),
inference(resolution,[status(thm)],[f3279,f606]) ).
fof(f18972,plain,
product(a,second_divided_by_1st(a,a),a),
inference(resolution,[status(thm)],[f3461,f822]) ).
fof(f19031,plain,
! [X0,X1] :
( ~ product(second_divided_by_1st(a,a),X0,X1)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f18972,f2891]) ).
fof(f22267,plain,
! [X0] : equalish(X0,multiply(X0,second_divided_by_1st(a,a))),
inference(resolution,[status(thm)],[f19031,f818]) ).
fof(f22328,plain,
! [X0] : divides(second_divided_by_1st(a,a),X0),
inference(resolution,[status(thm)],[f22267,f170]) ).
fof(f23015,plain,
~ divides(second_divided_by_1st(a,a),b),
inference(resolution,[status(thm)],[f22328,f62]) ).
fof(f23021,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f23015,f22328]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM017-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:01:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 136.52/17.78 % Refutation found
% 136.52/17.78 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 136.52/17.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 21.79/17.84 % Elapsed time: 17.447749 seconds
% 21.79/17.84 % CPU time: 138.192017 seconds
% 21.79/17.84 % Total memory used: 398.494 MB
% 21.79/17.84 % Net memory used: 333.236 MB
%------------------------------------------------------------------------------