%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM027-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 01:38:33 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.60s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 56 ( 25 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B,C] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] :
( equalish(Y,X)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B,C] :
( equalish(multiply(A,C),multiply(B,C))
| ~ equalish(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B] :
( ~ equalish(A,B)
| ~ less(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] :
( less(B,A)
| equalish(B,A)
| less(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] : ~ less(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B,C] :
( less(multiply(A,C),multiply(B,C))
| equalish(C,n0)
| ~ less(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
~ less(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
less(multiply(b,c),multiply(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ equalish(c,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,plain,
! [B,C] :
( less(C,B)
| ! [A] :
( ~ less(C,A)
| ~ less(A,B) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f29,plain,
! [X0,X1,X2] :
( less(X2,X1)
| ~ less(X2,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f34,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f37,plain,
! [A,B] :
( ! [C] : equalish(multiply(A,C),multiply(B,C))
| ~ equalish(A,B) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f38,plain,
! [X0,X1,X2] :
( equalish(multiply(X0,X2),multiply(X1,X2))
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f40,plain,
! [X0,X1] :
( less(X1,X0)
| equalish(X1,X0)
| less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f41,plain,
! [X0] : ~ less(X0,X0),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f43,plain,
! [X0,X1,X2] :
( less(multiply(X0,X2),multiply(X1,X2))
| equalish(X2,n0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f44,plain,
~ less(b,a),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
less(multiply(b,c),multiply(a,c)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
~ equalish(c,n0),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f98,plain,
! [X0,X1,X2] :
( less(multiply(X1,X2),multiply(X0,X2))
| equalish(X2,n0)
| equalish(X1,X0)
| less(X0,X1) ),
inference(resolution,[status(thm)],[f40,f43]) ).
fof(f241,plain,
! [X0] :
( less(X0,multiply(a,c))
| ~ less(X0,multiply(b,c)) ),
inference(resolution,[status(thm)],[f45,f29]) ).
fof(f242,plain,
~ equalish(multiply(b,c),multiply(a,c)),
inference(resolution,[status(thm)],[f45,f39]) ).
fof(f863,plain,
! [X0] :
( equalish(c,n0)
| equalish(X0,b)
| less(b,X0)
| less(multiply(X0,c),multiply(a,c)) ),
inference(resolution,[status(thm)],[f241,f98]) ).
fof(f870,plain,
! [X0] :
( equalish(X0,b)
| less(b,X0)
| less(multiply(X0,c),multiply(a,c)) ),
inference(forward_subsumption_resolution,[status(thm)],[f863,f46]) ).
fof(f878,plain,
( equalish(a,b)
| less(b,a) ),
inference(resolution,[status(thm)],[f870,f41]) ).
fof(f880,plain,
equalish(a,b),
inference(forward_subsumption_resolution,[status(thm)],[f878,f44]) ).
fof(f886,plain,
equalish(b,a),
inference(resolution,[status(thm)],[f880,f34]) ).
fof(f888,plain,
! [X0] : equalish(multiply(b,X0),multiply(a,X0)),
inference(resolution,[status(thm)],[f886,f38]) ).
fof(f982,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f242,f888]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM027-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n007.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 01:57:25 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.15/5.60 % Refutation found
% 0.15/5.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/5.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.63 % Elapsed time: 0.247025 seconds
% 0.15/5.63 % CPU time: 1.816671 seconds
% 0.15/5.63 % Total memory used: 30.593 MB
% 0.15/5.63 % Net memory used: 26.957 MB
%------------------------------------------------------------------------------