%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM420-1.000 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 01:40:28 PM UTC 2026
% Result : Unsatisfiable 38.53s 10.38s
% Output : CNFRefutation 38.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 47 ( 24 unt; 0 def)
% Number of atoms : 80 ( 49 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 72 ( 39 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X1,X2,X3] : plus(plus(X1,X2),X3) = plus(X1,plus(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X1] : plus(n0,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X1,X2] :
( X2 = n0
| X1 != plus(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X1,X2] : times(X1,X2) = times(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X1] : plus(X1,n1) != n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X1,X2] : plus(times(X1,X2),X1) = times(X1,plus(X2,n1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X1] : less(n0,plus(X1,n1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( p__0 = plus(s_7(p__0),n1)
| ~ less(n0,p__0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
! [X8,X9,X22] :
( plus(X8,times(X9,p__0)) != plus(n0,times(X22,p__0))
| ~ less(X8,p__0)
| ~ less(n0,p__0)
| ~ less(n0,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,negated_conjecture,
( less(n0,p__0)
| ~ less(plus(n0,n1),p__0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,negated_conjecture,
! [X7] :
( less(n1,X7)
| X7 != p__0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,negated_conjecture,
! [X10] :
( times(s_1(X10),s_4(X10)) = X10
| X10 = n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f87,negated_conjecture,
! [X10] :
( s_1(X10) = p__0
| X10 = n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,plain,
! [X0,X1,X2] : plus(plus(X0,X1),X2) = plus(X0,plus(X1,X2)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f102,plain,
! [X0] : plus(n0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f105,plain,
! [X2] :
( X2 = n0
| ! [X1] : X1 != plus(X1,X2) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f106,plain,
! [X0,X1] :
( X1 = n0
| X0 != plus(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f114,plain,
! [X0,X1] : times(X0,X1) = times(X1,X0),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f115,plain,
! [X0] : plus(X0,n1) != n0,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f124,plain,
! [X0,X1] : plus(times(X0,X1),X0) = times(X0,plus(X1,n1)),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f132,plain,
! [X0] : less(n0,plus(X0,n1)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f156,plain,
( p__0 = plus(s_7(p__0),n1)
| ~ less(n0,p__0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f164,plain,
! [X8] :
( ! [X9,X22] : plus(X8,times(X9,p__0)) != plus(n0,times(X22,p__0))
| ~ less(X8,p__0)
| ~ less(n0,p__0)
| ~ less(n0,X8) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f165,plain,
! [X0,X1,X2] :
( plus(X0,times(X1,p__0)) != plus(n0,times(X2,p__0))
| ~ less(X0,p__0)
| ~ less(n0,p__0)
| ~ less(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f177,plain,
( less(n0,p__0)
| ~ less(plus(n0,n1),p__0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f188,plain,
! [X0] :
( less(n1,X0)
| X0 != p__0 ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f193,plain,
! [X0] :
( times(s_1(X0),s_4(X0)) = X0
| X0 = n1 ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f198,plain,
! [X0] :
( s_1(X0) = p__0
| X0 = n1 ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f207,plain,
less(n1,p__0),
inference(destructive_equality_resolution,[status(thm)],[f188]) ).
fof(f268,plain,
! [X0,X1] : plus(X0,plus(X1,n1)) != n0,
inference(paramodulation,[status(thm)],[f97,f115]) ).
fof(f526,plain,
less(n0,n1),
inference(paramodulation,[status(thm)],[f102,f132]) ).
fof(f927,plain,
! [X0,X1,X2] :
( plus(X0,times(X1,p__0)) != times(X2,p__0)
| ~ less(X0,p__0)
| ~ less(n0,p__0)
| ~ less(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f102,f165]) ).
fof(f928,plain,
! [X0,X1] :
( plus(n1,times(X0,p__0)) != times(X1,p__0)
| ~ less(n0,p__0)
| ~ less(n0,n1) ),
inference(resolution,[status(thm)],[f927,f207]) ).
fof(f930,plain,
! [X0,X1] :
( plus(n1,times(X0,p__0)) != times(X1,p__0)
| ~ less(n0,p__0) ),
inference(forward_subsumption_resolution,[status(thm)],[f928,f526]) ).
fof(f957,plain,
( less(n0,p__0)
| ~ less(n1,p__0) ),
inference(forward_demodulation,[status(thm)],[f102,f177]) ).
fof(f963,plain,
p__0 = plus(s_7(p__0),n1),
inference(backward_subsumption_resolution,[status(thm)],[f156,f965]) ).
fof(f965,plain,
less(n0,p__0),
inference(forward_subsumption_resolution,[status(thm)],[f957,f207]) ).
fof(f1014,plain,
! [X0] :
( times(s_4(X0),s_1(X0)) = X0
| X0 = n1 ),
inference(forward_demodulation,[status(thm)],[f114,f193]) ).
fof(f1018,plain,
! [X0] :
( X0 = n1
| times(s_4(X0),p__0) = X0
| X0 = n1 ),
inference(paramodulation,[status(thm)],[f198,f1014]) ).
fof(f1030,plain,
! [X0] :
( times(s_4(X0),p__0) = X0
| X0 = n1 ),
inference(duplicate_literals_removal,[status(thm)],[f1018]) ).
fof(f1367,plain,
! [X0] : plus(X0,p__0) != n0,
inference(paramodulation,[status(thm)],[f963,f268]) ).
fof(f1739,plain,
! [X0] : times(p__0,plus(X0,n1)) != n0,
inference(paramodulation,[status(thm)],[f124,f1367]) ).
fof(f7253,plain,
times(p__0,p__0) != n0,
inference(paramodulation,[status(thm)],[f963,f1739]) ).
fof(f7655,plain,
! [X0] : X0 != plus(X0,times(p__0,p__0)),
inference(resolution,[status(thm)],[f7253,f106]) ).
fof(f8034,plain,
! [X0,X1] : plus(n1,times(X0,p__0)) != times(X1,p__0),
inference(forward_subsumption_resolution,[status(thm)],[f930,f965]) ).
fof(f8039,plain,
! [X0] : plus(n1,times(X0,p__0)) = n1,
inference(resolution,[status(thm)],[f8034,f1030]) ).
fof(f8078,plain,
$false,
inference(resolution,[status(thm)],[f8039,f7655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM420-1.000 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.41 % Computer : n010.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Mon Sep 21 02:28:00 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.43 % Drodi V4.1.1
% 38.53/10.38 % Refutation found
% 38.53/10.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 38.53/10.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.46/10.45 % Elapsed time: 5.017820 seconds
% 14.46/10.45 % CPU time: 39.368698 seconds
% 14.46/10.45 % Total memory used: 302.163 MB
% 14.46/10.45 % Net memory used: 292.676 MB
%------------------------------------------------------------------------------