%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL100-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /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 : Thu Sep 24 12:08:46 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 60 ( 14 unt; 5 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 145 ( 73 ~; 67 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 63 ( 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B,R] :
( member(pair(A,B),trancl(R))
| ~ member(pair(A,B),R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [R] : trans(trancl(R)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [R,A,B,C] :
( member(pair(A,C),R)
| ~ member(pair(B,C),R)
| ~ member(pair(A,B),R)
| ~ trans(R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [R,X,Y,YP] :
( member(pair(YP,diamond_strip_lemmaD_sk1(X,Y,YP,R)),trancl(R))
| ~ member(pair(X,YP),R)
| ~ member(pair(X,Y),trancl(R))
| ~ diamond(R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [R,X,Y,YP] :
( member(pair(Y,diamond_strip_lemmaD_sk1(X,Y,YP,R)),R)
| ~ member(pair(X,YP),R)
| ~ member(pair(X,Y),trancl(R))
| ~ diamond(R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
diamond(r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
member(pair(y,ya),trancl(r)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
member(pair(ya,z),r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
! [YP] :
( member(pair(ya,sk1(YP)),trancl(r))
| ~ member(pair(y,YP),trancl(r)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
! [YP] :
( member(pair(YP,sk1(YP)),trancl(r))
| ~ member(pair(y,YP),trancl(r)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
member(pair(y,yp),trancl(r)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
! [ZA] :
( ~ member(pair(yp,ZA),trancl(r))
| ~ member(pair(z,ZA),trancl(r)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,plain,
! [X0,X1,X2] :
( member(pair(X0,X1),trancl(X2))
| ~ member(pair(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f28,plain,
! [X0] : trans(trancl(X0)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f29,plain,
! [R,A,C] :
( member(pair(A,C),R)
| ! [B] :
( ~ member(pair(B,C),R)
| ~ member(pair(A,B),R)
| ~ trans(R) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( member(pair(X1,X3),X0)
| ~ member(pair(X2,X3),X0)
| ~ member(pair(X1,X2),X0)
| ~ trans(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( member(pair(X3,diamond_strip_lemmaD_sk1(X1,X2,X3,X0)),trancl(X0))
| ~ member(pair(X1,X3),X0)
| ~ member(pair(X1,X2),trancl(X0))
| ~ diamond(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( member(pair(X2,diamond_strip_lemmaD_sk1(X1,X2,X3,X0)),X0)
| ~ member(pair(X1,X3),X0)
| ~ member(pair(X1,X2),trancl(X0))
| ~ diamond(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f33,plain,
diamond(r),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f34,plain,
member(pair(y,ya),trancl(r)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f35,plain,
member(pair(ya,z),r),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f36,plain,
! [X0] :
( member(pair(ya,sk1(X0)),trancl(r))
| ~ member(pair(y,X0),trancl(r)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f37,plain,
! [X0] :
( member(pair(X0,sk1(X0)),trancl(r))
| ~ member(pair(y,X0),trancl(r)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f38,plain,
member(pair(y,yp),trancl(r)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f39,plain,
! [X0] :
( ~ member(pair(yp,X0),trancl(r))
| ~ member(pair(z,X0),trancl(r)) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f44,definition,
( sQ0_spl
<=> member(pair(y,yp),trancl(r)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( sQ0_spl
| ~ member(pair(y,yp),trancl(r)) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f51,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f46,f38]) ).
fof(f52,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f51]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( member(pair(X0,X3),trancl(X2))
| ~ member(pair(X1,X3),trancl(X2))
| ~ member(pair(X0,X1),trancl(X2)) ),
inference(resolution,[status(thm)],[f30,f28]) ).
fof(f56,plain,
! [X0,X1] :
( ~ member(pair(z,X1),trancl(r))
| ~ member(pair(X0,X1),trancl(r))
| ~ member(pair(yp,X0),trancl(r)) ),
inference(resolution,[status(thm)],[f54,f39]) ).
fof(f63,definition,
( sQ3_spl
<=> member(pair(y,z),trancl(r)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( sQ3_spl
| ~ member(pair(y,z),trancl(r)) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f67,plain,
! [X0] :
( ~ member(pair(y,yp),trancl(r))
| ~ member(pair(z,X0),trancl(r))
| ~ member(pair(sk1(yp),X0),trancl(r)) ),
inference(resolution,[status(thm)],[f56,f37]) ).
fof(f70,definition,
! [X0] :
( sQ4_spl
<=> ( ~ member(pair(z,X0),trancl(r))
| ~ member(pair(sk1(yp),X0),trancl(r)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f71,plain,
! [X0] :
( ~ sQ4_spl
| ~ member(pair(z,X0),trancl(r))
| ~ member(pair(sk1(yp),X0),trancl(r)) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,plain,
( ~ sQ0_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f67,f70,f44]) ).
fof(f78,plain,
! [X0] :
( ~ sQ4_spl
| ~ member(pair(sk1(yp),X0),r)
| ~ member(pair(z,X0),trancl(r)) ),
inference(resolution,[status(thm)],[f71,f27]) ).
fof(f98,plain,
! [X0] :
( sQ3_spl
| ~ member(pair(X0,z),trancl(r))
| ~ member(pair(y,X0),trancl(r)) ),
inference(resolution,[status(thm)],[f65,f54]) ).
fof(f103,plain,
! [X0] :
( sQ3_spl
| ~ member(pair(X0,z),r)
| ~ member(pair(y,X0),trancl(r)) ),
inference(resolution,[status(thm)],[f98,f27]) ).
fof(f104,plain,
( sQ3_spl
| ~ member(pair(y,ya),trancl(r)) ),
inference(resolution,[status(thm)],[f103,f35]) ).
fof(f105,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f104,f34]) ).
fof(f106,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f105]) ).
fof(f111,plain,
! [X0,X1,X2] :
( member(pair(X2,diamond_strip_lemmaD_sk1(X0,X1,X2,r)),trancl(r))
| ~ member(pair(X0,X2),r)
| ~ member(pair(X0,X1),trancl(r)) ),
inference(resolution,[status(thm)],[f31,f33]) ).
fof(f112,plain,
! [X0,X1,X2] :
( member(pair(X1,diamond_strip_lemmaD_sk1(X0,X1,X2,r)),r)
| ~ member(pair(X0,X2),r)
| ~ member(pair(X0,X1),trancl(r)) ),
inference(resolution,[status(thm)],[f32,f33]) ).
fof(f113,plain,
! [X0] :
( member(pair(z,diamond_strip_lemmaD_sk1(ya,X0,z,r)),trancl(r))
| ~ member(pair(ya,X0),trancl(r)) ),
inference(resolution,[status(thm)],[f111,f35]) ).
fof(f136,definition,
( sQ11_spl
<=> member(pair(y,ya),trancl(r)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( sQ11_spl
| ~ member(pair(y,ya),trancl(r)) ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f198,plain,
! [X0] :
( member(pair(X0,diamond_strip_lemmaD_sk1(ya,X0,z,r)),r)
| ~ member(pair(ya,X0),trancl(r)) ),
inference(resolution,[status(thm)],[f112,f35]) ).
fof(f199,plain,
! [X0] :
( ~ member(pair(y,X0),trancl(r))
| member(pair(sk1(X0),diamond_strip_lemmaD_sk1(ya,sk1(X0),z,r)),r) ),
inference(resolution,[status(thm)],[f198,f36]) ).
fof(f207,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f138,f34]) ).
fof(f208,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f207]) ).
fof(f256,plain,
( ~ sQ4_spl
| ~ member(pair(z,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r))
| ~ member(pair(y,yp),trancl(r)) ),
inference(resolution,[status(thm)],[f199,f78]) ).
fof(f271,definition,
( sQ23_spl
<=> member(pair(z,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( sQ23_spl
| ~ member(pair(z,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)) ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,plain,
( ~ sQ4_spl
| ~ sQ23_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f256,f44,f271,f70]) ).
fof(f283,plain,
( sQ23_spl
| ~ member(pair(ya,sk1(yp)),trancl(r)) ),
inference(resolution,[status(thm)],[f273,f113]) ).
fof(f286,plain,
( sQ23_spl
| ~ member(pair(y,yp),trancl(r)) ),
inference(resolution,[status(thm)],[f283,f36]) ).
fof(f289,plain,
( sQ23_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f286,f44,f271]) ).
fof(f290,plain,
$false,
inference(sat_refutation,[status(thm)],[f52,f73,f106,f208,f274,f289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL100-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 14:16:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 0.09/0.43 % Refutation found
% 0.09/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.48 % Elapsed time: 0.098333 seconds
% 0.14/0.48 % CPU time: 0.292163 seconds
% 0.14/0.48 % Total memory used: 23.716 MB
% 0.14/0.48 % Net memory used: 23.375 MB
%------------------------------------------------------------------------------