%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL091-2 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:08:44 PM UTC 2026
% Result : Unsatisfiable 2.53s 1.02s
% Output : CNFRefutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 43 ( 13 unt; 4 def)
% Number of atoms : 83 ( 12 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 78 ( 38 ~; 36 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f144,axiom,
! [P,Q] : combK != comb_app(P,Q),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f157,axiom,
! [P,Q,R] :
( ap_contractE_c4(P,Q,R)
| ap_contractE_c3(P,Q,R)
| ap_contractE_c2(P,Q,R)
| ap_contractE_c1(P,Q,R)
| ~ member(pair(comb_app(P,Q),R),contract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f160,axiom,
! [P,Q,R] :
( P = comb_app(combK,R)
| ~ ap_contractE_c1(P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f165,axiom,
! [P,Q,R] :
( P = comb_app(comb_app(combS,ap_contractE_sk1p(P,Q,R)),ap_contractE_sk1q(P,Q,R))
| ~ ap_contractE_c2(P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f166,axiom,
! [P,Q,R] :
( member(pair(P,ap_contractE_sk2q(P,Q,R)),contract)
| ~ ap_contractE_c3(P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f169,axiom,
! [P,Q,R] :
( member(pair(Q,ap_contractE_sk3q(P,Q,R)),contract)
| ~ ap_contractE_c4(P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f171,axiom,
! [P,Q,R] :
( R = comb_app(P,ap_contractE_sk3q(P,Q,R))
| ~ ap_contractE_c4(P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f172,axiom,
! [R] : ~ member(pair(combK,R),contract),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f174,hypothesis,
member(pair(comb_app(combK,p),r),contract),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f175,negated_conjecture,
! [Q] :
( ~ member(pair(p,Q),contract)
| r != comb_app(combK,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f382,plain,
! [X0,X1] : combK != comb_app(X0,X1),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f399,plain,
! [X0,X1,X2] :
( ap_contractE_c4(X0,X1,X2)
| ap_contractE_c3(X0,X1,X2)
| ap_contractE_c2(X0,X1,X2)
| ap_contractE_c1(X0,X1,X2)
| ~ member(pair(comb_app(X0,X1),X2),contract) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f404,plain,
! [P,R] :
( P = comb_app(combK,R)
| ! [Q] : ~ ap_contractE_c1(P,Q,R) ),
inference(miniscoping,[status(thm)],[f160]) ).
fof(f405,plain,
! [X0,X1,X2] :
( X0 = comb_app(combK,X2)
| ~ ap_contractE_c1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f404]) ).
fof(f411,plain,
! [X0,X1,X2] :
( X0 = comb_app(comb_app(combS,ap_contractE_sk1p(X0,X1,X2)),ap_contractE_sk1q(X0,X1,X2))
| ~ ap_contractE_c2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f412,plain,
! [X0,X1,X2] :
( member(pair(X0,ap_contractE_sk2q(X0,X1,X2)),contract)
| ~ ap_contractE_c3(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f416,plain,
! [X0,X1,X2] :
( member(pair(X1,ap_contractE_sk3q(X0,X1,X2)),contract)
| ~ ap_contractE_c4(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f419,plain,
! [X0,X1,X2] :
( X2 = comb_app(X0,ap_contractE_sk3q(X0,X1,X2))
| ~ ap_contractE_c4(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f420,plain,
! [X0] : ~ member(pair(combK,X0),contract),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f422,plain,
member(pair(comb_app(combK,p),r),contract),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f423,plain,
! [X0] :
( ~ member(pair(p,X0),contract)
| r != comb_app(combK,X0) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f1062,plain,
! [X0] :
( ~ member(pair(p,ap_contractE_sk3q(combK,X0,r)),contract)
| ~ ap_contractE_c4(combK,X0,r) ),
inference(resolution,[status(thm)],[f419,f423]) ).
fof(f3964,plain,
( ap_contractE_c4(combK,p,r)
| ap_contractE_c3(combK,p,r)
| ap_contractE_c2(combK,p,r)
| ap_contractE_c1(combK,p,r) ),
inference(resolution,[status(thm)],[f399,f422]) ).
fof(f3969,definition,
( sQ134_spl
<=> ap_contractE_c1(combK,p,r) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f3970,plain,
( ~ sQ134_spl
| ap_contractE_c1(combK,p,r) ),
inference(component_clause,[status(thm)],[f3969]) ).
fof(f3972,definition,
( sQ135_spl
<=> ap_contractE_c2(combK,p,r) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f3973,plain,
( ~ sQ135_spl
| ap_contractE_c2(combK,p,r) ),
inference(component_clause,[status(thm)],[f3972]) ).
fof(f3975,definition,
( sQ136_spl
<=> ap_contractE_c3(combK,p,r) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f3976,plain,
( ~ sQ136_spl
| ap_contractE_c3(combK,p,r) ),
inference(component_clause,[status(thm)],[f3975]) ).
fof(f3978,definition,
( sQ137_spl
<=> ap_contractE_c4(combK,p,r) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f3981,plain,
( sQ137_spl
| sQ136_spl
| sQ135_spl
| sQ134_spl ),
inference(split_clause,[status(thm)],[f3964,f3969,f3972,f3975,f3978]) ).
fof(f3991,plain,
! [X0,X1] : ~ ap_contractE_c2(combK,X0,X1),
inference(resolution,[status(thm)],[f411,f382]) ).
fof(f3998,plain,
( ~ sQ135_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3973,f3991]) ).
fof(f3999,plain,
~ sQ135_spl,
inference(contradiction_clause,[status(thm)],[f3998]) ).
fof(f4002,plain,
( ~ sQ134_spl
| combK = comb_app(combK,r) ),
inference(resolution,[status(thm)],[f3970,f405]) ).
fof(f4182,plain,
! [X0,X1] : ~ ap_contractE_c3(combK,X0,X1),
inference(resolution,[status(thm)],[f412,f420]) ).
fof(f4188,plain,
( ~ ap_contractE_c4(combK,p,r)
| ~ ap_contractE_c4(combK,p,r) ),
inference(resolution,[status(thm)],[f416,f1062]) ).
fof(f4195,plain,
~ sQ137_spl,
inference(split_clause,[status(thm)],[f4188,f3978]) ).
fof(f4196,plain,
( ~ sQ134_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4002,f382]) ).
fof(f4197,plain,
~ sQ134_spl,
inference(contradiction_clause,[status(thm)],[f4196]) ).
fof(f4230,plain,
( ~ sQ136_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3976,f4182]) ).
fof(f4231,plain,
~ sQ136_spl,
inference(contradiction_clause,[status(thm)],[f4230]) ).
fof(f4232,plain,
$false,
inference(sat_refutation,[status(thm)],[f3981,f3999,f4195,f4197,f4231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL091-2 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 14:10:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 2.53/1.02 % Refutation found
% 2.53/1.02 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.53/1.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/1.06 % Elapsed time: 0.666792 seconds
% 0.24/1.06 % CPU time: 5.005555 seconds
% 0.24/1.06 % Total memory used: 139.863 MB
% 0.24/1.06 % Net memory used: 131.151 MB
%------------------------------------------------------------------------------