%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL091-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:08:44 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 51 ( 10 unt; 5 def)
% Number of atoms : 119 ( 24 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 112 ( 44 ~; 63 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [P,Q] : combK != comb_app(P,Q),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,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(f18,axiom,
! [P,Q,R] :
( P = comb_app(combK,R)
| ~ ap_contractE_c1(P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,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(f24,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(f27,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(f29,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(f30,axiom,
! [R] : ~ member(pair(combK,R),contract),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,hypothesis,
member(pair(comb_app(combK,p),r),contract),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
! [Q] :
( ~ member(pair(p,Q),contract)
| r != comb_app(combK,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0,X1] : combK != comb_app(X0,X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f52,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)],[f15]) ).
fof(f57,plain,
! [P,R] :
( P = comb_app(combK,R)
| ! [Q] : ~ ap_contractE_c1(P,Q,R) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f58,plain,
! [X0,X1,X2] :
( X0 = comb_app(combK,X2)
| ~ ap_contractE_c1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f64,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)],[f23]) ).
fof(f65,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)],[f24]) ).
fof(f69,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)],[f27]) ).
fof(f72,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)],[f29]) ).
fof(f73,plain,
! [X0] : ~ member(pair(combK,X0),contract),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f75,plain,
member(pair(comb_app(combK,p),r),contract),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f76,plain,
! [X0] :
( ~ member(pair(p,X0),contract)
| r != comb_app(combK,X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ap_contractE_c3(X1,X0,X2)
| ap_contractE_c2(X1,X0,X2)
| ap_contractE_c1(X1,X0,X2)
| ~ member(pair(comb_app(X1,X0),X2),contract)
| member(pair(X0,ap_contractE_sk3q(X1,X0,X2)),contract) ),
inference(resolution,[status(thm)],[f69,f52]) ).
fof(f100,plain,
! [X0,X1,X2] :
( X1 = comb_app(combK,X2)
| ap_contractE_c3(X1,X0,X2)
| ap_contractE_c2(X1,X0,X2)
| ~ member(pair(comb_app(X1,X0),X2),contract)
| member(pair(X0,ap_contractE_sk3q(X1,X0,X2)),contract) ),
inference(resolution,[status(thm)],[f99,f58]) ).
fof(f102,plain,
( combK = comb_app(combK,r)
| ap_contractE_c3(combK,p,r)
| ap_contractE_c2(combK,p,r)
| member(pair(p,ap_contractE_sk3q(combK,p,r)),contract) ),
inference(resolution,[status(thm)],[f100,f75]) ).
fof(f103,definition,
( sQ2_spl
<=> member(pair(p,ap_contractE_sk3q(combK,p,r)),contract) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ2_spl
| member(pair(p,ap_contractE_sk3q(combK,p,r)),contract) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,definition,
( sQ3_spl
<=> ap_contractE_c2(combK,p,r) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ3_spl
| ap_contractE_c2(combK,p,r) ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,definition,
( sQ4_spl
<=> ap_contractE_c3(combK,p,r) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ4_spl
| ap_contractE_c3(combK,p,r) ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,definition,
( sQ5_spl
<=> combK = comb_app(combK,r) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( ~ sQ5_spl
| combK = comb_app(combK,r) ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,plain,
( sQ5_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f102,f103,f106,f109,f112]) ).
fof(f116,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f113,f35]) ).
fof(f117,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( ~ sQ4_spl
| member(pair(combK,ap_contractE_sk2q(combK,p,r)),contract) ),
inference(resolution,[status(thm)],[f110,f65]) ).
fof(f120,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f73]) ).
fof(f121,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f120]) ).
fof(f122,plain,
( ~ sQ2_spl
| r != comb_app(combK,ap_contractE_sk3q(combK,p,r)) ),
inference(resolution,[status(thm)],[f104,f76]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ap_contractE_c3(X1,X2,X0)
| ap_contractE_c2(X1,X2,X0)
| ap_contractE_c1(X1,X2,X0)
| ~ member(pair(comb_app(X1,X2),X0),contract)
| X0 = comb_app(X1,ap_contractE_sk3q(X1,X2,X0)) ),
inference(resolution,[status(thm)],[f72,f52]) ).
fof(f124,plain,
! [X0,X1,X2] :
( X1 = comb_app(combK,X0)
| ap_contractE_c3(X1,X2,X0)
| ap_contractE_c2(X1,X2,X0)
| ~ member(pair(comb_app(X1,X2),X0),contract)
| X0 = comb_app(X1,ap_contractE_sk3q(X1,X2,X0)) ),
inference(resolution,[status(thm)],[f123,f58]) ).
fof(f126,plain,
( combK = comb_app(combK,r)
| ap_contractE_c3(combK,p,r)
| ap_contractE_c2(combK,p,r)
| r = comb_app(combK,ap_contractE_sk3q(combK,p,r)) ),
inference(resolution,[status(thm)],[f124,f75]) ).
fof(f127,definition,
( sQ6_spl
<=> r = comb_app(combK,ap_contractE_sk3q(combK,p,r)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ6_spl
| r = comb_app(combK,ap_contractE_sk3q(combK,p,r)) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( sQ5_spl
| sQ4_spl
| sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f126,f127,f106,f109,f112]) ).
fof(f131,plain,
( ~ sQ3_spl
| combK = comb_app(comb_app(combS,ap_contractE_sk1p(combK,p,r)),ap_contractE_sk1q(combK,p,r)) ),
inference(resolution,[status(thm)],[f107,f64]) ).
fof(f133,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f35]) ).
fof(f134,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f133]) ).
fof(f135,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f122]) ).
fof(f136,plain,
( ~ sQ6_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f135]) ).
fof(f137,plain,
$false,
inference(sat_refutation,[status(thm)],[f115,f117,f121,f130,f134,f136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL091-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n026.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Mon Sep 21 14:12:57 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.14/5.41 % Refutation found
% 0.14/5.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.44 % Elapsed time: 0.049933 seconds
% 0.14/5.44 % CPU time: 0.139101 seconds
% 0.14/5.44 % Total memory used: 58.187 MB
% 0.14/5.44 % Net memory used: 58.067 MB
%------------------------------------------------------------------------------