%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL090-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 0.11s 0.37s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 58 ( 16 unt; 5 def)
% Number of atoms : 125 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 115 ( 48 ~; 62 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 66 ( 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
combK != combS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [P,Q] : combS != comb_app(P,Q),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [P1,Q1,P2,Q2] :
( P1 = P2
| comb_app(P1,Q1) != comb_app(P2,Q2) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [P,Q,R] :
( P = comb_app(combK,R)
| ~ ap_contractE_c1(P,Q,R) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [R] : ~ member(pair(combK,R),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [R] : ~ member(pair(combS,R),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,plain,
combK != combS,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f35,plain,
! [X0,X1] : combS != comb_app(X0,X1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f36,plain,
! [P1,P2] :
( P1 = P2
| ! [Q1,Q2] : comb_app(P1,Q1) != comb_app(P2,Q2) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| comb_app(X0,X1) != comb_app(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f51,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(f56,plain,
! [P,R] :
( P = comb_app(combK,R)
| ! [Q] : ~ ap_contractE_c1(P,Q,R) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f57,plain,
! [X0,X1,X2] :
( X0 = comb_app(combK,X2)
| ~ ap_contractE_c1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f63,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(f64,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(f68,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] : ~ member(pair(combK,X0),contract),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f73,plain,
! [X0] : ~ member(pair(combS,X0),contract),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f74,plain,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ap_contractE_c4(X0,X1,X2)
| ap_contractE_c2(X0,X1,X2)
| ap_contractE_c1(X0,X1,X2)
| ~ member(pair(comb_app(X0,X1),X2),contract)
| member(pair(X0,ap_contractE_sk2q(X0,X1,X2)),contract) ),
inference(resolution,[status(thm)],[f64,f51]) ).
fof(f81,plain,
! [X0,X1,X2] :
( X0 = comb_app(combK,X2)
| ap_contractE_c4(X0,X1,X2)
| ap_contractE_c2(X0,X1,X2)
| ~ member(pair(comb_app(X0,X1),X2),contract)
| member(pair(X0,ap_contractE_sk2q(X0,X1,X2)),contract) ),
inference(resolution,[status(thm)],[f77,f57]) ).
fof(f85,plain,
! [X0,X1] :
( combS = comb_app(combK,X1)
| ap_contractE_c4(combS,X0,X1)
| ap_contractE_c2(combS,X0,X1)
| ~ member(pair(comb_app(combS,X0),X1),contract) ),
inference(resolution,[status(thm)],[f81,f73]) ).
fof(f87,plain,
! [X0,X1] :
( ap_contractE_c4(combS,X0,X1)
| ap_contractE_c2(combS,X0,X1)
| ~ member(pair(comb_app(combS,X0),X1),contract) ),
inference(forward_subsumption_resolution,[status(thm)],[f85,f35]) ).
fof(f89,plain,
! [X0,X1,X2] :
( comb_app(combS,X0) = comb_app(combK,X2)
| ap_contractE_c4(comb_app(combS,X0),X1,X2)
| ap_contractE_c2(comb_app(combS,X0),X1,X2)
| ~ member(pair(comb_app(comb_app(combS,X0),X1),X2),contract)
| ap_contractE_c4(combS,X0,ap_contractE_sk2q(comb_app(combS,X0),X1,X2))
| ap_contractE_c2(combS,X0,ap_contractE_sk2q(comb_app(combS,X0),X1,X2)) ),
inference(resolution,[status(thm)],[f87,f81]) ).
fof(f91,plain,
( comb_app(combS,combK) = comb_app(combK,r)
| ap_contractE_c4(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(resolution,[status(thm)],[f89,f74]) ).
fof(f93,definition,
( sQ0_spl
<=> ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ0_spl
| ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,definition,
( sQ1_spl
<=> ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( ~ sQ1_spl
| ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,definition,
( sQ2_spl
<=> ap_contractE_c2(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ2_spl
| ap_contractE_c2(comb_app(combS,combK),combK,r) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,definition,
( sQ3_spl
<=> ap_contractE_c4(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( ~ sQ3_spl
| ap_contractE_c4(comb_app(combS,combK),combK,r) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,definition,
( sQ4_spl
<=> comb_app(combS,combK) = comb_app(combK,r) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ4_spl
| comb_app(combS,combK) = comb_app(combK,r) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( sQ4_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f91,f93,f96,f99,f102,f105]) ).
fof(f111,plain,
( ~ sQ4_spl
| combS = combK ),
inference(resolution,[status(thm)],[f106,f37]) ).
fof(f126,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f111,f33]) ).
fof(f127,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f126]) ).
fof(f128,plain,
( ~ sQ3_spl
| member(pair(combK,ap_contractE_sk3q(comb_app(combS,combK),combK,r)),contract) ),
inference(resolution,[status(thm)],[f103,f68]) ).
fof(f130,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f72]) ).
fof(f131,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f138,plain,
( ~ sQ2_spl
| comb_app(combS,combK) = comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r)) ),
inference(resolution,[status(thm)],[f100,f63]) ).
fof(f210,plain,
( ~ sQ2_spl
| combS = comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)) ),
inference(resolution,[status(thm)],[f138,f37]) ).
fof(f225,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f35]) ).
fof(f226,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f225]) ).
fof(f227,plain,
( ~ sQ0_spl
| combS = comb_app(comb_app(combS,ap_contractE_sk1p(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),ap_contractE_sk1q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))) ),
inference(resolution,[status(thm)],[f94,f63]) ).
fof(f229,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f227,f35]) ).
fof(f230,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f244,plain,
( ~ sQ1_spl
| member(pair(combK,ap_contractE_sk3q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract) ),
inference(resolution,[status(thm)],[f97,f68]) ).
fof(f246,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f244,f72]) ).
fof(f247,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f246]) ).
fof(f248,plain,
$false,
inference(sat_refutation,[status(thm)],[f108,f127,f131,f226,f230,f247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL090-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n011.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 14:10:26 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.11/0.37 % Refutation found
% 0.11/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.40 % Elapsed time: 0.053569 seconds
% 0.11/0.40 % CPU time: 0.186465 seconds
% 0.11/0.40 % Total memory used: 82.772 MB
% 0.11/0.40 % Net memory used: 82.496 MB
%------------------------------------------------------------------------------