%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL090-3 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of formulae : 68 ( 18 unt; 8 def)
% Number of atoms : 137 ( 26 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 124 ( 55 ~; 61 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 9 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 56 !; 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(f7,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(f10,axiom,
! [P,Q,R] :
( P = comb_app(combK,R)
| ~ ap_contractE_c1(P,Q,R) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,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(f16,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(f19,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(f22,axiom,
! [R] : ~ member(pair(combK,R),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [R] : ~ member(pair(combS,R),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,plain,
combK != combS,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f27,plain,
! [X0,X1] : combS != comb_app(X0,X1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
! [P1,P2] :
( P1 = P2
| ! [Q1,Q2] : comb_app(P1,Q1) != comb_app(P2,Q2) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| comb_app(X0,X1) != comb_app(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f33,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)],[f7]) ).
fof(f38,plain,
! [P,R] :
( P = comb_app(combK,R)
| ! [Q] : ~ ap_contractE_c1(P,Q,R) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f39,plain,
! [X0,X1,X2] :
( X0 = comb_app(combK,X2)
| ~ ap_contractE_c1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f45,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)],[f15]) ).
fof(f46,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)],[f16]) ).
fof(f50,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)],[f19]) ).
fof(f54,plain,
! [X0] : ~ member(pair(combK,X0),contract),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f55,plain,
! [X0] : ~ member(pair(combS,X0),contract),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f56,plain,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ap_contractE_c4(X0,X2,X1)
| ap_contractE_c3(X0,X2,X1)
| ap_contractE_c2(X0,X2,X1)
| ~ member(pair(comb_app(X0,X2),X1),contract)
| X0 = comb_app(combK,X1) ),
inference(resolution,[status(thm)],[f39,f33]) ).
fof(f60,plain,
( ap_contractE_c4(comb_app(combS,combK),combK,r)
| ap_contractE_c3(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| comb_app(combS,combK) = comb_app(combK,r) ),
inference(resolution,[status(thm)],[f59,f56]) ).
fof(f61,definition,
( sQ0_spl
<=> comb_app(combS,combK) = comb_app(combK,r) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ0_spl
| comb_app(combS,combK) = comb_app(combK,r) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,definition,
( sQ1_spl
<=> ap_contractE_c2(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ1_spl
| ap_contractE_c2(comb_app(combS,combK),combK,r) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,definition,
( sQ2_spl
<=> ap_contractE_c3(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ2_spl
| ap_contractE_c3(comb_app(combS,combK),combK,r) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,definition,
( sQ3_spl
<=> ap_contractE_c4(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ3_spl
| ap_contractE_c4(comb_app(combS,combK),combK,r) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,plain,
( sQ3_spl
| sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f60,f61,f64,f67,f70]) ).
fof(f74,plain,
( ~ sQ3_spl
| member(pair(combK,ap_contractE_sk3q(comb_app(combS,combK),combK,r)),contract) ),
inference(resolution,[status(thm)],[f71,f50]) ).
fof(f76,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f54]) ).
fof(f77,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f76]) ).
fof(f78,plain,
( ~ sQ2_spl
| member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract) ),
inference(resolution,[status(thm)],[f68,f46]) ).
fof(f80,plain,
( ~ sQ2_spl
| ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c3(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))
| combS = comb_app(combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(resolution,[status(thm)],[f78,f59]) ).
fof(f81,definition,
( sQ4_spl
<=> combS = comb_app(combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ4_spl
| combS = comb_app(combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,definition,
( sQ5_spl
<=> ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( ~ sQ5_spl
| ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,definition,
( sQ6_spl
<=> ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ6_spl
| ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,definition,
( sQ7_spl
<=> ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ7_spl
| ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( ~ sQ2_spl
| sQ7_spl
| sQ6_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f80,f81,f84,f87,f90,f67]) ).
fof(f94,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f27]) ).
fof(f95,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f94]) ).
fof(f97,plain,
( ~ sQ1_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)],[f65,f45]) ).
fof(f105,plain,
( ~ sQ7_spl
| member(pair(combK,ap_contractE_sk3q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract) ),
inference(resolution,[status(thm)],[f91,f50]) ).
fof(f107,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f54]) ).
fof(f108,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f107]) ).
fof(f109,plain,
( ~ sQ6_spl
| member(pair(combS,ap_contractE_sk2q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract) ),
inference(resolution,[status(thm)],[f88,f46]) ).
fof(f111,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f109,f55]) ).
fof(f112,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( ~ sQ1_spl
| combS = comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)) ),
inference(resolution,[status(thm)],[f97,f29]) ).
fof(f124,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f114,f27]) ).
fof(f125,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( ~ sQ0_spl
| combS = combK ),
inference(resolution,[status(thm)],[f62,f29]) ).
fof(f137,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f127,f25]) ).
fof(f138,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f137]) ).
fof(f142,plain,
( ~ sQ5_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)],[f85,f45]) ).
fof(f143,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f27]) ).
fof(f144,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f143]) ).
fof(f145,plain,
$false,
inference(sat_refutation,[status(thm)],[f73,f77,f93,f95,f108,f112,f125,f138,f144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL090-3 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.36 % Computer : n015.cluster.edu
% 0.11/5.36 % Model : x86_64 x86_64
% 0.11/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.36 % Memory : 8046.5625MB
% 0.11/5.36 % OS : Linux 6.8.0-71-generic
% 0.11/5.36 % CPULimit : 300
% 0.11/5.36 % WCLimit : 300
% 0.11/5.36 % DateTime : Mon Sep 21 14:13:27 UTC 2026
% 0.11/5.36 % CPUTime :
% 0.11/5.38 % Drodi V4.1.1
% 0.11/5.40 % Refutation found
% 0.11/5.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.42 % Elapsed time: 0.048387 seconds
% 0.14/5.42 % CPU time: 0.148292 seconds
% 0.14/5.42 % Total memory used: 71.028 MB
% 0.14/5.42 % Net memory used: 70.761 MB
%------------------------------------------------------------------------------