%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL092-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 0.13s 0.48s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 22
% Syntax : Number of formulae : 74 ( 8 unt; 8 def)
% Number of atoms : 156 ( 26 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 155 ( 73 ~; 74 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 9 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [P,Q] : combK != comb_app(P,Q),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [P,Q] :
( member(Q,comb)
| ~ member(comb_app(P,Q),comb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [P] :
( member(pair(P,P),parcontract)
| ~ member(P,comb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [R] :
( R = combK
| ~ member(pair(combK,R),parcontract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [P,Q,R] :
( ap_parcontractE_c4(P,Q,R)
| ap_parcontractE_c3(P,Q,R)
| ap_parcontractE_c2(P,Q,R)
| ap_parcontractE_c1(P,Q,R)
| ~ member(pair(comb_app(P,Q),R),parcontract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [P,Q,R] :
( member(comb_app(P,Q),comb)
| ~ ap_parcontractE_c1(P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [P,Q,R] :
( R = comb_app(P,Q)
| ~ ap_parcontractE_c1(P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [P,Q,R] :
( P = comb_app(combK,R)
| ~ ap_parcontractE_c2(P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [P,Q,R] :
( P = comb_app(comb_app(combS,ap_parcontractE_sk1p(P,Q,R)),ap_parcontractE_sk1q(P,Q,R))
| ~ ap_parcontractE_c3(P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [P,Q,R] :
( member(pair(P,ap_parcontractE_sk2q(P,Q,R)),parcontract)
| ~ ap_parcontractE_c4(P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [P,Q,R] :
( member(pair(Q,ap_parcontractE_sk2s(P,Q,R)),parcontract)
| ~ ap_parcontractE_c4(P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [P,Q,R] :
( R = comb_app(ap_parcontractE_sk2q(P,Q,R),ap_parcontractE_sk2s(P,Q,R))
| ~ ap_parcontractE_c4(P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,hypothesis,
member(pair(comb_app(combK,p),r),parcontract),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
! [PP] :
( ~ member(pair(p,PP),parcontract)
| r != comb_app(combK,PP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,plain,
! [X0,X1] : combK != comb_app(X0,X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f66,plain,
! [Q] :
( member(Q,comb)
| ! [P] : ~ member(comb_app(P,Q),comb) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f67,plain,
! [X0,X1] :
( member(X1,comb)
| ~ member(comb_app(X0,X1),comb) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f97,plain,
! [X0] :
( member(pair(X0,X0),parcontract)
| ~ member(X0,comb) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f103,plain,
! [X0] :
( X0 = combK
| ~ member(pair(combK,X0),parcontract) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ap_parcontractE_c4(X0,X1,X2)
| ap_parcontractE_c3(X0,X1,X2)
| ap_parcontractE_c2(X0,X1,X2)
| ap_parcontractE_c1(X0,X1,X2)
| ~ member(pair(comb_app(X0,X1),X2),parcontract) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f108,plain,
! [P,Q] :
( member(comb_app(P,Q),comb)
| ! [R] : ~ ap_parcontractE_c1(P,Q,R) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f109,plain,
! [X0,X1,X2] :
( member(comb_app(X0,X1),comb)
| ~ ap_parcontractE_c1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,plain,
! [X0,X1,X2] :
( X2 = comb_app(X0,X1)
| ~ ap_parcontractE_c1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f115,plain,
! [P,R] :
( P = comb_app(combK,R)
| ! [Q] : ~ ap_parcontractE_c2(P,Q,R) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f116,plain,
! [X0,X1,X2] :
( X0 = comb_app(combK,X2)
| ~ ap_parcontractE_c2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f122,plain,
! [X0,X1,X2] :
( X0 = comb_app(comb_app(combS,ap_parcontractE_sk1p(X0,X1,X2)),ap_parcontractE_sk1q(X0,X1,X2))
| ~ ap_parcontractE_c3(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f123,plain,
! [X0,X1,X2] :
( member(pair(X0,ap_parcontractE_sk2q(X0,X1,X2)),parcontract)
| ~ ap_parcontractE_c4(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f124,plain,
! [X0,X1,X2] :
( member(pair(X1,ap_parcontractE_sk2s(X0,X1,X2)),parcontract)
| ~ ap_parcontractE_c4(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f125,plain,
! [X0,X1,X2] :
( X2 = comb_app(ap_parcontractE_sk2q(X0,X1,X2),ap_parcontractE_sk2s(X0,X1,X2))
| ~ ap_parcontractE_c4(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f126,plain,
member(pair(comb_app(combK,p),r),parcontract),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f127,plain,
! [X0] :
( ~ member(pair(p,X0),parcontract)
| r != comb_app(combK,X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f203,plain,
( r != comb_app(combK,p)
| ~ member(p,comb) ),
inference(resolution,[status(thm)],[f97,f127]) ).
fof(f208,definition,
( sQ7_spl
<=> member(p,comb) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f211,definition,
( sQ8_spl
<=> r = comb_app(combK,p) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( ~ sQ8_spl
| r = comb_app(combK,p) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f213,plain,
( sQ8_spl
| r != comb_app(combK,p) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f203,f208,f211]) ).
fof(f286,plain,
( ap_parcontractE_c4(combK,p,r)
| ap_parcontractE_c3(combK,p,r)
| ap_parcontractE_c2(combK,p,r)
| ap_parcontractE_c1(combK,p,r) ),
inference(resolution,[status(thm)],[f107,f126]) ).
fof(f342,definition,
( sQ31_spl
<=> ap_parcontractE_c1(combK,p,r) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( ~ sQ31_spl
| ap_parcontractE_c1(combK,p,r) ),
inference(component_clause,[status(thm)],[f342]) ).
fof(f345,definition,
( sQ32_spl
<=> ap_parcontractE_c2(combK,p,r) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( ~ sQ32_spl
| ap_parcontractE_c2(combK,p,r) ),
inference(component_clause,[status(thm)],[f345]) ).
fof(f348,definition,
( sQ33_spl
<=> ap_parcontractE_c3(combK,p,r) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f349,plain,
( ~ sQ33_spl
| ap_parcontractE_c3(combK,p,r) ),
inference(component_clause,[status(thm)],[f348]) ).
fof(f351,definition,
( sQ34_spl
<=> ap_parcontractE_c4(combK,p,r) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f352,plain,
( ~ sQ34_spl
| ap_parcontractE_c4(combK,p,r) ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f354,plain,
( sQ34_spl
| sQ33_spl
| sQ32_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f286,f342,f345,f348,f351]) ).
fof(f355,plain,
( ~ sQ34_spl
| r = comb_app(ap_parcontractE_sk2q(combK,p,r),ap_parcontractE_sk2s(combK,p,r)) ),
inference(resolution,[status(thm)],[f352,f125]) ).
fof(f356,plain,
( ~ sQ34_spl
| member(pair(p,ap_parcontractE_sk2s(combK,p,r)),parcontract) ),
inference(resolution,[status(thm)],[f352,f124]) ).
fof(f357,plain,
( ~ sQ34_spl
| member(pair(combK,ap_parcontractE_sk2q(combK,p,r)),parcontract) ),
inference(resolution,[status(thm)],[f352,f123]) ).
fof(f359,plain,
( ~ sQ33_spl
| combK = comb_app(comb_app(combS,ap_parcontractE_sk1p(combK,p,r)),ap_parcontractE_sk1q(combK,p,r)) ),
inference(resolution,[status(thm)],[f349,f122]) ).
fof(f361,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f359,f57]) ).
fof(f362,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f361]) ).
fof(f372,plain,
( ~ sQ32_spl
| combK = comb_app(combK,r) ),
inference(resolution,[status(thm)],[f346,f116]) ).
fof(f377,plain,
( ~ sQ31_spl
| r = comb_app(combK,p) ),
inference(resolution,[status(thm)],[f343,f110]) ).
fof(f378,plain,
( ~ sQ31_spl
| sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f377,f213]) ).
fof(f379,plain,
( ~ sQ31_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f378]) ).
fof(f394,plain,
( ~ sQ8_spl
| member(p,comb)
| ~ member(r,comb) ),
inference(paramodulation,[status(thm)],[f212,f67]) ).
fof(f395,plain,
! [X0] :
( ~ sQ8_spl
| member(r,comb)
| ~ ap_parcontractE_c1(combK,p,X0) ),
inference(paramodulation,[status(thm)],[f212,f109]) ).
fof(f432,definition,
( sQ42_spl
<=> member(r,comb) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( ~ sQ8_spl
| sQ7_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f394,f432,f208,f211]) ).
fof(f446,definition,
! [X0] :
( sQ45_spl
<=> ~ ap_parcontractE_c1(combK,p,X0) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f447,plain,
! [X0] :
( ~ sQ45_spl
| ~ ap_parcontractE_c1(combK,p,X0) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( ~ sQ8_spl
| sQ42_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f395,f446,f432,f211]) ).
fof(f474,plain,
( ~ sQ34_spl
| r != comb_app(combK,ap_parcontractE_sk2s(combK,p,r)) ),
inference(resolution,[status(thm)],[f356,f127]) ).
fof(f475,plain,
( ~ sQ34_spl
| ap_parcontractE_sk2q(combK,p,r) = combK ),
inference(resolution,[status(thm)],[f357,f103]) ).
fof(f501,plain,
( ~ sQ34_spl
| r = comb_app(combK,ap_parcontractE_sk2s(combK,p,r)) ),
inference(forward_demodulation,[status(thm)],[f475,f355]) ).
fof(f502,plain,
( ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f474]) ).
fof(f503,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f505,plain,
( ~ sQ31_spl
| ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f343,f447]) ).
fof(f506,plain,
( ~ sQ31_spl
| ~ sQ45_spl ),
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f507,plain,
( ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f372,f57]) ).
fof(f508,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f509,plain,
$false,
inference(sat_refutation,[status(thm)],[f214,f354,f362,f379,f445,f449,f503,f506,f508]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL092-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 14:13:07 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.13/0.48 % Refutation found
% 0.13/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.50 % Elapsed time: 0.132313 seconds
% 0.13/0.50 % CPU time: 0.758012 seconds
% 0.13/0.50 % Total memory used: 102.968 MB
% 0.13/0.50 % Net memory used: 101.708 MB
%------------------------------------------------------------------------------