%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL093-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 0.44s
% 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(f3,axiom,
! [P,Q] : combS != comb_app(P,Q),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [P,Q] :
( member(Q,comb)
| ~ member(comb_app(P,Q),comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [P] :
( member(pair(P,P),parcontract)
| ~ member(P,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [R] :
( R = combS
| ~ member(pair(combS,R),parcontract) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [P,Q,R] :
( member(comb_app(P,Q),comb)
| ~ ap_parcontractE_c1(P,Q,R) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [P,Q,R] :
( R = comb_app(P,Q)
| ~ ap_parcontractE_c1(P,Q,R) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [P,Q,R] :
( P = comb_app(combK,R)
| ~ ap_parcontractE_c2(P,Q,R) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f54,hypothesis,
member(pair(comb_app(combS,p),r),parcontract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
! [PP] :
( ~ member(pair(p,PP),parcontract)
| r != comb_app(combS,PP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,plain,
! [X0,X1] : combS != comb_app(X0,X1),
inference(cnf_transformation,[status(thm)],[f3]) ).
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(f106,plain,
! [X0] :
( X0 = combS
| ~ member(pair(combS,X0),parcontract) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
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(combS,p),r),parcontract),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f127,plain,
! [X0] :
( ~ member(pair(p,X0),parcontract)
| r != comb_app(combS,X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f203,plain,
( r != comb_app(combS,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(combS,p) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( ~ sQ8_spl
| r = comb_app(combS,p) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f213,plain,
( sQ8_spl
| r != comb_app(combS,p) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f203,f208,f211]) ).
fof(f287,plain,
( ap_parcontractE_c4(combS,p,r)
| ap_parcontractE_c3(combS,p,r)
| ap_parcontractE_c2(combS,p,r)
| ap_parcontractE_c1(combS,p,r) ),
inference(resolution,[status(thm)],[f107,f126]) ).
fof(f343,definition,
( sQ31_spl
<=> ap_parcontractE_c1(combS,p,r) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( ~ sQ31_spl
| ap_parcontractE_c1(combS,p,r) ),
inference(component_clause,[status(thm)],[f343]) ).
fof(f346,definition,
( sQ32_spl
<=> ap_parcontractE_c2(combS,p,r) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f347,plain,
( ~ sQ32_spl
| ap_parcontractE_c2(combS,p,r) ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f349,definition,
( sQ33_spl
<=> ap_parcontractE_c3(combS,p,r) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f350,plain,
( ~ sQ33_spl
| ap_parcontractE_c3(combS,p,r) ),
inference(component_clause,[status(thm)],[f349]) ).
fof(f352,definition,
( sQ34_spl
<=> ap_parcontractE_c4(combS,p,r) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( ~ sQ34_spl
| ap_parcontractE_c4(combS,p,r) ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f355,plain,
( sQ34_spl
| sQ33_spl
| sQ32_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f287,f343,f346,f349,f352]) ).
fof(f356,plain,
( ~ sQ34_spl
| r = comb_app(ap_parcontractE_sk2q(combS,p,r),ap_parcontractE_sk2s(combS,p,r)) ),
inference(resolution,[status(thm)],[f353,f125]) ).
fof(f357,plain,
( ~ sQ34_spl
| member(pair(p,ap_parcontractE_sk2s(combS,p,r)),parcontract) ),
inference(resolution,[status(thm)],[f353,f124]) ).
fof(f358,plain,
( ~ sQ34_spl
| member(pair(combS,ap_parcontractE_sk2q(combS,p,r)),parcontract) ),
inference(resolution,[status(thm)],[f353,f123]) ).
fof(f369,plain,
( ~ sQ33_spl
| combS = comb_app(comb_app(combS,ap_parcontractE_sk1p(combS,p,r)),ap_parcontractE_sk1q(combS,p,r)) ),
inference(resolution,[status(thm)],[f350,f122]) ).
fof(f371,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f369,f58]) ).
fof(f372,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f371]) ).
fof(f375,plain,
( ~ sQ32_spl
| combS = comb_app(combK,r) ),
inference(resolution,[status(thm)],[f347,f116]) ).
fof(f380,plain,
( ~ sQ31_spl
| r = comb_app(combS,p) ),
inference(resolution,[status(thm)],[f344,f110]) ).
fof(f381,plain,
( ~ sQ31_spl
| sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f380,f213]) ).
fof(f382,plain,
( ~ sQ31_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f381]) ).
fof(f395,plain,
( ~ sQ8_spl
| member(p,comb)
| ~ member(r,comb) ),
inference(paramodulation,[status(thm)],[f212,f67]) ).
fof(f396,plain,
! [X0] :
( ~ sQ8_spl
| member(r,comb)
| ~ ap_parcontractE_c1(combS,p,X0) ),
inference(paramodulation,[status(thm)],[f212,f109]) ).
fof(f427,definition,
( sQ40_spl
<=> member(r,comb) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( ~ sQ8_spl
| sQ7_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f395,f427,f208,f211]) ).
fof(f441,definition,
! [X0] :
( sQ43_spl
<=> ~ ap_parcontractE_c1(combS,p,X0) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f442,plain,
! [X0] :
( ~ sQ43_spl
| ~ ap_parcontractE_c1(combS,p,X0) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( ~ sQ8_spl
| sQ40_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f396,f441,f427,f211]) ).
fof(f477,plain,
( ~ sQ34_spl
| r != comb_app(combS,ap_parcontractE_sk2s(combS,p,r)) ),
inference(resolution,[status(thm)],[f357,f127]) ).
fof(f478,plain,
( ~ sQ34_spl
| ap_parcontractE_sk2q(combS,p,r) = combS ),
inference(resolution,[status(thm)],[f358,f106]) ).
fof(f504,plain,
( ~ sQ34_spl
| r = comb_app(combS,ap_parcontractE_sk2s(combS,p,r)) ),
inference(forward_demodulation,[status(thm)],[f478,f356]) ).
fof(f505,plain,
( ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f477]) ).
fof(f506,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f508,plain,
( ~ sQ31_spl
| ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f344,f442]) ).
fof(f509,plain,
( ~ sQ31_spl
| ~ sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f508]) ).
fof(f510,plain,
( ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f375,f58]) ).
fof(f511,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f512,plain,
$false,
inference(sat_refutation,[status(thm)],[f214,f355,f372,f382,f440,f444,f506,f509,f511]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL093-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 14:10:11 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.44 % Refutation found
% 0.13/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.47 % Elapsed time: 0.104620 seconds
% 0.13/0.47 % CPU time: 0.534049 seconds
% 0.13/0.47 % Total memory used: 95.997 MB
% 0.13/0.47 % Net memory used: 95.104 MB
%------------------------------------------------------------------------------