%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO111+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 12:24:06 PM UTC 2026
% Result : Theorem 0.24s 0.79s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 57 ( 19 unt; 0 def)
% Number of atoms : 238 ( 38 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 282 ( 101 ~; 103 |; 68 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 132 ( 119 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C1)
=> incident_c(P,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [P,C] :
( end_point(P,C)
<=> ( ! [C1,C2] :
( ( incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
=> ( part_of(C2,C1)
| part_of(C1,C2) ) )
& incident_c(P,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [P,C] :
( inner_point(P,C)
<=> ( ~ end_point(P,C)
& incident_c(P,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
<=> ( ? [Cpp] :
( inner_point(Q,Cpp)
& end_point(R,Cpp)
& end_point(P,Cpp)
& part_of(Cpp,C) )
& P != R ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> ( P != R
& Q != R
& P != Q
& incident_c(R,C)
& incident_c(Q,C)
& incident_c(P,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> ( P != R
& Q != R
& P != Q
& incident_c(R,C)
& incident_c(Q,C)
& incident_c(P,C) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C)
| ~ incident_c(P,C1) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [C,C1] :
( ( ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) )
| part_of(C1,C) )
& ( ! [P] :
( incident_c(P,C)
| ~ incident_c(P,C1) )
| ~ part_of(C1,C) ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
( ! [C,C1] :
( ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) )
| part_of(C1,C) )
& ! [C,C1] :
( ! [P] :
( incident_c(P,C)
| ~ incident_c(P,C1) )
| ~ part_of(C1,C) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
( ! [C,C1] :
( ( ~ incident_c(sK0_skl(C1,C),C)
& incident_c(sK0_skl(C1,C),C1) )
| part_of(C1,C) )
& ! [C,C1] :
( ! [P] :
( incident_c(P,C)
| ~ incident_c(P,C1) )
| ~ part_of(C1,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(P,sK0_skl(C1,C))],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( incident_c(X2,X1)
| ~ incident_c(X2,X0)
| ~ part_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f36,plain,
! [P,C] :
( end_point(P,C)
<=> ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f37,plain,
! [P,C] :
( ( ? [C1,C2] :
( ~ part_of(C2,C1)
& ~ part_of(C1,C2)
& incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
| ~ incident_c(P,C)
| end_point(P,C) )
& ( ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) )
| ~ end_point(P,C) ) ),
inference(NNF_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
( ! [P,C] :
( ? [C1,C2] :
( ~ part_of(C2,C1)
& ~ part_of(C1,C2)
& incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
| ~ incident_c(P,C)
| end_point(P,C) )
& ! [P,C] :
( ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) )
| ~ end_point(P,C) ) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f39,plain,
( ! [P,C] :
( ( ~ part_of(sK3_skl(C,P),sK2_skl(C,P))
& ~ part_of(sK2_skl(C,P),sK3_skl(C,P))
& incident_c(P,sK3_skl(C,P))
& incident_c(P,sK2_skl(C,P))
& part_of(sK3_skl(C,P),C)
& part_of(sK2_skl(C,P),C) )
| ~ incident_c(P,C)
| end_point(P,C) )
& ! [P,C] :
( ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) )
| ~ end_point(P,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(C1,sK2_skl(C,P)),skolemize(C2,sK3_skl(C,P))],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( incident_c(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f48,plain,
! [P,C] :
( ( end_point(P,C)
| ~ incident_c(P,C)
| inner_point(P,C) )
& ( ( ~ end_point(P,C)
& incident_c(P,C) )
| ~ inner_point(P,C) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f49,plain,
( ! [P,C] :
( end_point(P,C)
| ~ incident_c(P,C)
| inner_point(P,C) )
& ! [P,C] :
( ( ~ end_point(P,C)
& incident_c(P,C) )
| ~ inner_point(P,C) ) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( incident_c(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f105,plain,
! [C,P,Q,R] :
( ( ! [Cpp] :
( ~ inner_point(Q,Cpp)
| ~ end_point(R,Cpp)
| ~ end_point(P,Cpp)
| ~ part_of(Cpp,C) )
| P = R
| between_c(C,P,Q,R) )
& ( ( ? [Cpp] :
( inner_point(Q,Cpp)
& end_point(R,Cpp)
& end_point(P,Cpp)
& part_of(Cpp,C) )
& P != R )
| ~ between_c(C,P,Q,R) ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f106,plain,
( ! [C,P,Q,R] :
( ! [Cpp] :
( ~ inner_point(Q,Cpp)
| ~ end_point(R,Cpp)
| ~ end_point(P,Cpp)
| ~ part_of(Cpp,C) )
| P = R
| between_c(C,P,Q,R) )
& ! [C,P,Q,R] :
( ( ? [Cpp] :
( inner_point(Q,Cpp)
& end_point(R,Cpp)
& end_point(P,Cpp)
& part_of(Cpp,C) )
& P != R )
| ~ between_c(C,P,Q,R) ) ),
inference(miniscoping,[status(thm)],[f105]) ).
fof(f107,plain,
( ! [C,P,Q,R] :
( ! [Cpp] :
( ~ inner_point(Q,Cpp)
| ~ end_point(R,Cpp)
| ~ end_point(P,Cpp)
| ~ part_of(Cpp,C) )
| P = R
| between_c(C,P,Q,R) )
& ! [C,P,Q,R] :
( ( inner_point(Q,sK13_skl(R,Q,P,C))
& end_point(R,sK13_skl(R,Q,P,C))
& end_point(P,sK13_skl(R,Q,P,C))
& part_of(sK13_skl(R,Q,P,C),C)
& P != R )
| ~ between_c(C,P,Q,R) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(Cpp,sK13_skl(R,Q,P,C))],[f106]) ).
fof(f108,plain,
! [X0,X1,X2,X3] :
( X1 != X3
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
! [X0,X1,X2,X3] :
( part_of(sK13_skl(X3,X2,X1,X0),X0)
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f110,plain,
! [X0,X1,X2,X3] :
( end_point(X1,sK13_skl(X3,X2,X1,X0))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( end_point(X3,sK13_skl(X3,X2,X1,X0))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( inner_point(X2,sK13_skl(X3,X2,X1,X0))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f114,plain,
? [C,P,Q,R] :
( ( P = R
| Q = R
| P = Q
| ~ incident_c(R,C)
| ~ incident_c(Q,C)
| ~ incident_c(P,C) )
& between_c(C,P,Q,R) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f115,plain,
( ( sK15_skl = sK17_skl
| sK16_skl = sK17_skl
| sK15_skl = sK16_skl
| ~ incident_c(sK17_skl,sK14_skl)
| ~ incident_c(sK16_skl,sK14_skl)
| ~ incident_c(sK15_skl,sK14_skl) )
& between_c(sK14_skl,sK15_skl,sK16_skl,sK17_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl,sK17_skl]),skolemize(C,sK14_skl),skolemize(P,sK15_skl),skolemize(Q,sK16_skl),skolemize(R,sK17_skl)],[f114]) ).
fof(f116,plain,
between_c(sK14_skl,sK15_skl,sK16_skl,sK17_skl),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
( sK15_skl = sK17_skl
| sK16_skl = sK17_skl
| sK15_skl = sK16_skl
| ~ incident_c(sK17_skl,sK14_skl)
| ~ incident_c(sK16_skl,sK14_skl)
| ~ incident_c(sK15_skl,sK14_skl) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
! [X0,X1,X2] : ~ between_c(X0,X1,X2,X1),
inference(destructive_equality_resolution,[status(thm)],[f108]) ).
fof(f380,plain,
part_of(sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl),sK14_skl),
inference(resolution,[status(thm)],[f109,f116]) ).
fof(f384,plain,
! [X0] :
( incident_c(X0,sK14_skl)
| ~ incident_c(X0,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl)) ),
inference(resolution,[status(thm)],[f380,f24]) ).
fof(f386,plain,
end_point(sK15_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl)),
inference(resolution,[status(thm)],[f110,f116]) ).
fof(f395,plain,
~ inner_point(sK15_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl)),
inference(resolution,[status(thm)],[f386,f51]) ).
fof(f396,plain,
incident_c(sK15_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl)),
inference(resolution,[status(thm)],[f386,f40]) ).
fof(f409,plain,
incident_c(sK15_skl,sK14_skl),
inference(resolution,[status(thm)],[f384,f396]) ).
fof(f422,plain,
( sK15_skl = sK17_skl
| sK16_skl = sK17_skl
| sK15_skl = sK16_skl
| ~ incident_c(sK17_skl,sK14_skl)
| ~ incident_c(sK16_skl,sK14_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f117,f409]) ).
fof(f547,plain,
end_point(sK17_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl)),
inference(resolution,[status(thm)],[f111,f116]) ).
fof(f557,plain,
~ inner_point(sK17_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl)),
inference(resolution,[status(thm)],[f547,f51]) ).
fof(f558,plain,
incident_c(sK17_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl)),
inference(resolution,[status(thm)],[f547,f40]) ).
fof(f561,plain,
incident_c(sK17_skl,sK14_skl),
inference(resolution,[status(thm)],[f558,f384]) ).
fof(f570,plain,
( sK15_skl = sK17_skl
| sK16_skl = sK17_skl
| sK15_skl = sK16_skl
| ~ incident_c(sK16_skl,sK14_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f422,f561]) ).
fof(f770,plain,
inner_point(sK16_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl)),
inference(resolution,[status(thm)],[f112,f116]) ).
fof(f777,plain,
incident_c(sK16_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl)),
inference(resolution,[status(thm)],[f770,f50]) ).
fof(f780,plain,
incident_c(sK16_skl,sK14_skl),
inference(resolution,[status(thm)],[f777,f384]) ).
fof(f791,plain,
( sK15_skl = sK17_skl
| sK16_skl = sK17_skl
| sK15_skl = sK16_skl ),
inference(backward_subsumption_resolution,[status(thm)],[f570,f780]) ).
fof(f863,plain,
( sK15_skl = sK17_skl
| sK16_skl = sK17_skl
| ~ inner_point(sK16_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl)) ),
inference(paramodulation,[status(thm)],[f791,f395]) ).
fof(f871,plain,
( sK15_skl = sK17_skl
| sK16_skl = sK17_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f863,f770]) ).
fof(f904,plain,
( sK16_skl = sK17_skl
| between_c(sK14_skl,sK17_skl,sK16_skl,sK17_skl) ),
inference(paramodulation,[status(thm)],[f871,f116]) ).
fof(f905,plain,
sK16_skl = sK17_skl,
inference(forward_subsumption_resolution,[status(thm)],[f904,f118]) ).
fof(f914,plain,
inner_point(sK16_skl,sK13_skl(sK17_skl,sK17_skl,sK15_skl,sK14_skl)),
inference(backward_demodulation,[status(thm)],[f905,f770]) ).
fof(f918,plain,
~ inner_point(sK17_skl,sK13_skl(sK17_skl,sK17_skl,sK15_skl,sK14_skl)),
inference(backward_demodulation,[status(thm)],[f905,f557]) ).
fof(f931,plain,
inner_point(sK17_skl,sK13_skl(sK17_skl,sK17_skl,sK15_skl,sK14_skl)),
inference(forward_demodulation,[status(thm)],[f905,f914]) ).
fof(f974,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f918,f931]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO111+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.67 % Computer : n013.cluster.edu
% 0.19/0.67 % Model : x86_64 x86_64
% 0.19/0.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.67 % Memory : 8046.5625MB
% 0.19/0.67 % OS : Linux 6.8.0-71-generic
% 0.19/0.67 % CPULimit : 300
% 0.19/0.67 % WCLimit : 300
% 0.19/0.67 % DateTime : Sun Sep 20 11:22:40 UTC 2026
% 0.19/0.67 % CPUTime :
% 0.19/0.69 % Drodi V4.1.1
% 0.24/0.79 % Refutation found
% 0.24/0.79 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.24/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.83 % Elapsed time: 0.146476 seconds
% 0.24/0.83 % CPU time: 0.845519 seconds
% 0.24/0.83 % Total memory used: 82.560 MB
% 0.24/0.83 % Net memory used: 81.629 MB
%------------------------------------------------------------------------------