%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO124+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 12:24:08 PM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 7 unt; 0 def)
% Number of atoms : 213 ( 31 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 267 ( 97 ~; 93 |; 67 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-5 aty)
% Number of variables : 168 ( 152 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [O,P,Q,R] :
( between_o(O,P,Q,R)
<=> ( ( ordered_by(O,Q,P)
& ordered_by(O,R,Q) )
| ( ordered_by(O,Q,R)
& ordered_by(O,P,Q) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [P,O] :
( start_point(P,O)
<=> ( ! [Q] :
( ( incident_o(Q,O)
& P != Q )
=> ordered_by(O,P,Q) )
& incident_o(P,O) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [O,P,Q] :
( ordered_by(O,P,Q)
=> ( incident_o(Q,O)
& incident_o(P,O) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [P,Q,R,O] :
( between_o(O,P,Q,R)
<=> ? [C] :
( between_c(C,P,Q,R)
& ! [P] :
( incident_o(P,O)
<=> incident_c(P,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [O,P,Q] :
( ( start_point(Q,O)
& start_point(P,O) )
=> P = Q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [O,P,Q] :
( ( start_point(Q,O)
& start_point(P,O) )
=> P = Q ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f115,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(f116,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)],[f115]) ).
fof(f117,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))],[f116]) ).
fof(f118,plain,
! [X0,X1,X2,X3] :
( X1 != X3
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f124,plain,
! [O,P,Q,R] :
( ( ( ( ~ ordered_by(O,Q,P)
| ~ ordered_by(O,R,Q) )
& ( ~ ordered_by(O,Q,R)
| ~ ordered_by(O,P,Q) ) )
| between_o(O,P,Q,R) )
& ( ( ordered_by(O,Q,P)
& ordered_by(O,R,Q) )
| ( ordered_by(O,Q,R)
& ordered_by(O,P,Q) )
| ~ between_o(O,P,Q,R) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f125,plain,
( ! [O,P,Q,R] :
( ( ( ~ ordered_by(O,Q,P)
| ~ ordered_by(O,R,Q) )
& ( ~ ordered_by(O,Q,R)
| ~ ordered_by(O,P,Q) ) )
| between_o(O,P,Q,R) )
& ! [O,P,Q,R] :
( ( ordered_by(O,Q,P)
& ordered_by(O,R,Q) )
| ( ordered_by(O,Q,R)
& ordered_by(O,P,Q) )
| ~ between_o(O,P,Q,R) ) ),
inference(miniscoping,[status(thm)],[f124]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X3,X2)
| between_o(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f132,plain,
! [P,O] :
( start_point(P,O)
<=> ( ! [Q] :
( ordered_by(O,P,Q)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) ) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f133,plain,
! [P,O] :
( ( ? [Q] :
( ~ ordered_by(O,P,Q)
& incident_o(Q,O)
& P != Q )
| ~ incident_o(P,O)
| start_point(P,O) )
& ( ( ! [Q] :
( ordered_by(O,P,Q)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) )
| ~ start_point(P,O) ) ),
inference(NNF_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
( ! [P,O] :
( ? [Q] :
( ~ ordered_by(O,P,Q)
& incident_o(Q,O)
& P != Q )
| ~ incident_o(P,O)
| start_point(P,O) )
& ! [P,O] :
( ( ! [Q] :
( ordered_by(O,P,Q)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) )
| ~ start_point(P,O) ) ),
inference(miniscoping,[status(thm)],[f133]) ).
fof(f135,plain,
( ! [P,O] :
( ( ~ ordered_by(O,P,sK14_skl(O,P))
& incident_o(sK14_skl(O,P),O)
& P != sK14_skl(O,P) )
| ~ incident_o(P,O)
| start_point(P,O) )
& ! [P,O] :
( ( ! [Q] :
( ordered_by(O,P,Q)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) )
| ~ start_point(P,O) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(Q,sK14_skl(O,P))],[f134]) ).
fof(f136,plain,
! [X0,X1] :
( incident_o(X0,X1)
| ~ start_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ordered_by(X1,X0,X2)
| ~ incident_o(X2,X1)
| X0 = X2
| ~ start_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f150,plain,
! [O,P,Q] :
( ( incident_o(Q,O)
& incident_o(P,O) )
| ~ ordered_by(O,P,Q) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f151,plain,
! [X0,X1,X2] :
( incident_o(X1,X0)
| ~ ordered_by(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f159,plain,
! [P,Q,R,O] :
( ( ! [C] :
( ~ between_c(C,P,Q,R)
| ? [P] :
( ( incident_c(P,C)
| incident_o(P,O) )
& ( ~ incident_c(P,C)
| ~ incident_o(P,O) ) ) )
| between_o(O,P,Q,R) )
& ( ? [C] :
( between_c(C,P,Q,R)
& ! [P] :
( ( ~ incident_c(P,C)
| incident_o(P,O) )
& ( incident_c(P,C)
| ~ incident_o(P,O) ) ) )
| ~ between_o(O,P,Q,R) ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f160,plain,
( ! [P,Q,R,O] :
( ! [C] :
( ~ between_c(C,P,Q,R)
| ? [P] :
( ( incident_c(P,C)
| incident_o(P,O) )
& ( ~ incident_c(P,C)
| ~ incident_o(P,O) ) ) )
| between_o(O,P,Q,R) )
& ! [P,Q,R,O] :
( ? [C] :
( between_c(C,P,Q,R)
& ! [P] :
( ~ incident_c(P,C)
| incident_o(P,O) )
& ! [P] :
( incident_c(P,C)
| ~ incident_o(P,O) ) )
| ~ between_o(O,P,Q,R) ) ),
inference(miniscoping,[status(thm)],[f159]) ).
fof(f161,plain,
( ! [P,Q,R,O] :
( ! [C] :
( ~ between_c(C,P,Q,R)
| ( ( incident_c(sK18_skl(C,O,R,Q,P),C)
| incident_o(sK18_skl(C,O,R,Q,P),O) )
& ( ~ incident_c(sK18_skl(C,O,R,Q,P),C)
| ~ incident_o(sK18_skl(C,O,R,Q,P),O) ) ) )
| between_o(O,P,Q,R) )
& ! [P,Q,R,O] :
( ( between_c(sK17_skl(O,R,Q,P),P,Q,R)
& ! [P] :
( ~ incident_c(P,sK17_skl(O,R,Q,P))
| incident_o(P,O) )
& ! [P] :
( incident_c(P,sK17_skl(O,R,Q,P))
| ~ incident_o(P,O) ) )
| ~ between_o(O,P,Q,R) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(C,sK17_skl(O,R,Q,P)),skolemize(P,sK18_skl(C,O,R,Q,P))],[f160]) ).
fof(f164,plain,
! [X0,X1,X2,X3] :
( between_c(sK17_skl(X0,X3,X2,X1),X1,X2,X3)
| ~ between_o(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f188,plain,
? [O,P,Q] :
( P != Q
& start_point(Q,O)
& start_point(P,O) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f189,plain,
? [P,Q] :
( P != Q
& ? [O] :
( start_point(Q,O)
& start_point(P,O) ) ),
inference(miniscoping,[status(thm)],[f188]) ).
fof(f190,plain,
( sK24_skl != sK25_skl
& start_point(sK25_skl,sK26_skl)
& start_point(sK24_skl,sK26_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl,sK25_skl,sK26_skl]),skolemize(P,sK24_skl),skolemize(Q,sK25_skl),skolemize(O,sK26_skl)],[f189]) ).
fof(f191,plain,
start_point(sK24_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f192,plain,
start_point(sK25_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f193,plain,
sK24_skl != sK25_skl,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f198,plain,
! [X0,X1,X2] : ~ between_c(X0,X1,X2,X1),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f502,plain,
! [X0,X1,X2] : ~ between_o(X0,X1,X2,X1),
inference(resolution,[status(thm)],[f164,f198]) ).
fof(f527,plain,
! [X0,X1,X2] :
( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X1,X2) ),
inference(resolution,[status(thm)],[f502,f131]) ).
fof(f537,plain,
! [X0,X1,X2] :
( ~ incident_o(X1,X0)
| X2 = X1
| ~ start_point(X2,X0)
| ~ ordered_by(X0,X1,X2) ),
inference(resolution,[status(thm)],[f527,f137]) ).
fof(f539,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ start_point(X2,X0)
| ~ ordered_by(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f537,f151]) ).
fof(f541,plain,
! [X0,X1,X2] :
( ~ incident_o(X0,X1)
| X2 = X0
| ~ start_point(X2,X1)
| X0 = X2
| ~ start_point(X0,X1) ),
inference(resolution,[status(thm)],[f539,f137]) ).
fof(f543,plain,
! [X0,X1,X2] :
( ~ incident_o(X0,X1)
| ~ start_point(X2,X1)
| X0 = X2
| ~ start_point(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f541]) ).
fof(f544,plain,
! [X0,X1,X2] :
( ~ start_point(X2,X1)
| X0 = X2
| ~ start_point(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f543,f136]) ).
fof(f546,plain,
! [X0] :
( X0 = sK25_skl
| ~ start_point(X0,sK26_skl) ),
inference(resolution,[status(thm)],[f544,f192]) ).
fof(f553,plain,
sK24_skl = sK25_skl,
inference(resolution,[status(thm)],[f546,f191]) ).
fof(f554,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f553,f193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO124+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 11:54:02 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.46 % Refutation found
% 0.11/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.71/0.50 % Elapsed time: 0.111161 seconds
% 0.71/0.50 % CPU time: 0.497345 seconds
% 0.71/0.50 % Total memory used: 89.214 MB
% 0.71/0.50 % Net memory used: 88.544 MB
%------------------------------------------------------------------------------