%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO124+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 : Fri Sep 25 01:17:06 PM UTC 2026
% Result : Theorem 18.23s 2.74s
% Output : Proof 18.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 8 unt; 0 def)
% Number of atoms : 164 ( 31 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 189 ( 63 ~; 67 |; 51 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 89 ( 4 sgn 57 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,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/sandbox/benchmark/theBenchmark.p',o3) ).
fof(f22_nnf,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)],[f22]) ).
fof(f22_sk,plain,
! [O,P,Q,R,C] :
( ( ~ between_c(C,P,Q,R)
| ( incident_c(sk18(P,Q,R,O,C),C)
& ~ incident_o(sk18(P,Q,R,O,C),O) )
| ( ~ incident_c(sk18(P,Q,R,O,C),C)
& incident_o(sk18(P,Q,R,O,C),O) )
| between_o(O,P,Q,R) )
& ( ( between_c(sk17(P,Q,R,O),P,Q,R)
& ( ~ incident_c(P,sk17(P,Q,R,O))
| incident_o(P,O) )
& ( incident_c(P,sk17(P,Q,R,O))
| ~ incident_o(P,O) ) )
| ~ between_o(O,P,Q,R) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk17,sk18])],[f22_nnf]) ).
cnf(c77,plain,
( between_c(sk17(X0,X1,X2,X3),X0,X1,X2)
| ~ between_o(X3,X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
fof(f18,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/sandbox/benchmark/theBenchmark.p',start_point_defn) ).
fof(f18_nnf,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)],[f18]) ).
fof(f18_sk,plain,
! [P,O,Q] :
( ( ( ~ ordered_by(O,P,sk14(P,O))
& incident_o(sk14(P,O),O)
& P != sk14(P,O) )
| ~ incident_o(P,O)
| start_point(P,O) )
& ( ( ( ordered_by(O,P,Q)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) )
| ~ start_point(P,O) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk14])],[f18_nnf]) ).
cnf(c61,plain,
( ordered_by(X1,X0,X2)
| ~ incident_o(X2,X1)
| X0 = X2
| ~ start_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f27,conjecture,
! [O,P,Q] :
( ( start_point(Q,O)
& start_point(P,O) )
=> P = Q ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_4_10_1) ).
fof(f27_neg,negated_conjecture,
~ ! [O,P,Q] :
( ( start_point(Q,O)
& start_point(P,O) )
=> P = Q ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f27_nnf,plain,
? [O,P,Q] :
( P != Q
& start_point(Q,O)
& start_point(P,O) ),
inference(nnf_transformation,[status(thm)],[f27_neg]) ).
fof(f27_sk,plain,
( sk25 != sk26
& start_point(sk26,sk24)
& start_point(sk25,sk24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk24,sk25,sk26])],[f27_nnf]) ).
cnf(c96,plain,
start_point(sk25,sk24),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p1557,plain,
( ordered_by(sk24,sk25,X0)
| ~ incident_o(X0,sk24)
| sk25 = X0 ),
inference(resolution,[status(thm)],[c61,c96]) ).
cnf(c60,plain,
( incident_o(X0,X1)
| ~ start_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(c97,plain,
start_point(sk26,sk24),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p110,plain,
incident_o(sk26,sk24),
inference(resolution,[status(thm)],[c60,c97]) ).
cnf(p1560,plain,
( ordered_by(sk24,sk25,sk26)
| sk25 = sk26 ),
inference(resolution,[status(thm)],[p1557,p110]) ).
fof(f17,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/sandbox/benchmark/theBenchmark.p',between_o_defn) ).
fof(f17_nnf,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)],[f17]) ).
fof(f17_sk,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(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c58,plain,
( ~ ordered_by(X0,X2,X3)
| ~ ordered_by(X0,X1,X2)
| between_o(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p1577,plain,
( ~ ordered_by(sk24,sk26,X0)
| between_o(sk24,sk25,sk26,X0)
| sk25 = sk26 ),
inference(resolution,[status(thm)],[p1560,c58]) ).
cnf(p1558,plain,
( ordered_by(sk24,sk26,X0)
| ~ incident_o(X0,sk24)
| sk26 = X0 ),
inference(resolution,[status(thm)],[c61,c97]) ).
cnf(p109,plain,
incident_o(sk25,sk24),
inference(resolution,[status(thm)],[c60,c96]) ).
cnf(p1581,plain,
( ordered_by(sk24,sk26,sk25)
| sk26 = sk25 ),
inference(resolution,[status(thm)],[p1558,p109]) ).
cnf(p1640,plain,
( sk26 = sk25
| between_o(sk24,sk25,sk26,sk25)
| sk25 = sk26 ),
inference(resolution,[status(thm)],[p1577,p1581]) ).
cnf(p1851,plain,
( sk26 = sk25
| sk25 = sk26
| between_c(sk17(sk25,sk26,sk25,sk24),sk25,sk26,sk25) ),
inference(resolution,[status(thm)],[c77,p1640]) ).
fof(f16,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',between_c_defn) ).
fof(f16_nnf,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)],[f16]) ).
fof(f16_sk,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) )
& ( ( inner_point(Q,sk13(C,P,Q,R))
& end_point(R,sk13(C,P,Q,R))
& end_point(P,sk13(C,P,Q,R))
& part_of(sk13(C,P,Q,R),C)
& P != R )
| ~ between_c(C,P,Q,R) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f16_nnf]) ).
cnf(c48,plain,
( X1 != X3
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p136,plain,
~ between_c(X0,X1,X2,X1),
inference(equality_resolution,[status(thm)],[c48]) ).
cnf(p1914,plain,
( sk26 = sk25
| sk25 = sk26 ),
inference(resolution,[status(thm)],[p1851,p136]) ).
cnf(c98,plain,
sk25 != sk26,
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p1915,plain,
( sk25 != sk25
| sk25 = sk26 ),
inference(superposition,[status(thm)],[p1914,c98]) ).
cnf(p2041,plain,
sk25 = sk26,
inference(equality_resolution,[status(thm)],[p1915]) ).
cnf(p2042,plain,
$false,
inference(resolution,[status(thm)],[p2041,c98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO124+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 11:01:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 18.23/2.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.23/2.74 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------