%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO117+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 01:17:05 PM UTC 2026
% Result : Theorem 11.73s 2.04s
% Output : Proof 11.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 20 unt; 0 def)
% Number of atoms : 154 ( 24 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 178 ( 70 ~; 56 |; 45 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-5 aty)
% Number of variables : 118 ( 3 sgn 63 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/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(c59,plain,
( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X3,X2)
| between_o(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi50,axiom,
ifeq(ordered_by(X0,X1,X2),true,ifeq(ordered_by(X0,X2,X3),true,between_o(X0,X3,X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c59]) ).
fof(f27,conjecture,
! [O,P] : ~ ordered_by(O,P,P),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_4_4) ).
fof(f27_neg,negated_conjecture,
~ ! [O,P] : ~ ordered_by(O,P,P),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f27_nnf,plain,
? [O,P] : ordered_by(O,P,P),
inference(nnf_transformation,[status(thm)],[f27_neg]) ).
fof(f27_sk,plain,
ordered_by(sk24,sk25,sk25),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk24,sk25])],[f27_nnf]) ).
cnf(c96,plain,
ordered_by(sk24,sk25,sk25),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi81,negated_conjecture,
ordered_by(sk24,sk25,sk25) = true,
inference(equality_encoding,[status(esa)],[c96]) ).
cnf(h6,plain,
between_o(sk24,sk25,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi50,hi81,hi81]) ).
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/sandbox2/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]) ).
cnf(hi68,axiom,
ifeq(between_o(X0,X1,X2,X3),true,between_c(sk17(X1,X2,X3,X0),X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c77]) ).
cnf(h60,plain,
between_c(sk17(sk25,sk25,sk25,sk24),sk25,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi68,h6]) ).
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/sandbox2/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(c51,plain,
( end_point(X3,sk13(X0,X1,X2,X3))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi42,axiom,
ifeq(between_c(X0,X1,X2,X3),true,end_point(X3,sk13(X0,X1,X2,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c51]) ).
cnf(h950,plain,
end_point(sk25,sk13(sk17(sk25,sk25,sk25,sk24),sk25,sk25,sk25)) = true,
inference(hyper_resolution,[status(thm)],[hi42,h60]) ).
cnf(c52,plain,
( inner_point(X2,sk13(X0,X1,X2,X3))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi43,axiom,
ifeq(between_c(X0,X1,X2,X3),true,inner_point(X2,sk13(X0,X1,X2,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(h949,plain,
inner_point(sk25,sk13(sk17(sk25,sk25,sk25,sk24),sk25,sk25,sk25)) = true,
inference(hyper_resolution,[status(thm)],[hi43,h60]) ).
fof(f3,axiom,
! [P,C] :
( inner_point(P,C)
<=> ( ~ end_point(P,C)
& incident_c(P,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_point_defn) ).
fof(f3_nnf,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)],[f3]) ).
fof(f3_sk,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(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c21,plain,
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi82,axiom,
ifeq(inner_point(X0,X1),true,ifeq(end_point(X0,X1),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi82,h949,h950]) ).
cnf(t336,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f5,axiom,
! [C] :
( closed(C)
<=> ~ ? [P] : end_point(P,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closed_defn) ).
fof(f5_nnf,plain,
! [C] :
( ( ? [P] : end_point(P,C)
| closed(C) )
& ( ! [P] : ~ end_point(P,C)
| ~ closed(C) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [C,P] :
( ( end_point(sk5(C),C)
| closed(C) )
& ( ~ end_point(P,C)
| ~ closed(C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f5_nnf]) ).
cnf(c30,plain,
( ~ end_point(X1,X0)
| ~ closed(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f12,axiom,
! [C,P] :
( end_point(P,C)
=> ? [Q] :
( P != Q
& end_point(Q,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c6) ).
fof(f12_nnf,plain,
! [C,P] :
( ? [Q] :
( P != Q
& end_point(Q,C) )
| ~ end_point(P,C) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [P,C] :
( ( P != sk10(C,P)
& end_point(sk10(C,P),C) )
| ~ end_point(P,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f12_nnf]) ).
cnf(c41,plain,
( X1 != sk10(X0,X1)
| ~ end_point(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(c48,plain,
( X1 != X3
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c21,c30,c41,c48]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t336]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO117+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.44 % Computer : n003.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Wed Sep 23 10:59:20 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 11.73/2.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.73/2.04 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------