%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO118+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 : Sun Sep 27 07:17:06 AM UTC 2026
% Result : Theorem 1.36s 0.61s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 80 ( 3 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 94 ( 34 ~; 33 |; 21 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 79 ( 2 sgn 55 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(between_c_defn,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('theBenchmark.p',between_c_defn) ).
fof(between_o_defn,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('theBenchmark.p',between_o_defn) ).
fof(o3,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('theBenchmark.p',o3) ).
fof(theorem_4_5,conjecture,
! [O,P,Q] :
( ordered_by(O,P,Q)
=> ~ ordered_by(O,Q,P) ),
file('theBenchmark.p',theorem_4_5) ).
fof(theorem_4_5_neg,negated_conjecture,
~ ! [O,P,Q] :
( ordered_by(O,P,Q)
=> ~ ordered_by(O,Q,P) ),
inference(assume_negation,[status(cth)],[theorem_4_5]) ).
fof(nnf_23,plain,
! [P,Q,R,O] :
( ( ! [C] :
( ~ between_c(C,P,Q,R)
| ? [X2] :
( ( ~ incident_c(X2,C)
| ~ incident_o(X2,O) )
& ( incident_c(X2,C)
| incident_o(X2,O) ) ) )
| between_o(O,P,Q,R) )
& ( ? [X0] :
( between_c(X0,P,Q,R)
& ! [X1] :
( ( ~ incident_c(X1,X0)
| incident_o(X1,O) )
& ( incident_c(X1,X0)
| ~ incident_o(X1,O) ) ) )
| ~ between_o(O,P,Q,R) ) ),
inference(fof_nnf,[status(thm)],[o3]) ).
fof(sk_o3_sk,plain,
! [P,Q,R,O] :
( ( ! [C] :
( ~ between_c(C,P,Q,R)
| ( ( ~ incident_c(sK4(P,Q,R,O,C),C)
| ~ incident_o(sK4(P,Q,R,O,C),O) )
& ( incident_c(sK4(P,Q,R,O,C),C)
| incident_o(sK4(P,Q,R,O,C),O) ) ) )
| between_o(O,P,Q,R) )
& ( ( between_c(sK0(P,Q,R,O),P,Q,R)
& ! [X1] :
( ( ~ incident_c(X1,sK0(P,Q,R,O))
| incident_o(X1,O) )
& ( incident_c(X1,sK0(P,Q,R,O))
| ~ incident_o(X1,O) ) ) )
| ~ between_o(O,P,Q,R) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK4]),skolemize(X0,sK0(P,Q,R,O)),skolemize(X2,sK4(P,Q,R,O,C))],[nnf_23]) ).
fof(sk_o3,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ between_c(VAR_4,VAR_1,VAR_2,VAR_3)
| ~ incident_c(sK4(VAR_1,VAR_2,VAR_3,VAR_0,VAR_4),VAR_4)
| ~ incident_o(sK4(VAR_1,VAR_2,VAR_3,VAR_0,VAR_4),VAR_0)
| between_o(VAR_0,VAR_1,VAR_2,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ between_c(VAR_4,VAR_1,VAR_2,VAR_3)
| incident_c(sK4(VAR_1,VAR_2,VAR_3,VAR_0,VAR_4),VAR_4)
| incident_o(sK4(VAR_1,VAR_2,VAR_3,VAR_0,VAR_4),VAR_0)
| between_o(VAR_0,VAR_1,VAR_2,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between_c(sK0(VAR_1,VAR_2,VAR_3,VAR_0),VAR_1,VAR_2,VAR_3)
| ~ between_o(VAR_0,VAR_1,VAR_2,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ incident_c(VAR_4,sK0(VAR_1,VAR_2,VAR_3,VAR_0))
| incident_o(VAR_4,VAR_0)
| ~ between_o(VAR_0,VAR_1,VAR_2,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( incident_c(VAR_4,sK0(VAR_1,VAR_2,VAR_3,VAR_0))
| ~ incident_o(VAR_4,VAR_0)
| ~ between_o(VAR_0,VAR_1,VAR_2,VAR_3) ) ),
inference(cnf_transformation,[status(thm)],[sk_o3_sk]) ).
cnf(c_47,plain,
( between_c(sK0(B,C,D,A),B,C,D)
| ~ between_o(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_o3]) ).
cnf(c_52,plain,
( ~ ordered_by(A,C,B)
| ~ ordered_by(A,D,C)
| between_o(A,B,C,D) ),
inference(clausify,[status(thm)],[between_o_defn]) ).
cnf(c_83,plain,
( between_c(sK0(D,C,B,A),D,C,B)
| ~ ordered_by(A,C,D)
| ~ ordered_by(A,B,C) ),
inference(resolve,[status(thm)],[c_52,c_47]) ).
cnf(c_126,plain,
( D != B
| ~ between_c(A,B,C,D) ),
inference(clausify,[status(thm)],[between_c_defn]) ).
fof(nnf_28,plain,
? [O,P,Q] :
( ordered_by(O,Q,P)
& ordered_by(O,P,Q) ),
inference(fof_nnf,[status(thm)],[theorem_4_5_neg]) ).
fof(sk_theorem_4_5_neg,plain,
( ordered_by(sK1,sK3,sK2)
& ordered_by(sK1,sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(O,sK1),skolemize(P,sK2),skolemize(Q,sK3)],[nnf_28]) ).
cnf(c_140,negated_conjecture,
ordered_by(sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_theorem_4_5_neg]) ).
cnf(c_141,negated_conjecture,
ordered_by(sK1,sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_theorem_4_5_neg]) ).
cnf(c_427,plain,
( between_c(sK0(sK3,sK2,A,sK1),sK3,sK2,A)
| ~ ordered_by(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_140,c_83]) ).
cnf(c_1955,plain,
between_c(sK0(sK3,sK2,sK3,sK1),sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_427,c_141]) ).
cnf(c_1971,plain,
sK3 != sK3,
inference(resolve,[status(thm)],[c_1955,c_126]) ).
cnf(c_1970,plain,
$false,
inference(copy,[status(thm)],[c_1971]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO118+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 12:48:56 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2945894 was started by sandbox2 on n006,
% 0.09/0.37 % Fri Sep 25 12:48:56 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 1.36/0.61
% 1.36/0.61 % SZS status Theorem for theBenchmark
% 1.36/0.61
% 1.36/0.61 % Proof 1 at 0.16 (+ 0.05) seconds.
% 1.36/0.61 % Length of proof is 13.
% 1.36/0.61 % Level of proof is 5.
% 1.36/0.61 % Maximum clause weight is 27.000.
% 1.36/0.61 % Given clauses 269.
% 1.36/0.61
% 1.36/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------