%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO124+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 07:17:07 AM UTC 2026
% Result : Theorem 0.87s 0.54s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 118 ( 17 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 126 ( 43 ~; 48 |; 27 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 91 ( 2 sgn 58 !; 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(start_point_defn,axiom,
! [P,O] :
( start_point(P,O)
<=> ( ! [Q] :
( ( incident_o(Q,O)
& P != Q )
=> ordered_by(O,P,Q) )
& incident_o(P,O) ) ),
file('theBenchmark.p',start_point_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(corollary_4_10_1,conjecture,
! [O,P,Q] :
( ( start_point(Q,O)
& start_point(P,O) )
=> P = Q ),
file('theBenchmark.p',corollary_4_10_1) ).
fof(corollary_4_10_1_neg,negated_conjecture,
~ ! [O,P,Q] :
( ( start_point(Q,O)
& start_point(P,O) )
=> P = Q ),
inference(assume_negation,[status(cth)],[corollary_4_10_1]) ).
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_59,plain,
( ordered_by(B,A,C)
| ~ incident_o(C,B)
| C = A
| ~ start_point(A,B) ),
inference(clausify,[status(thm)],[start_point_defn]) ).
cnf(c_60,plain,
( incident_o(A,B)
| ~ start_point(A,B) ),
inference(clausify,[status(thm)],[start_point_defn]) ).
fof(nnf_28,plain,
? [O,P,Q] :
( Q != P
& start_point(Q,O)
& start_point(P,O) ),
inference(fof_nnf,[status(thm)],[corollary_4_10_1_neg]) ).
fof(sk_corollary_4_10_1_neg,plain,
( sK3 != sK1
& start_point(sK3,sK2)
& start_point(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(O,sK2),skolemize(P,sK1),skolemize(Q,sK3)],[nnf_28]) ).
cnf(c_64,negated_conjecture,
start_point(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_corollary_4_10_1_neg]) ).
cnf(c_65,negated_conjecture,
start_point(sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_corollary_4_10_1_neg]) ).
cnf(c_85,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_128,plain,
( D != B
| ~ between_c(A,B,C,D) ),
inference(clausify,[status(thm)],[between_c_defn]) ).
cnf(c_142,negated_conjecture,
sK3 != sK1,
inference(split_conjunct,[status(thm)],[sk_corollary_4_10_1_neg]) ).
cnf(c_174,negated_conjecture,
( ordered_by(sK2,sK1,A)
| ~ incident_o(A,sK2)
| A = sK1 ),
inference(resolve,[status(thm)],[c_64,c_59]) ).
cnf(c_175,negated_conjecture,
( ordered_by(sK2,sK1,A)
| ~ incident_o(A,sK2)
| sK1 = A ),
inference(copy,[status(thm)],[c_174]) ).
cnf(c_176,negated_conjecture,
incident_o(sK1,sK2),
inference(resolve,[status(thm)],[c_64,c_60]) ).
cnf(c_177,negated_conjecture,
( ordered_by(sK2,sK3,A)
| ~ incident_o(A,sK2)
| A = sK3 ),
inference(resolve,[status(thm)],[c_65,c_59]) ).
cnf(c_178,negated_conjecture,
( ordered_by(sK2,sK3,A)
| ~ incident_o(A,sK2)
| sK3 = A ),
inference(copy,[status(thm)],[c_177]) ).
cnf(c_179,negated_conjecture,
incident_o(sK3,sK2),
inference(resolve,[status(thm)],[c_65,c_60]) ).
cnf(c_2068,negated_conjecture,
( ordered_by(sK2,sK3,sK1)
| sK3 = sK1 ),
inference(resolve,[status(thm)],[c_178,c_176]) ).
cnf(c_578,negated_conjecture,
ordered_by(sK2,sK3,sK1),
inference(resolve,[status(thm)],[c_142,c_2068]) ).
cnf(c_2069,negated_conjecture,
( ordered_by(sK2,sK1,sK3)
| sK1 = sK3 ),
inference(resolve,[status(thm)],[c_179,c_175]) ).
cnf(c_2070,negated_conjecture,
( ordered_by(sK2,sK1,sK3)
| sK3 = sK1 ),
inference(copy,[status(thm)],[c_2069]) ).
cnf(c_581,negated_conjecture,
ordered_by(sK2,sK1,sK3),
inference(resolve,[status(thm)],[c_142,c_2070]) ).
cnf(c_770,plain,
( between_c(sK0(sK1,sK3,A,sK2),sK1,sK3,A)
| ~ ordered_by(sK2,A,sK3) ),
inference(resolve,[status(thm)],[c_578,c_85]) ).
cnf(c_2053,plain,
between_c(sK0(sK1,sK3,sK1,sK2),sK1,sK3,sK1),
inference(resolve,[status(thm)],[c_770,c_581]) ).
cnf(c_2071,plain,
sK1 != sK1,
inference(resolve,[status(thm)],[c_2053,c_128]) ).
cnf(c_2067,plain,
$false,
inference(copy,[status(thm)],[c_2071]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO124+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 12:50:35 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 2793825 was started by sandbox on n019,
% 0.08/0.37 % Fri Sep 25 12:50:35 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 0.87/0.54
% 0.87/0.54 % SZS status Theorem for theBenchmark
% 0.87/0.54
% 0.87/0.54 % Proof 1 at 0.12 (+ 0.03) seconds.
% 0.87/0.54 % Length of proof is 25.
% 0.87/0.54 % Level of proof is 7.
% 0.87/0.54 % Maximum clause weight is 27.000.
% 0.87/0.54 % Given clauses 277.
% 0.87/0.54
% 0.87/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------