%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO111+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 : 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 : Sun Sep 27 07:17:05 AM UTC 2026
% Result : Theorem 0.84s 0.52s
% Output : CNFRefutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 15 unt; 0 def)
% Number of atoms : 150 ( 34 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 171 ( 65 ~; 62 |; 36 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 100 ( 2 sgn 56 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(part_of_defn,axiom,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C1)
=> incident_c(P,C) ) ),
file('theBenchmark.p',part_of_defn) ).
fof(end_point_defn,axiom,
! [P,C] :
( end_point(P,C)
<=> ( ! [C1,C2] :
( ( incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
=> ( part_of(C2,C1)
| part_of(C1,C2) ) )
& incident_c(P,C) ) ),
file('theBenchmark.p',end_point_defn) ).
fof(inner_point_defn,axiom,
! [P,C] :
( inner_point(P,C)
<=> ( ~ end_point(P,C)
& incident_c(P,C) ) ),
file('theBenchmark.p',inner_point_defn) ).
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(theorem_3_8_1,conjecture,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> ( P != R
& Q != R
& P != Q
& incident_c(R,C)
& incident_c(Q,C)
& incident_c(P,C) ) ),
file('theBenchmark.p',theorem_3_8_1) ).
fof(theorem_3_8_1_neg,negated_conjecture,
~ ! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> ( P != R
& Q != R
& P != Q
& incident_c(R,C)
& incident_c(Q,C)
& incident_c(P,C) ) ),
inference(assume_negation,[status(cth)],[theorem_3_8_1]) ).
cnf(c_20,plain,
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
inference(clausify,[status(thm)],[inner_point_defn]) ).
cnf(c_21,plain,
( incident_c(A,B)
| ~ inner_point(A,B) ),
inference(clausify,[status(thm)],[inner_point_defn]) ).
fof(nnf_17,plain,
! [C,P,Q,R] :
( ( ! [Cpp] :
( ~ inner_point(Q,Cpp)
| ~ end_point(R,Cpp)
| ~ end_point(P,Cpp)
| ~ part_of(Cpp,C) )
| R = P
| between_c(C,P,Q,R) )
& ( ( ? [X0] :
( inner_point(Q,X0)
& end_point(R,X0)
& end_point(P,X0)
& part_of(X0,C) )
& R != P )
| ~ between_c(C,P,Q,R) ) ),
inference(fof_nnf,[status(thm)],[between_c_defn]) ).
fof(sk_between_c_defn_sk,plain,
! [C,P,Q,R] :
( ( ! [Cpp] :
( ~ inner_point(Q,Cpp)
| ~ end_point(R,Cpp)
| ~ end_point(P,Cpp)
| ~ part_of(Cpp,C) )
| R = P
| between_c(C,P,Q,R) )
& ( ( inner_point(Q,sK0(C,P,Q,R))
& end_point(R,sK0(C,P,Q,R))
& end_point(P,sK0(C,P,Q,R))
& part_of(sK0(C,P,Q,R),C)
& R != P )
| ~ between_c(C,P,Q,R) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(C,P,Q,R))],[nnf_17]) ).
fof(sk_between_c_defn,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ inner_point(VAR_2,VAR_4)
| ~ end_point(VAR_3,VAR_4)
| ~ end_point(VAR_1,VAR_4)
| ~ part_of(VAR_4,VAR_0)
| VAR_3 = VAR_1
| between_c(VAR_0,VAR_1,VAR_2,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( inner_point(VAR_2,sK0(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ between_c(VAR_0,VAR_1,VAR_2,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( end_point(VAR_3,sK0(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ between_c(VAR_0,VAR_1,VAR_2,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( end_point(VAR_1,sK0(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ between_c(VAR_0,VAR_1,VAR_2,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( part_of(sK0(VAR_0,VAR_1,VAR_2,VAR_3),VAR_0)
| ~ between_c(VAR_0,VAR_1,VAR_2,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 != VAR_1
| ~ between_c(VAR_0,VAR_1,VAR_2,VAR_3) ) ),
inference(cnf_transformation,[status(thm)],[sk_between_c_defn_sk]) ).
cnf(c_25,plain,
( inner_point(C,sK0(A,B,C,D))
| ~ between_c(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_between_c_defn]) ).
cnf(c_38,plain,
( incident_c(C,sK0(A,B,C,D))
| ~ between_c(A,B,C,D) ),
inference(resolve,[status(thm)],[c_25,c_21]) ).
cnf(c_39,plain,
( ~ end_point(C,sK0(A,B,C,D))
| ~ between_c(A,B,C,D) ),
inference(resolve,[status(thm)],[c_25,c_20]) ).
fof(nnf_18,plain,
? [C,P,Q,R] :
( ( R = P
| R = Q
| Q = P
| ~ incident_c(R,C)
| ~ incident_c(Q,C)
| ~ incident_c(P,C) )
& between_c(C,P,Q,R) ),
inference(fof_nnf,[status(thm)],[theorem_3_8_1_neg]) ).
fof(sk_theorem_3_8_1_neg,plain,
( ( sK4 = sK1
| sK4 = sK3
| sK3 = sK1
| ~ incident_c(sK4,sK2)
| ~ incident_c(sK3,sK2)
| ~ incident_c(sK1,sK2) )
& between_c(sK2,sK1,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK1,sK3,sK4]),skolemize(C,sK2),skolemize(P,sK1),skolemize(Q,sK3),skolemize(R,sK4)],[nnf_18]) ).
cnf(c_48,negated_conjecture,
( sK4 = sK1
| sK4 = sK3
| sK3 = sK1
| ~ incident_c(sK4,sK2)
| ~ incident_c(sK3,sK2)
| ~ incident_c(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_theorem_3_8_1_neg]) ).
cnf(c_49,negated_conjecture,
between_c(sK2,sK1,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_theorem_3_8_1_neg]) ).
cnf(c_50,plain,
( end_point(D,sK0(A,B,C,D))
| ~ between_c(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_between_c_defn]) ).
cnf(c_51,plain,
( end_point(B,sK0(A,B,C,D))
| ~ between_c(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_between_c_defn]) ).
cnf(c_52,plain,
( part_of(sK0(A,B,C,D),A)
| ~ between_c(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_between_c_defn]) ).
cnf(c_53,plain,
( D != B
| ~ between_c(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_between_c_defn]) ).
cnf(c_76,plain,
( incident_c(A,B)
| ~ end_point(A,B) ),
inference(clausify,[status(thm)],[end_point_defn]) ).
cnf(c_85,plain,
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(clausify,[status(thm)],[part_of_defn]) ).
cnf(c_103,plain,
~ end_point(sK3,sK0(sK2,sK1,sK3,sK4)),
inference(resolve,[status(thm)],[c_49,c_39]) ).
cnf(c_104,plain,
incident_c(sK3,sK0(sK2,sK1,sK3,sK4)),
inference(resolve,[status(thm)],[c_49,c_38]) ).
cnf(c_106,plain,
end_point(sK4,sK0(sK2,sK1,sK3,sK4)),
inference(resolve,[status(thm)],[c_50,c_49]) ).
cnf(c_107,plain,
end_point(sK1,sK0(sK2,sK1,sK3,sK4)),
inference(resolve,[status(thm)],[c_51,c_49]) ).
cnf(c_108,plain,
part_of(sK0(sK2,sK1,sK3,sK4),sK2),
inference(resolve,[status(thm)],[c_52,c_49]) ).
cnf(c_109,plain,
sK4 != sK1,
inference(resolve,[status(thm)],[c_53,c_49]) ).
cnf(c_113,negated_conjecture,
( sK4 = sK3
| sK3 = sK1
| ~ incident_c(sK4,sK2)
| ~ incident_c(sK3,sK2)
| ~ incident_c(sK1,sK2) ),
inference(resolve,[status(thm)],[c_109,c_48]) ).
cnf(c_368,plain,
incident_c(sK4,sK0(sK2,sK1,sK3,sK4)),
inference(resolve,[status(thm)],[c_106,c_76]) ).
cnf(c_373,plain,
incident_c(sK1,sK0(sK2,sK1,sK3,sK4)),
inference(resolve,[status(thm)],[c_107,c_76]) ).
cnf(c_379,plain,
( incident_c(A,sK2)
| ~ incident_c(A,sK0(sK2,sK1,sK3,sK4)) ),
inference(resolve,[status(thm)],[c_108,c_85]) ).
cnf(c_494,plain,
incident_c(sK1,sK2),
inference(resolve,[status(thm)],[c_379,c_373]) ).
cnf(c_495,plain,
incident_c(sK4,sK2),
inference(resolve,[status(thm)],[c_379,c_368]) ).
cnf(c_496,plain,
incident_c(sK3,sK2),
inference(resolve,[status(thm)],[c_379,c_104]) ).
cnf(c_615,negated_conjecture,
( sK4 = sK3
| sK3 = sK1
| ~ incident_c(sK4,sK2)
| ~ incident_c(sK3,sK2) ),
inference(resolve,[status(thm)],[c_494,c_113]) ).
cnf(c_616,negated_conjecture,
( sK4 = sK3
| sK3 = sK1
| ~ incident_c(sK4,sK2) ),
inference(resolve,[status(thm)],[c_496,c_615]) ).
cnf(c_505,negated_conjecture,
( sK4 = sK3
| sK3 = sK1 ),
inference(resolve,[status(thm)],[c_495,c_616]) ).
cnf(c_617,plain,
( end_point(sK3,sK0(sK2,sK1,sK3,sK4))
| sK3 = sK1 ),
inference(paramod,[status(thm)],[c_505,c_106]) ).
cnf(c_600,plain,
sK3 = sK1,
inference(resolve,[status(thm)],[c_103,c_617]) ).
cnf(c_618,plain,
~ end_point(sK1,sK0(sK2,sK1,sK3,sK4)),
inference(paramod,[status(thm)],[c_600,c_103]) ).
cnf(c_614,plain,
$false,
inference(resolve,[status(thm)],[c_107,c_618]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO111+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 12:48:24 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 1072895 was started by sandbox2 on n008,
% 0.09/0.38 % Fri Sep 25 12:48:24 2026
% 0.09/0.38 % 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).
% 0.84/0.52
% 0.84/0.52 % SZS status Theorem for theBenchmark
% 0.84/0.52
% 0.84/0.52 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.84/0.52 % Length of proof is 34.
% 0.84/0.52 % Level of proof is 7.
% 0.84/0.52 % Maximum clause weight is 23.000.
% 0.84/0.52 % Given clauses 110.
% 0.84/0.52
% 0.84/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------