%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO112+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 : n005.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 0.16s 0.49s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 28 ( 9 unt; 0 def)
% Number of atoms : 99 ( 13 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 128 ( 57 ~; 47 |; 21 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 91 ( 2 sgn 47 !; 6 ?)
% 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(theorem_3_8_2,conjecture,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> between_c(C,R,Q,P) ),
file('theBenchmark.p',theorem_3_8_2) ).
fof(theorem_3_8_2_neg,negated_conjecture,
~ ! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> between_c(C,R,Q,P) ),
inference(assume_negation,[status(cth)],[theorem_3_8_2]) ).
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_26,plain,
( ~ inner_point(C,E)
| ~ end_point(D,E)
| ~ end_point(B,E)
| ~ part_of(E,A)
| D = B
| between_c(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_between_c_defn]) ).
cnf(c_37,plain,
( ~ between_c(E,F,C,V6)
| ~ end_point(D,sK0(E,F,C,V6))
| ~ end_point(B,sK0(E,F,C,V6))
| ~ part_of(sK0(E,F,C,V6),A)
| D = B
| between_c(A,B,C,D) ),
inference(resolve,[status(thm)],[c_26,c_25]) ).
fof(nnf_18,plain,
? [C,P,Q,R] :
( ~ between_c(C,R,Q,P)
& between_c(C,P,Q,R) ),
inference(fof_nnf,[status(thm)],[theorem_3_8_2_neg]) ).
fof(sk_theorem_3_8_2_neg,plain,
( ~ between_c(sK1,sK2,sK3,sK4)
& between_c(sK1,sK4,sK3,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK4,sK3,sK2]),skolemize(C,sK1),skolemize(P,sK4),skolemize(Q,sK3),skolemize(R,sK2)],[nnf_18]) ).
cnf(c_48,negated_conjecture,
~ between_c(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_theorem_3_8_2_neg]) ).
cnf(c_49,negated_conjecture,
between_c(sK1,sK4,sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_theorem_3_8_2_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_106,plain,
end_point(sK2,sK0(sK1,sK4,sK3,sK2)),
inference(resolve,[status(thm)],[c_50,c_49]) ).
cnf(c_107,plain,
end_point(sK4,sK0(sK1,sK4,sK3,sK2)),
inference(resolve,[status(thm)],[c_51,c_49]) ).
cnf(c_108,plain,
part_of(sK0(sK1,sK4,sK3,sK2),sK1),
inference(resolve,[status(thm)],[c_52,c_49]) ).
cnf(c_109,plain,
sK2 != sK4,
inference(resolve,[status(thm)],[c_53,c_49]) ).
cnf(c_392,negated_conjecture,
( ~ between_c(A,B,sK3,C)
| ~ end_point(sK4,sK0(A,B,sK3,C))
| ~ end_point(sK2,sK0(A,B,sK3,C))
| ~ part_of(sK0(A,B,sK3,C),sK1)
| sK4 = sK2 ),
inference(resolve,[status(thm)],[c_37,c_48]) ).
cnf(c_393,plain,
sK4 != sK2,
inference(copy,[status(thm)],[c_109]) ).
cnf(c_394,negated_conjecture,
( ~ between_c(A,B,sK3,C)
| ~ end_point(sK4,sK0(A,B,sK3,C))
| ~ end_point(sK2,sK0(A,B,sK3,C))
| ~ part_of(sK0(A,B,sK3,C),sK1) ),
inference(resolve,[status(thm)],[c_392,c_393]) ).
cnf(c_395,negated_conjecture,
( ~ between_c(sK1,sK4,sK3,sK2)
| ~ end_point(sK4,sK0(sK1,sK4,sK3,sK2))
| ~ part_of(sK0(sK1,sK4,sK3,sK2),sK1) ),
inference(resolve,[status(thm)],[c_394,c_106]) ).
cnf(c_396,negated_conjecture,
( ~ between_c(sK1,sK4,sK3,sK2)
| ~ part_of(sK0(sK1,sK4,sK3,sK2),sK1) ),
inference(resolve,[status(thm)],[c_395,c_107]) ).
cnf(c_397,negated_conjecture,
~ part_of(sK0(sK1,sK4,sK3,sK2),sK1),
inference(resolve,[status(thm)],[c_396,c_49]) ).
cnf(c_391,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_108,c_397]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO112+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n005.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 12:48:02 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 3520554 was started by sandbox on n005,
% 0.16/0.42 % Fri Sep 25 12:48:02 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 0.16/0.49
% 0.16/0.49 % SZS status Theorem for theBenchmark
% 0.16/0.49
% 0.16/0.49 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.16/0.49 % Length of proof is 16.
% 0.16/0.49 % Level of proof is 3.
% 0.16/0.49 % Maximum clause weight is 44.000.
% 0.16/0.49 % Given clauses 70.
% 0.16/0.49
% 0.16/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------