%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO094+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 : n012.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 07:17:03 AM UTC 2026
% Result : Theorem 0.09s 6.62s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 18 unt; 0 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 117 ( 47 ~; 42 |; 19 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 67 ( 4 sgn 24 !; 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(meet_defn,axiom,
! [P,C,C1] :
( meet(P,C,C1)
<=> ( ! [Q] :
( ( incident_c(Q,C1)
& incident_c(Q,C) )
=> ( end_point(Q,C1)
& end_point(Q,C) ) )
& incident_c(P,C1)
& incident_c(P,C) ) ),
file('theBenchmark.p',meet_defn) ).
fof(c3,axiom,
! [C] :
? [P] : inner_point(P,C),
file('theBenchmark.p',c3) ).
fof(proposition_2_14_3,conjecture,
! [C,C1,C2,P] :
( ( part_of(C2,C)
& part_of(C1,C)
& meet(P,C1,C2) )
=> ~ end_point(P,C) ),
file('theBenchmark.p',proposition_2_14_3) ).
fof(proposition_2_14_3_neg,negated_conjecture,
~ ! [C,C1,C2,P] :
( ( part_of(C2,C)
& part_of(C1,C)
& meet(P,C1,C2) )
=> ~ end_point(P,C) ),
inference(assume_negation,[status(cth)],[proposition_2_14_3]) ).
cnf(c_19,plain,
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
inference(clausify,[status(thm)],[inner_point_defn]) ).
cnf(c_20,plain,
( incident_c(A,B)
| ~ inner_point(A,B) ),
inference(clausify,[status(thm)],[inner_point_defn]) ).
fof(nnf_10,plain,
! [C] :
? [P] : inner_point(P,C),
inference(fof_nnf,[status(thm)],[c3]) ).
fof(sk_c3,plain,
! [C] : inner_point(sK0(C),C),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(P,sK0(C))],[nnf_10]) ).
cnf(c_21,plain,
inner_point(sK0(A),A),
inference(split_conjunct,[status(thm)],[sk_c3]) ).
cnf(c_36,plain,
incident_c(sK0(A),A),
inference(resolve,[status(thm)],[c_21,c_20]) ).
cnf(c_37,plain,
~ end_point(sK0(A),A),
inference(resolve,[status(thm)],[c_21,c_19]) ).
fof(nnf_17,plain,
? [C,C1,C2,P] :
( end_point(P,C)
& part_of(C2,C)
& part_of(C1,C)
& meet(P,C1,C2) ),
inference(fof_nnf,[status(thm)],[proposition_2_14_3_neg]) ).
fof(sk_proposition_2_14_3_neg,plain,
( end_point(sK1,sK2)
& part_of(sK3,sK2)
& part_of(sK4,sK2)
& meet(sK1,sK4,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK4,sK3,sK2]),skolemize(C,sK2),skolemize(C1,sK4),skolemize(C2,sK3),skolemize(P,sK1)],[nnf_17]) ).
cnf(c_38,negated_conjecture,
end_point(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_proposition_2_14_3_neg]) ).
cnf(c_39,negated_conjecture,
part_of(sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_proposition_2_14_3_neg]) ).
cnf(c_40,negated_conjecture,
part_of(sK4,sK2),
inference(split_conjunct,[status(thm)],[sk_proposition_2_14_3_neg]) ).
cnf(c_41,negated_conjecture,
meet(sK1,sK4,sK3),
inference(split_conjunct,[status(thm)],[sk_proposition_2_14_3_neg]) ).
cnf(c_53,plain,
( end_point(D,C)
| ~ incident_c(D,C)
| ~ incident_c(D,B)
| ~ meet(A,B,C) ),
inference(clausify,[status(thm)],[meet_defn]) ).
cnf(c_54,plain,
( end_point(D,B)
| ~ incident_c(D,C)
| ~ incident_c(D,B)
| ~ meet(A,B,C) ),
inference(clausify,[status(thm)],[meet_defn]) ).
cnf(c_55,plain,
( incident_c(A,C)
| ~ meet(A,B,C) ),
inference(clausify,[status(thm)],[meet_defn]) ).
cnf(c_56,plain,
( incident_c(A,B)
| ~ meet(A,B,C) ),
inference(clausify,[status(thm)],[meet_defn]) ).
cnf(c_63,plain,
( part_of(D,C)
| part_of(C,D)
| ~ incident_c(A,D)
| ~ incident_c(A,C)
| ~ part_of(D,B)
| ~ part_of(C,B)
| ~ end_point(A,B) ),
inference(clausify,[status(thm)],[end_point_defn]) ).
cnf(c_73,plain,
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(clausify,[status(thm)],[part_of_defn]) ).
cnf(c_416,negated_conjecture,
( end_point(A,sK3)
| ~ incident_c(A,sK3)
| ~ incident_c(A,sK4) ),
inference(resolve,[status(thm)],[c_53,c_41]) ).
cnf(c_417,negated_conjecture,
( end_point(sK0(sK3),sK3)
| ~ incident_c(sK0(sK3),sK4) ),
inference(resolve,[status(thm)],[c_416,c_36]) ).
cnf(c_122,negated_conjecture,
~ incident_c(sK0(sK3),sK4),
inference(resolve,[status(thm)],[c_417,c_37]) ).
cnf(c_418,negated_conjecture,
( end_point(A,sK4)
| ~ incident_c(A,sK3)
| ~ incident_c(A,sK4) ),
inference(resolve,[status(thm)],[c_54,c_41]) ).
cnf(c_419,negated_conjecture,
( end_point(sK0(sK4),sK4)
| ~ incident_c(sK0(sK4),sK3) ),
inference(resolve,[status(thm)],[c_418,c_36]) ).
cnf(c_128,negated_conjecture,
~ incident_c(sK0(sK4),sK3),
inference(resolve,[status(thm)],[c_419,c_37]) ).
cnf(c_130,plain,
incident_c(sK1,sK3),
inference(resolve,[status(thm)],[c_55,c_41]) ).
cnf(c_132,plain,
incident_c(sK1,sK4),
inference(resolve,[status(thm)],[c_56,c_41]) ).
cnf(c_420,plain,
( incident_c(sK0(A),B)
| ~ part_of(A,B) ),
inference(resolve,[status(thm)],[c_73,c_36]) ).
cnf(c_348,plain,
~ part_of(sK3,sK4),
inference(resolve,[status(thm)],[c_420,c_122]) ).
cnf(c_421,plain,
( incident_c(sK0(A),B)
| ~ part_of(A,B) ),
inference(resolve,[status(thm)],[c_73,c_36]) ).
cnf(c_359,plain,
~ part_of(sK4,sK3),
inference(resolve,[status(thm)],[c_421,c_128]) ).
cnf(c_422,negated_conjecture,
( part_of(B,sK3)
| part_of(sK3,B)
| ~ incident_c(A,B)
| ~ incident_c(A,sK3)
| ~ part_of(B,sK2)
| ~ end_point(A,sK2) ),
inference(resolve,[status(thm)],[c_63,c_39]) ).
cnf(c_423,negated_conjecture,
( part_of(sK4,sK3)
| part_of(sK3,sK4)
| ~ incident_c(A,sK4)
| ~ incident_c(A,sK3)
| ~ end_point(A,sK2) ),
inference(resolve,[status(thm)],[c_422,c_40]) ).
cnf(c_424,negated_conjecture,
( part_of(sK4,sK3)
| part_of(sK3,sK4)
| ~ incident_c(sK1,sK4)
| ~ end_point(sK1,sK2) ),
inference(resolve,[status(thm)],[c_423,c_130]) ).
cnf(c_425,negated_conjecture,
( part_of(sK4,sK3)
| part_of(sK3,sK4)
| ~ end_point(sK1,sK2) ),
inference(resolve,[status(thm)],[c_424,c_132]) ).
cnf(c_426,negated_conjecture,
( part_of(sK4,sK3)
| ~ end_point(sK1,sK2) ),
inference(resolve,[status(thm)],[c_425,c_348]) ).
cnf(c_427,negated_conjecture,
~ end_point(sK1,sK2),
inference(resolve,[status(thm)],[c_426,c_359]) ).
cnf(c_415,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_38,c_427]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO094+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.05/6.58 % Computer : n012.cluster.edu
% 0.05/6.58 % Model : x86_64 x86_64
% 0.05/6.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/6.58 % Memory : 8046.5625MB
% 0.05/6.58 % OS : Linux 6.8.0-71-generic
% 0.05/6.58 % CPULimit : 300
% 0.05/6.58 % WCLimit : 300
% 0.05/6.58 % DateTime : Fri Sep 25 12:43:18 UTC 2026
% 0.05/6.58 % CPUTime :
% 0.05/6.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/6.58 % Process 2109434 was started by sandbox2 on n012,
% 0.05/6.58 % Fri Sep 25 12:43:18 2026
% 0.05/6.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.05/6.58
% 0.05/6.58 % From the command line: assign(max_seconds, 300).
% 0.09/6.62
% 0.09/6.62 % SZS status Theorem for theBenchmark
% 0.09/6.62
% 0.09/6.62 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.09/6.62 % Length of proof is 28.
% 0.09/6.62 % Level of proof is 5.
% 0.09/6.62 % Maximum clause weight is 21.000.
% 0.09/6.62 % Given clauses 64.
% 0.09/6.62
% 0.09/6.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------