%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO087+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 07:17:02 AM UTC 2026
% Result : Theorem 0.05s 5.36s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 44 ( 19 ~; 11 |; 7 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 40 ( 1 sgn 16 !; 7 ?)
% 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(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(corollary_2_9,conjecture,
! [C1,C2] :
( part_of(C1,C2)
=> ~ ? [P] : meet(P,C1,C2) ),
file('theBenchmark.p',corollary_2_9) ).
fof(corollary_2_9_neg,negated_conjecture,
~ ! [C1,C2] :
( part_of(C1,C2)
=> ~ ? [P] : meet(P,C1,C2) ),
inference(assume_negation,[status(cth)],[corollary_2_9]) ).
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,
? [C1,C2] :
( ? [P] : meet(P,C1,C2)
& part_of(C1,C2) ),
inference(fof_nnf,[status(thm)],[corollary_2_9_neg]) ).
fof(sk_corollary_2_9_neg,plain,
( meet(sK1,sK2,sK3)
& part_of(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK1]),skolemize(C1,sK2),skolemize(C2,sK3),skolemize(P,sK1)],[nnf_17]) ).
cnf(c_38,negated_conjecture,
meet(sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_corollary_2_9_neg]) ).
cnf(c_39,negated_conjecture,
part_of(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_corollary_2_9_neg]) ).
cnf(c_52,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_71,plain,
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(clausify,[status(thm)],[part_of_defn]) ).
cnf(c_347,negated_conjecture,
( end_point(A,sK2)
| ~ incident_c(A,sK3)
| ~ incident_c(A,sK2) ),
inference(resolve,[status(thm)],[c_52,c_38]) ).
cnf(c_348,negated_conjecture,
( end_point(sK0(sK2),sK2)
| ~ incident_c(sK0(sK2),sK3) ),
inference(resolve,[status(thm)],[c_347,c_36]) ).
cnf(c_118,negated_conjecture,
~ incident_c(sK0(sK2),sK3),
inference(resolve,[status(thm)],[c_348,c_37]) ).
cnf(c_349,plain,
( incident_c(sK0(A),B)
| ~ part_of(A,B) ),
inference(resolve,[status(thm)],[c_71,c_36]) ).
cnf(c_350,plain,
~ part_of(sK2,sK3),
inference(resolve,[status(thm)],[c_349,c_118]) ).
cnf(c_346,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_39,c_350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO087+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.05/5.32 % Computer : n012.cluster.edu
% 0.05/5.32 % Model : x86_64 x86_64
% 0.05/5.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.32 % Memory : 8046.5625MB
% 0.05/5.32 % OS : Linux 6.8.0-71-generic
% 0.05/5.32 % CPULimit : 300
% 0.05/5.32 % WCLimit : 300
% 0.05/5.32 % DateTime : Fri Sep 25 12:41:42 UTC 2026
% 0.05/5.32 % CPUTime :
% 0.05/5.32 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/5.32 % Process 2108022 was started by sandbox2 on n012,
% 0.05/5.32 % Fri Sep 25 12:41:42 2026
% 0.05/5.32 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.05/5.32
% 0.05/5.32 % From the command line: assign(max_seconds, 300).
% 0.05/5.36
% 0.05/5.36 % SZS status Theorem for theBenchmark
% 0.05/5.36
% 0.05/5.36 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.05/5.36 % Length of proof is 16.
% 0.05/5.36 % Level of proof is 4.
% 0.05/5.36 % Maximum clause weight is 13.000.
% 0.05/5.36 % Given clauses 56.
% 0.05/5.36
% 0.05/5.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------