%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO080+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 : n002.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 07:17:00 AM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 8 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 35 ( 15 ~; 12 |; 6 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 18 !; 2 ?)
% 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(prove_reflexivity,conjecture,
! [C] : part_of(C,C),
file('theBenchmark.p',prove_reflexivity) ).
fof(prove_reflexivity_neg,negated_conjecture,
~ ! [C] : part_of(C,C),
inference(assume_negation,[status(cth)],[prove_reflexivity]) ).
fof(nnf_17,plain,
? [C] : ~ part_of(C,C),
inference(fof_nnf,[status(thm)],[prove_reflexivity_neg]) ).
fof(sk_prove_reflexivity_neg,plain,
~ part_of(sK0,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0)],[nnf_17]) ).
cnf(c_38,negated_conjecture,
~ part_of(sK0,sK0),
inference(split_conjunct,[status(thm)],[sk_prove_reflexivity_neg]) ).
fof(nnf_1,plain,
! [C,C1] :
( ( ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) )
| part_of(C1,C) )
& ( ! [X0] :
( incident_c(X0,C)
| ~ incident_c(X0,C1) )
| ~ part_of(C1,C) ) ),
inference(fof_nnf,[status(thm)],[part_of_defn]) ).
fof(sk_part_of_defn_sk,plain,
! [C,C1] :
( ( ( ~ incident_c(sK1(C,C1),C)
& incident_c(sK1(C,C1),C1) )
| part_of(C1,C) )
& ( ! [X0] :
( incident_c(X0,C)
| ~ incident_c(X0,C1) )
| ~ part_of(C1,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(P,sK1(C,C1))],[nnf_1]) ).
fof(sk_part_of_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ incident_c(sK1(VAR_1,VAR_0),VAR_1)
| part_of(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( incident_c(sK1(VAR_1,VAR_0),VAR_0)
| part_of(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( incident_c(VAR_2,VAR_1)
| ~ incident_c(VAR_2,VAR_0)
| ~ part_of(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_part_of_defn_sk]) ).
cnf(c_68,plain,
( ~ incident_c(sK1(B,A),B)
| part_of(A,B) ),
inference(split_conjunct,[status(thm)],[sk_part_of_defn]) ).
cnf(c_69,plain,
( incident_c(sK1(B,A),A)
| part_of(A,B) ),
inference(split_conjunct,[status(thm)],[sk_part_of_defn]) ).
cnf(c_281,negated_conjecture,
~ incident_c(sK1(sK0,sK0),sK0),
inference(resolve,[status(thm)],[c_68,c_38]) ).
cnf(c_287,negated_conjecture,
incident_c(sK1(sK0,sK0),sK0),
inference(resolve,[status(thm)],[c_69,c_38]) ).
cnf(c_286,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_281,c_287]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO080+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 12:43:50 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3285288 was started by sandbox2 on n002,
% 0.08/0.35 % Fri Sep 25 12:43:50 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.40
% 0.12/0.40 % SZS status Theorem for theBenchmark
% 0.12/0.40
% 0.12/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.12/0.40 % Length of proof is 7.
% 0.12/0.40 % Level of proof is 3.
% 0.12/0.40 % Maximum clause weight is 8.000.
% 0.12/0.40 % Given clauses 39.
% 0.12/0.40
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------