%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO081+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 : n014.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 0.23s 0.72s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 53 ( 21 ~; 16 |; 12 &)
% ( 1 <=>; 3 =>; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 22 !; 4 ?)
% 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(part_of_transitivity,conjecture,
! [C1,C2,C3] :
( ( part_of(C2,C3)
& part_of(C1,C2) )
=> part_of(C1,C3) ),
file('theBenchmark.p',part_of_transitivity) ).
fof(part_of_transitivity_neg,negated_conjecture,
~ ! [C1,C2,C3] :
( ( part_of(C2,C3)
& part_of(C1,C2) )
=> part_of(C1,C3) ),
inference(assume_negation,[status(cth)],[part_of_transitivity]) ).
fof(nnf_17,plain,
? [C1,C2,C3] :
( ~ part_of(C1,C3)
& part_of(C2,C3)
& part_of(C1,C2) ),
inference(fof_nnf,[status(thm)],[part_of_transitivity_neg]) ).
fof(sk_part_of_transitivity_neg,plain,
( ~ part_of(sK0,sK1)
& part_of(sK2,sK1)
& part_of(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(C1,sK0),skolemize(C2,sK2),skolemize(C3,sK1)],[nnf_17]) ).
cnf(c_38,negated_conjecture,
~ part_of(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_part_of_transitivity_neg]) ).
cnf(c_39,negated_conjecture,
part_of(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_part_of_transitivity_neg]) ).
cnf(c_40,negated_conjecture,
part_of(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_part_of_transitivity_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(sK3(C,C1),C)
& incident_c(sK3(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,[sK3]),skolemize(P,sK3(C,C1))],[nnf_1]) ).
fof(sk_part_of_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ incident_c(sK3(VAR_1,VAR_0),VAR_1)
| part_of(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( incident_c(sK3(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_70,plain,
( ~ incident_c(sK3(B,A),B)
| part_of(A,B) ),
inference(split_conjunct,[status(thm)],[sk_part_of_defn]) ).
cnf(c_71,plain,
( incident_c(sK3(B,A),A)
| part_of(A,B) ),
inference(split_conjunct,[status(thm)],[sk_part_of_defn]) ).
cnf(c_72,plain,
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(split_conjunct,[status(thm)],[sk_part_of_defn]) ).
cnf(c_241,negated_conjecture,
~ incident_c(sK3(sK1,sK0),sK1),
inference(resolve,[status(thm)],[c_70,c_38]) ).
cnf(c_247,plain,
incident_c(sK3(sK1,sK0),sK0),
inference(resolve,[status(thm)],[c_71,c_38]) ).
cnf(c_412,negated_conjecture,
( incident_c(A,sK1)
| ~ incident_c(A,sK2) ),
inference(resolve,[status(thm)],[c_72,c_39]) ).
cnf(c_386,negated_conjecture,
~ incident_c(sK3(sK1,sK0),sK2),
inference(resolve,[status(thm)],[c_412,c_241]) ).
cnf(c_413,negated_conjecture,
( incident_c(A,sK2)
| ~ incident_c(A,sK0) ),
inference(resolve,[status(thm)],[c_72,c_40]) ).
cnf(c_414,negated_conjecture,
~ incident_c(sK3(sK1,sK0),sK0),
inference(resolve,[status(thm)],[c_413,c_386]) ).
cnf(c_411,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_247,c_414]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO081+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.65 % Computer : n014.cluster.edu
% 0.17/0.65 % Model : x86_64 x86_64
% 0.17/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.65 % Memory : 8046.5625MB
% 0.17/0.65 % OS : Linux 6.8.0-71-generic
% 0.17/0.65 % CPULimit : 300
% 0.17/0.65 % WCLimit : 300
% 0.17/0.65 % DateTime : Fri Sep 25 12:40:48 UTC 2026
% 0.23/0.65 % CPUTime :
% 0.23/0.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.23/0.65 % Process 246458 was started by sandbox2 on n014,
% 0.23/0.65 % Fri Sep 25 12:40:48 2026
% 0.23/0.65 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.23/0.66
% 0.23/0.66 % From the command line: assign(max_seconds, 300).
% 0.23/0.72
% 0.23/0.72 % SZS status Theorem for theBenchmark
% 0.23/0.72
% 0.23/0.72 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.23/0.72 % Length of proof is 12.
% 0.23/0.72 % Level of proof is 4.
% 0.23/0.72 % Maximum clause weight is 12.000.
% 0.23/0.72 % Given clauses 55.
% 0.23/0.72
% 0.23/0.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------