%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO081+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 : Fri Sep 25 01:16:59 PM UTC 2026
% Result : Theorem 25.29s 13.66s
% Output : Proof 25.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 44 ( 15 ~; 15 |; 10 &)
% ( 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 : 30 ( 0 sgn 15 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C1)
=> incident_c(P,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn) ).
fof(f0_nnf,plain,
! [C,C1] :
( ( ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) )
| part_of(C1,C) )
& ( ! [P] :
( incident_c(P,C)
| ~ incident_c(P,C1) )
| ~ part_of(C1,C) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [C1,C,P] :
( ( ( ~ incident_c(sk0(C,C1),C)
& incident_c(sk0(C,C1),C1) )
| part_of(C1,C) )
& ( incident_c(P,C)
| ~ incident_c(P,C1)
| ~ part_of(C1,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c2,plain,
( ~ incident_c(sk0(X0,X1),X0)
| part_of(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c1,plain,
( incident_c(sk0(X0,X1),X1)
| part_of(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c0,plain,
( incident_c(X2,X0)
| ~ incident_c(X2,X1)
| ~ part_of(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f16,conjecture,
! [C1,C2,C3] :
( ( part_of(C2,C3)
& part_of(C1,C2) )
=> part_of(C1,C3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_transitivity) ).
fof(f16_neg,negated_conjecture,
~ ! [C1,C2,C3] :
( ( part_of(C2,C3)
& part_of(C1,C2) )
=> part_of(C1,C3) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [C1,C2,C3] :
( ~ part_of(C1,C3)
& part_of(C2,C3)
& part_of(C1,C2) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( ~ part_of(sk13,sk15)
& part_of(sk14,sk15)
& part_of(sk13,sk14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14,sk15])],[f16_nnf]) ).
cnf(c48,plain,
part_of(sk13,sk14),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p51,plain,
( incident_c(X0,sk14)
| ~ incident_c(X0,sk13) ),
inference(resolution,[status(thm)],[c0,c48]) ).
cnf(p53,plain,
( incident_c(sk0(X0,sk13),sk14)
| part_of(sk13,X0) ),
inference(resolution,[status(thm)],[c1,p51]) ).
cnf(c49,plain,
part_of(sk14,sk15),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p52,plain,
( incident_c(X0,sk15)
| ~ incident_c(X0,sk14) ),
inference(resolution,[status(thm)],[c0,c49]) ).
cnf(p55,plain,
( incident_c(sk0(X0,sk13),sk15)
| part_of(sk13,X0) ),
inference(resolution,[status(thm)],[p53,p52]) ).
cnf(p57,plain,
( part_of(sk13,sk15)
| part_of(sk13,sk15) ),
inference(resolution,[status(thm)],[c2,p55]) ).
cnf(p58,plain,
part_of(sk13,sk15),
inference(factoring,[status(thm)],[p57]) ).
cnf(c50,plain,
~ part_of(sk13,sk15),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p59,plain,
$false,
inference(resolution,[status(thm)],[p58,c50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO081+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/10.39 % Computer : n017.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Wed Sep 23 10:40:41 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.29/13.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.29/13.66 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------