%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO087+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 01:17:00 PM UTC 2026
% Result : Theorem 3.96s 1.30s
% Output : Proof 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 21 unt; 0 def)
% Number of atoms : 128 ( 18 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 136 ( 54 ~; 41 |; 32 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 87 ( 3 sgn 45 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [P,C] :
( inner_point(P,C)
<=> ( ~ end_point(P,C)
& incident_c(P,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn) ).
fof(f3_nnf,plain,
! [P,C] :
( ( end_point(P,C)
| ~ incident_c(P,C)
| inner_point(P,C) )
& ( ( ~ end_point(P,C)
& incident_c(P,C) )
| ~ inner_point(P,C) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [P,C] :
( ( end_point(P,C)
| ~ incident_c(P,C)
| inner_point(P,C) )
& ( ( ~ end_point(P,C)
& incident_c(P,C) )
| ~ inner_point(P,C) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c20,plain,
( incident_c(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi17,axiom,
ifeq(inner_point(X0,X1),true,incident_c(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
fof(f9,axiom,
! [C] :
? [P] : inner_point(P,C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3) ).
fof(f9_nnf,plain,
! [C] :
? [P] : inner_point(P,C),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [C] : inner_point(sk7(C),C),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f9_nnf]) ).
cnf(c36,plain,
inner_point(sk7(X0),X0),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi31,axiom,
inner_point(sk7(X0),X0) = true,
inference(equality_encoding,[status(esa)],[c36]) ).
cnf(h3,plain,
incident_c(sk7(V0),V0) = true,
inference(hyper_resolution,[status(thm)],[hi17,hi31]) ).
fof(f0,axiom,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C1)
=> incident_c(P,C) ) ),
file('/export/starexec/sandbox/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(c0,plain,
( incident_c(X2,X0)
| ~ incident_c(X2,X1)
| ~ part_of(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(part_of(X0,X1),true,ifeq(incident_c(X2,X0),true,incident_c(X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f16,conjecture,
! [C1,C2] :
( part_of(C1,C2)
=> ~ ? [P] : meet(P,C1,C2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_9) ).
fof(f16_neg,negated_conjecture,
~ ! [C1,C2] :
( part_of(C1,C2)
=> ~ ? [P] : meet(P,C1,C2) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [C1,C2] :
( ? [P] : meet(P,C1,C2)
& part_of(C1,C2) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( meet(sk15,sk13,sk14)
& 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(hi40,negated_conjecture,
part_of(sk13,sk14) = true,
inference(equality_encoding,[status(esa)],[c48]) ).
cnf(h54,plain,
incident_c(sk7(sk13),sk14) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi40,h3]) ).
fof(f4,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('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn) ).
fof(f4_nnf,plain,
! [P,C,C1] :
( ( ? [Q] :
( ( ~ end_point(Q,C1)
| ~ end_point(Q,C) )
& incident_c(Q,C1)
& incident_c(Q,C) )
| ~ incident_c(P,C1)
| ~ incident_c(P,C)
| meet(P,C,C1) )
& ( ( ! [Q] :
( ( end_point(Q,C1)
& end_point(Q,C) )
| ~ incident_c(Q,C1)
| ~ incident_c(Q,C) )
& incident_c(P,C1)
& incident_c(P,C) )
| ~ meet(P,C,C1) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [P,C,C1,Q] :
( ( ( ( ~ end_point(sk4(P,C,C1),C1)
| ~ end_point(sk4(P,C,C1),C) )
& incident_c(sk4(P,C,C1),C1)
& incident_c(sk4(P,C,C1),C) )
| ~ incident_c(P,C1)
| ~ incident_c(P,C)
| meet(P,C,C1) )
& ( ( ( ( end_point(Q,C1)
& end_point(Q,C) )
| ~ incident_c(Q,C1)
| ~ incident_c(Q,C) )
& incident_c(P,C1)
& incident_c(P,C) )
| ~ meet(P,C,C1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f4_nnf]) ).
cnf(c25,plain,
( end_point(X3,X1)
| ~ incident_c(X3,X2)
| ~ incident_c(X3,X1)
| ~ meet(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi21,axiom,
ifeq(meet(X0,X1,X2),true,ifeq(incident_c(X3,X1),true,ifeq(incident_c(X3,X2),true,end_point(X3,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(c49,plain,
meet(sk15,sk13,sk14),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi41,negated_conjecture,
meet(sk15,sk13,sk14) = true,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(h79,plain,
end_point(sk7(sk13),sk13) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi41,h3,h54]) ).
cnf(c21,plain,
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi42,axiom,
ifeq(inner_point(X0,X1),true,ifeq(end_point(X0,X1),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi42,hi31,h79]) ).
cnf(t1223,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f5,axiom,
! [C] :
( closed(C)
<=> ~ ? [P] : end_point(P,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_defn) ).
fof(f5_nnf,plain,
! [C] :
( ( ? [P] : end_point(P,C)
| closed(C) )
& ( ! [P] : ~ end_point(P,C)
| ~ closed(C) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [C,P] :
( ( end_point(sk5(C),C)
| closed(C) )
& ( ~ end_point(P,C)
| ~ closed(C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f5_nnf]) ).
cnf(c30,plain,
( ~ end_point(X1,X0)
| ~ closed(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f12,axiom,
! [C,P] :
( end_point(P,C)
=> ? [Q] :
( P != Q
& end_point(Q,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c6) ).
fof(f12_nnf,plain,
! [C,P] :
( ? [Q] :
( P != Q
& end_point(Q,C) )
| ~ end_point(P,C) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [P,C] :
( ( P != sk10(C,P)
& end_point(sk10(C,P),C) )
| ~ end_point(P,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f12_nnf]) ).
cnf(c41,plain,
( X1 != sk10(X0,X1)
| ~ end_point(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c21,c30,c41]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1223]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO087+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 10:47:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.96/1.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.96/1.30 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------