%------------------------------------------------------------------------------
% 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 : n006.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 : Unsatisfiable 6.31s 1.28s
% Output : Proof 6.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 25 unt; 0 def)
% Number of atoms : 85 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 86 ( 50 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 77 ( 5 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f20,axiom,
( incident_c(A,B)
| ~ inner_point(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn_21) ).
fof(f20_nnf,plain,
! [A,B] :
( incident_c(A,B)
| ~ inner_point(A,B) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B] :
( incident_c(A,B)
| ~ inner_point(A,B) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( incident_c(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi17,axiom,
ifeq(inner_point(X0,X1),true,incident_c(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(f36,axiom,
inner_point(ax0_sk8(A),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3_37) ).
fof(f36_nnf,plain,
! [A] : inner_point(ax0_sk8(A),A),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [A] : inner_point(ax0_sk8(A),A),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c36,plain,
inner_point(ax0_sk8(X0),X0),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(hi31,axiom,
inner_point(ax0_sk8(X0),X0) = true,
inference(equality_encoding,[status(esa)],[c36]) ).
cnf(h2,plain,
incident_c(ax0_sk8(V0),V0) = true,
inference(hyper_resolution,[status(thm)],[hi17,hi31]) ).
cnf(f0,axiom,
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn_1) ).
fof(f0_nnf,plain,
! [A,B,C] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( incident_c(X2,X1)
| ~ incident_c(X2,X0)
| ~ part_of(X0,X1) ),
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]) ).
cnf(f48,negated_conjecture,
part_of(sk14,sk15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_9_67) ).
fof(f48_nnf,plain,
part_of(sk14,sk15),
inference(nnf_transformation,[status(thm)],[f48]) ).
cnf(c48,plain,
part_of(sk14,sk15),
inference(cnf_transformation,[status(esa)],[f48_nnf]) ).
cnf(hi40,negated_conjecture,
part_of(sk14,sk15) = true,
inference(equality_encoding,[status(esa)],[c48]) ).
cnf(h28,plain,
incident_c(ax0_sk8(sk14),sk15) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi40,h2]) ).
cnf(f25,axiom,
( end_point(D,B)
| ~ incident_c(D,C)
| ~ incident_c(D,B)
| ~ meet(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_26) ).
fof(f25_nnf,plain,
! [A,B,C,D] :
( end_point(D,B)
| ~ incident_c(D,C)
| ~ incident_c(D,B)
| ~ meet(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [A,B,C,D] :
( end_point(D,B)
| ~ incident_c(D,C)
| ~ incident_c(D,B)
| ~ meet(A,B,C) ),
inference(skolemisation,[status(esa)],[f25_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)],[f25_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(f49,negated_conjecture,
meet(sk16,sk14,sk15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_9_68) ).
fof(f49_nnf,plain,
meet(sk16,sk14,sk15),
inference(nnf_transformation,[status(thm)],[f49]) ).
cnf(c49,plain,
meet(sk16,sk14,sk15),
inference(cnf_transformation,[status(esa)],[f49_nnf]) ).
cnf(hi41,negated_conjecture,
meet(sk16,sk14,sk15) = true,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(h242,plain,
end_point(ax0_sk8(sk14),sk14) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi41,h2,h28]) ).
cnf(f21,axiom,
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn_22) ).
fof(f21_nnf,plain,
! [A,B] :
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B] :
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21_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,h242]) ).
cnf(t415,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f30,axiom,
( ~ end_point(B,A)
| ~ closed(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_defn_31) ).
fof(f30_nnf,plain,
! [A,B] :
( ~ end_point(B,A)
| ~ closed(A) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [A,B] :
( ~ end_point(B,A)
| ~ closed(A) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( ~ end_point(X1,X0)
| ~ closed(X0) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(f41,axiom,
( A != ax0_sk11(A,B)
| ~ end_point(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c6_42) ).
fof(f41_nnf,plain,
! [A,B] :
( A != ax0_sk11(A,B)
| ~ end_point(A,B) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [A,B] :
( A != ax0_sk11(A,B)
| ~ end_point(A,B) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c41,plain,
( X0 != ax0_sk11(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f41_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,t415]) ).
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.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 10:46:56 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.31/1.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.31/1.28 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------