%------------------------------------------------------------------------------
% 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 : n003.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 : Unsatisfiable 10.28s 6.97s
% Output : Proof 10.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 72 ( 48 unt; 0 def)
% Number of atoms : 100 ( 41 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 42 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 80 ( 4 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,axiom,
( part_of(A,B)
| ~ incident_c(ax0_sk1(A,B),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn_3) ).
fof(f2_nnf,plain,
! [A,B] :
( part_of(A,B)
| ~ incident_c(ax0_sk1(A,B),B) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( part_of(A,B)
| ~ incident_c(ax0_sk1(A,B),B) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( part_of(X0,X1)
| ~ incident_c(ax0_sk1(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t26,plain,
ifeq(incident_c(ax0_sk1(X1,X2),X2),true,part_of(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t81,plain,
ifeq(incident_c(ax0_sk1(X1,X2),X2),true,part_of(X1,X2),true) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(f0,axiom,
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
file('/export/starexec/sandbox2/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(t41,plain,
ifeq(part_of(X1,X2),true,ifeq(incident_c(X3,X1),true,incident_c(X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t88,plain,
ifeq(part_of(X1,X2),true,ifeq(incident_c(X3,X1),true,incident_c(X3,X2),true),true) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(f49,negated_conjecture,
part_of(sk15,sk16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_transitivity_68) ).
fof(f49_nnf,plain,
part_of(sk15,sk16),
inference(nnf_transformation,[status(thm)],[f49]) ).
cnf(c49,plain,
part_of(sk15,sk16),
inference(cnf_transformation,[status(esa)],[f49_nnf]) ).
cnf(t9,plain,
part_of(sk15,sk16) = true,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(t129,plain,
part_of(sk15,sk16) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t131,plain,
true = ifeq(true,true,ifeq(incident_c(X1,sk15),true,incident_c(X1,sk16),true),true),
inference(cp,[status(thm)],[t88,t129]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t60,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t606,plain,
true = ifeq(incident_c(X1,sk15),true,incident_c(X1,sk16),true),
inference(step,[status(thm)],[t131,t60]) ).
cnf(t459,plain,
ifeq(incident_c(X1,sk15),true,incident_c(X1,sk16),true) = true,
inference(orient,[status(thm)],[t606]) ).
cnf(f48,negated_conjecture,
part_of(sk14,sk15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_transitivity_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(t7,plain,
part_of(sk14,sk15) = true,
inference(equality_encoding,[status(esa)],[c48]) ).
cnf(t112,plain,
part_of(sk14,sk15) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t114,plain,
true = ifeq(true,true,ifeq(incident_c(X1,sk14),true,incident_c(X1,sk15),true),true),
inference(cp,[status(thm)],[t88,t112]) ).
cnf(t603,plain,
true = ifeq(incident_c(X1,sk14),true,incident_c(X1,sk15),true),
inference(step,[status(thm)],[t114,t60]) ).
cnf(t381,plain,
ifeq(incident_c(X1,sk14),true,incident_c(X1,sk15),true) = true,
inference(orient,[status(thm)],[t603]) ).
cnf(f1,axiom,
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn_2) ).
fof(f1_nnf,plain,
! [A,B] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( part_of(X0,X1)
| incident_c(ax0_sk1(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t21,plain,
or(incident_c(ax0_sk1(X1,X2),X1),part_of(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t107,plain,
or(incident_c(ax0_sk1(X1,X2),X1),part_of(X1,X2)) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(f50,negated_conjecture,
~ part_of(sk14,sk16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_transitivity_69) ).
fof(f50_nnf,plain,
~ part_of(sk14,sk16),
inference(nnf_transformation,[status(thm)],[f50]) ).
fof(f50_sk,plain,
~ part_of(sk14,sk16),
inference(skolemisation,[status(esa)],[f50_nnf]) ).
cnf(c50,plain,
~ part_of(sk14,sk16),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(t8,plain,
part_of(sk14,sk16) = false,
inference(equality_encoding,[status(esa)],[c50]) ).
cnf(t164,plain,
part_of(sk14,sk16) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t165,plain,
true = or(incident_c(ax0_sk1(sk14,sk16),sk14),false),
inference(cp,[status(thm)],[t107,t164]) ).
cnf(t3,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t63,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t582,plain,
true = incident_c(ax0_sk1(sk14,sk16),sk14),
inference(step,[status(thm)],[t165,t63]) ).
cnf(t216,plain,
incident_c(ax0_sk1(sk14,sk16),sk14) = true,
inference(orient,[status(thm)],[t582]) ).
cnf(t383,plain,
true = ifeq(true,true,incident_c(ax0_sk1(sk14,sk16),sk15),true),
inference(cp,[status(thm)],[t381,t216]) ).
cnf(t605,plain,
true = incident_c(ax0_sk1(sk14,sk16),sk15),
inference(step,[status(thm)],[t383,t60]) ).
cnf(t420,plain,
incident_c(ax0_sk1(sk14,sk16),sk15) = true,
inference(orient,[status(thm)],[t605]) ).
cnf(t462,plain,
true = ifeq(true,true,incident_c(ax0_sk1(sk14,sk16),sk16),true),
inference(cp,[status(thm)],[t459,t420]) ).
cnf(t609,plain,
true = incident_c(ax0_sk1(sk14,sk16),sk16),
inference(step,[status(thm)],[t462,t60]) ).
cnf(t532,plain,
incident_c(ax0_sk1(sk14,sk16),sk16) = true,
inference(orient,[status(thm)],[t609]) ).
cnf(t541,plain,
true = ifeq(true,true,part_of(sk14,sk16),true),
inference(cp,[status(thm)],[t81,t532]) ).
cnf(t610,plain,
true = part_of(sk14,sk16),
inference(step,[status(thm)],[t541,t60]) ).
cnf(t611,plain,
true = false,
inference(step,[status(thm)],[t610,t164]) ).
cnf(t566,plain,
false = true,
inference(orient,[status(thm)],[t611]) ).
cnf(f21,axiom,
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
file('/export/starexec/sandbox2/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(f30,axiom,
( ~ end_point(B,A)
| ~ closed(A) ),
file('/export/starexec/sandbox2/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/sandbox2/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,c50]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t566]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----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
% 0.09/5.37 % Computer : n003.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Wed Sep 23 10:47:09 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.28/6.97 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.28/6.97 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------