%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO188+1 : TPTP v9.3.1. Released v3.3.0.
% 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 01:17:21 PM UTC 2026
% Result : Theorem 8.35s 1.64s
% Output : Proof 8.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 17
% Syntax : Number of formulae : 144 ( 108 unt; 0 def)
% Number of atoms : 220 ( 91 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 141 ( 65 ~; 51 |; 15 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 165 ( 2 sgn 78 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X,Y,U,V] :
( ( distinct_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).
fof(f10_nnf,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t39,plain,
ifeq(distinct_points(X1,X2),true,ifeq(distinct_lines(X3,X4),true,or(apart_point_and_line(X1,X3),or(apart_point_and_line(X1,X4),or(apart_point_and_line(X2,X3),apart_point_and_line(X2,X4)))),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t60,plain,
ifeq(distinct_points(X1,X2),true,ifeq(distinct_lines(X3,X4),true,or(apart_point_and_line(X1,X3),or(apart_point_and_line(X1,X4),or(apart_point_and_line(X2,X3),apart_point_and_line(X2,X4)))),true),true) = true,
inference(orient,[status(thm)],[t39]) ).
fof(f14,conjecture,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> ~ apart_point_and_line(X,line_connecting(Z,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> ~ apart_point_and_line(X,line_connecting(Z,Y)) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [X,Y,Z] :
( apart_point_and_line(X,line_connecting(Z,Y))
& ~ apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
( apart_point_and_line(sk0,line_connecting(sk2,sk1))
& ~ apart_point_and_line(sk2,line_connecting(sk0,sk1))
& distinct_points(sk1,sk2)
& distinct_points(sk0,sk2)
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f14_nnf]) ).
cnf(c16,plain,
distinct_points(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t7,plain,
distinct_points(sk1,sk2) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t92,plain,
distinct_points(sk1,sk2) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t100,plain,
true = ifeq(true,true,ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(sk1,X1),or(apart_point_and_line(sk1,X2),or(apart_point_and_line(sk2,X1),apart_point_and_line(sk2,X2)))),true),true),
inference(cp,[status(thm)],[t60,t92]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t42,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t836,plain,
true = ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(sk1,X1),or(apart_point_and_line(sk1,X2),or(apart_point_and_line(sk2,X1),apart_point_and_line(sk2,X2)))),true),
inference(step,[status(thm)],[t100,t42]) ).
cnf(t589,plain,
ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(sk1,X1),or(apart_point_and_line(sk1,X2),or(apart_point_and_line(sk2,X1),apart_point_and_line(sk2,X2)))),true) = true,
inference(orient,[status(thm)],[t836]) ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart5) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t33,plain,
ifeq(distinct_lines(X1,X2),true,or(distinct_lines(X1,X3),distinct_lines(X2,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t72,plain,
ifeq(distinct_lines(X1,X2),true,or(distinct_lines(X1,X3),distinct_lines(X2,X3)),true) = true,
inference(orient,[status(thm)],[t33]) ).
fof(f1,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
fof(f1_nnf,plain,
! [X] : ~ distinct_lines(X,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : ~ distinct_lines(X,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t3,plain,
distinct_lines(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t143,plain,
distinct_lines(X1,X1) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t145,plain,
true = ifeq(distinct_lines(X1,X2),true,or(false,distinct_lines(X2,X1)),true),
inference(cp,[status(thm)],[t72,t143]) ).
cnf(t10,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t41,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t775,plain,
true = ifeq(distinct_lines(X1,X2),true,distinct_lines(X2,X1),true),
inference(step,[status(thm)],[t145,t41]) ).
cnf(t375,plain,
ifeq(distinct_lines(X1,X2),true,distinct_lines(X2,X1),true) = true,
inference(orient,[status(thm)],[t775]) ).
fof(f12,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).
fof(f12_nnf,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi5,axiom,
ifeq(apart_point_and_line(X0,X1),true,or(distinct_lines(X1,X2),apart_point_and_line(X0,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(c18,plain,
apart_point_and_line(sk0,line_connecting(sk2,sk1)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi10,negated_conjecture,
apart_point_and_line(sk0,line_connecting(sk2,sk1)) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t23,plain,
or(distinct_lines(line_connecting(sk2,sk1),X1),apart_point_and_line(sk0,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi10]) ).
cnf(t53,plain,
or(distinct_lines(line_connecting(sk2,sk1),X1),apart_point_and_line(sk0,X1)) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t15,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t109,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t15]) ).
fof(f6,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci1) ).
fof(f6_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t27,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X1,line_connecting(X1,X2)))) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t50,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X1,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(c14,plain,
distinct_points(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t5,plain,
distinct_points(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t83,plain,
distinct_points(sk0,sk1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t90,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(cp,[status(thm)],[t50,t83]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t132,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t757,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t90,t132]) ).
cnf(t758,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t757,t41]) ).
cnf(t322,plain,
not(apart_point_and_line(sk0,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t758]) ).
cnf(t323,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t109,t322]) ).
cnf(t759,plain,
false = apart_point_and_line(sk0,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t323,t42]) ).
cnf(t324,plain,
apart_point_and_line(sk0,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t759]) ).
cnf(t329,plain,
true = or(distinct_lines(line_connecting(sk2,sk1),line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t53,t324]) ).
cnf(t8,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t40,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t760,plain,
true = distinct_lines(line_connecting(sk2,sk1),line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t329,t40]) ).
cnf(t334,plain,
distinct_lines(line_connecting(sk2,sk1),line_connecting(sk0,sk1)) = true,
inference(orient,[status(thm)],[t760]) ).
cnf(t377,plain,
true = ifeq(true,true,distinct_lines(line_connecting(sk0,sk1),line_connecting(sk2,sk1)),true),
inference(cp,[status(thm)],[t375,t334]) ).
cnf(t777,plain,
true = distinct_lines(line_connecting(sk0,sk1),line_connecting(sk2,sk1)),
inference(step,[status(thm)],[t377,t42]) ).
cnf(t392,plain,
distinct_lines(line_connecting(sk0,sk1),line_connecting(sk2,sk1)) = true,
inference(orient,[status(thm)],[t777]) ).
cnf(t594,plain,
true = ifeq(true,true,or(apart_point_and_line(sk1,line_connecting(sk0,sk1)),or(apart_point_and_line(sk1,line_connecting(sk2,sk1)),or(apart_point_and_line(sk2,line_connecting(sk0,sk1)),apart_point_and_line(sk2,line_connecting(sk2,sk1))))),true),
inference(cp,[status(thm)],[t589,t392]) ).
cnf(t837,plain,
true = or(apart_point_and_line(sk1,line_connecting(sk0,sk1)),or(apart_point_and_line(sk1,line_connecting(sk2,sk1)),or(apart_point_and_line(sk2,line_connecting(sk0,sk1)),apart_point_and_line(sk2,line_connecting(sk2,sk1))))),
inference(step,[status(thm)],[t594,t42]) ).
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci2) ).
fof(f7_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t28,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X2,line_connecting(X1,X2)))) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t49,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X2,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t28]) ).
cnf(t87,plain,
true = or(not(true),not(apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(cp,[status(thm)],[t49,t83]) ).
cnf(t753,plain,
true = or(false,not(apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t87,t132]) ).
cnf(t754,plain,
true = not(apart_point_and_line(sk1,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t753,t41]) ).
cnf(t310,plain,
not(apart_point_and_line(sk1,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t754]) ).
cnf(t311,plain,
false = ifeq(true,true,apart_point_and_line(sk1,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t109,t310]) ).
cnf(t755,plain,
false = apart_point_and_line(sk1,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t311,t42]) ).
cnf(t312,plain,
apart_point_and_line(sk1,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t755]) ).
cnf(t838,plain,
true = or(false,or(apart_point_and_line(sk1,line_connecting(sk2,sk1)),or(apart_point_and_line(sk2,line_connecting(sk0,sk1)),apart_point_and_line(sk2,line_connecting(sk2,sk1))))),
inference(step,[status(thm)],[t837,t312]) ).
cnf(t839,plain,
true = or(apart_point_and_line(sk1,line_connecting(sk2,sk1)),or(apart_point_and_line(sk2,line_connecting(sk0,sk1)),apart_point_and_line(sk2,line_connecting(sk2,sk1)))),
inference(step,[status(thm)],[t838,t41]) ).
fof(f3,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart4) ).
fof(f3_nnf,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi0,axiom,
ifeq(distinct_points(X0,X1),true,or(distinct_points(X0,X2),distinct_points(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(hi9,negated_conjecture,
distinct_points(sk1,sk2) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t21,plain,
or(distinct_points(sk1,X1),distinct_points(sk2,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi9]) ).
cnf(t48,plain,
or(distinct_points(sk1,X1),distinct_points(sk2,X1)) = true,
inference(orient,[status(thm)],[t21]) ).
fof(f0,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
fof(f0_nnf,plain,
! [X] : ~ distinct_points(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : ~ distinct_points(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,plain,
distinct_points(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t110,plain,
distinct_points(X1,X1) = false,
inference(orient,[status(thm)],[t4]) ).
cnf(t112,plain,
true = or(false,distinct_points(sk2,sk1)),
inference(cp,[status(thm)],[t48,t110]) ).
cnf(t711,plain,
true = distinct_points(sk2,sk1),
inference(step,[status(thm)],[t112,t41]) ).
cnf(t161,plain,
distinct_points(sk2,sk1) = true,
inference(orient,[status(thm)],[t711]) ).
cnf(t166,plain,
true = or(not(true),not(apart_point_and_line(sk1,line_connecting(sk2,sk1)))),
inference(cp,[status(thm)],[t49,t161]) ).
cnf(t719,plain,
true = or(false,not(apart_point_and_line(sk1,line_connecting(sk2,sk1)))),
inference(step,[status(thm)],[t166,t132]) ).
cnf(t720,plain,
true = not(apart_point_and_line(sk1,line_connecting(sk2,sk1))),
inference(step,[status(thm)],[t719,t41]) ).
cnf(t206,plain,
not(apart_point_and_line(sk1,line_connecting(sk2,sk1))) = true,
inference(orient,[status(thm)],[t720]) ).
cnf(t207,plain,
false = ifeq(true,true,apart_point_and_line(sk1,line_connecting(sk2,sk1)),false),
inference(cp,[status(thm)],[t109,t206]) ).
cnf(t721,plain,
false = apart_point_and_line(sk1,line_connecting(sk2,sk1)),
inference(step,[status(thm)],[t207,t42]) ).
cnf(t208,plain,
apart_point_and_line(sk1,line_connecting(sk2,sk1)) = false,
inference(orient,[status(thm)],[t721]) ).
cnf(t840,plain,
true = or(false,or(apart_point_and_line(sk2,line_connecting(sk0,sk1)),apart_point_and_line(sk2,line_connecting(sk2,sk1)))),
inference(step,[status(thm)],[t839,t208]) ).
cnf(t841,plain,
true = or(apart_point_and_line(sk2,line_connecting(sk0,sk1)),apart_point_and_line(sk2,line_connecting(sk2,sk1))),
inference(step,[status(thm)],[t840,t41]) ).
cnf(c17,plain,
~ apart_point_and_line(sk2,line_connecting(sk0,sk1)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t13,plain,
apart_point_and_line(sk2,line_connecting(sk0,sk1)) = false,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t122,plain,
apart_point_and_line(sk2,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t13]) ).
cnf(t842,plain,
true = or(false,apart_point_and_line(sk2,line_connecting(sk2,sk1))),
inference(step,[status(thm)],[t841,t122]) ).
cnf(t843,plain,
true = apart_point_and_line(sk2,line_connecting(sk2,sk1)),
inference(step,[status(thm)],[t842,t41]) ).
cnf(t169,plain,
true = or(not(true),not(apart_point_and_line(sk2,line_connecting(sk2,sk1)))),
inference(cp,[status(thm)],[t50,t161]) ).
cnf(t723,plain,
true = or(false,not(apart_point_and_line(sk2,line_connecting(sk2,sk1)))),
inference(step,[status(thm)],[t169,t132]) ).
cnf(t724,plain,
true = not(apart_point_and_line(sk2,line_connecting(sk2,sk1))),
inference(step,[status(thm)],[t723,t41]) ).
cnf(t220,plain,
not(apart_point_and_line(sk2,line_connecting(sk2,sk1))) = true,
inference(orient,[status(thm)],[t724]) ).
cnf(t221,plain,
false = ifeq(true,true,apart_point_and_line(sk2,line_connecting(sk2,sk1)),false),
inference(cp,[status(thm)],[t109,t220]) ).
cnf(t725,plain,
false = apart_point_and_line(sk2,line_connecting(sk2,sk1)),
inference(step,[status(thm)],[t221,t42]) ).
cnf(t222,plain,
apart_point_and_line(sk2,line_connecting(sk2,sk1)) = false,
inference(orient,[status(thm)],[t725]) ).
cnf(t844,plain,
true = false,
inference(step,[status(thm)],[t843,t222]) ).
cnf(t617,plain,
false = true,
inference(orient,[status(thm)],[t844]) ).
fof(f2,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
fof(f2_nnf,plain,
! [X] : ~ convergent_lines(X,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : ~ convergent_lines(X,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f8,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci3) ).
fof(f8_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci4) ).
fof(f9_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c6,c7,c8,c9,c17]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t617]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO188+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 11:23:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.35/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.35/1.64 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------