%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO222+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 01:17:35 PM UTC 2026
% Result : Theorem 19.77s 3.02s
% Output : Proof 19.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 22
% Syntax : Number of formulae : 170 ( 133 unt; 0 def)
% Number of atoms : 243 ( 99 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 151 ( 78 ~; 58 |; 7 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 329 ( 35 sgn 106 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [L,M,N] :
( ( unorthogonal_lines(L,M)
& convergent_lines(L,M) )
=> ( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oac1) ).
fof(f18_nnf,plain,
! [L,M,N] :
( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [L,M,N] :
( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c19,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t42,plain,
ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,or(convergent_lines(X1,X3),unorthogonal_lines(X2,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t53,plain,
ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,or(convergent_lines(X1,X3),unorthogonal_lines(X2,X3)),true),true) = true,
inference(orient,[status(thm)],[t42]) ).
fof(f2,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox/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]) ).
cnf(t2,plain,
convergent_lines(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t106,plain,
convergent_lines(X1,X1) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t121,plain,
true = ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,or(false,unorthogonal_lines(X2,X1)),true),true),
inference(cp,[status(thm)],[t53,t106]) ).
cnf(t7,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t49,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t2563,plain,
true = ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,unorthogonal_lines(X2,X1),true),true),
inference(step,[status(thm)],[t121,t49]) ).
cnf(t1042,plain,
ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,unorthogonal_lines(X2,X1),true),true) = true,
inference(orient,[status(thm)],[t2563]) ).
fof(f5,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(f5_nnf,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t32,plain,
ifeq(convergent_lines(X1,X2),true,or(convergent_lines(X1,X3),convergent_lines(X2,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t56,plain,
ifeq(convergent_lines(X1,X2),true,or(convergent_lines(X1,X3),convergent_lines(X2,X3)),true) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t109,plain,
true = ifeq(convergent_lines(X1,X2),true,or(false,convergent_lines(X2,X1)),true),
inference(cp,[status(thm)],[t56,t106]) ).
cnf(t2399,plain,
true = ifeq(convergent_lines(X1,X2),true,convergent_lines(X2,X1),true),
inference(step,[status(thm)],[t109,t49]) ).
cnf(t297,plain,
ifeq(convergent_lines(X1,X2),true,convergent_lines(X2,X1),true) = true,
inference(orient,[status(thm)],[t2399]) ).
fof(f17,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
fof(f17_nnf,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t19,plain,
or(convergent_lines(X1,X2),unorthogonal_lines(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t76,plain,
or(convergent_lines(X1,X2),unorthogonal_lines(X1,X2)) = true,
inference(orient,[status(thm)],[t19]) ).
fof(f19,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
fof(f19_nnf,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [L,A] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c22,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t13,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t174,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(orient,[status(thm)],[t13]) ).
cnf(t175,plain,
true = or(convergent_lines(orthogonal_through_point(X1,X2),X1),false),
inference(cp,[status(thm)],[t76,t174]) ).
cnf(t5,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t48,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t2385,plain,
true = convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(step,[status(thm)],[t175,t48]) ).
cnf(t231,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1) = true,
inference(orient,[status(thm)],[t2385]) ).
cnf(t298,plain,
true = ifeq(true,true,convergent_lines(X1,orthogonal_through_point(X1,X2)),true),
inference(cp,[status(thm)],[t297,t231]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t47,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t2400,plain,
true = convergent_lines(X1,orthogonal_through_point(X1,X2)),
inference(step,[status(thm)],[t298,t47]) ).
cnf(t302,plain,
convergent_lines(X1,orthogonal_through_point(X1,X2)) = true,
inference(orient,[status(thm)],[t2400]) ).
cnf(t1043,plain,
true = ifeq(true,true,ifeq(unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),true,unorthogonal_lines(orthogonal_through_point(X1,X2),X1),true),true),
inference(cp,[status(thm)],[t1042,t302]) ).
cnf(t2564,plain,
true = ifeq(unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),true,unorthogonal_lines(orthogonal_through_point(X1,X2),X1),true),
inference(step,[status(thm)],[t1043,t47]) ).
cnf(t2565,plain,
true = ifeq(unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),true,false,true),
inference(step,[status(thm)],[t2564,t174]) ).
cnf(t1055,plain,
ifeq(unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),true,false,true) = true,
inference(orient,[status(thm)],[t2565]) ).
cnf(c21,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t44,plain,
ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,or(unorthogonal_lines(X1,X3),unorthogonal_lines(X2,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t55,plain,
ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,or(unorthogonal_lines(X1,X3),unorthogonal_lines(X2,X3)),true),true) = true,
inference(orient,[status(thm)],[t44]) ).
cnf(t177,plain,
true = ifeq(convergent_lines(orthogonal_through_point(X1,X2),X3),true,ifeq(unorthogonal_lines(orthogonal_through_point(X1,X2),X3),true,or(false,unorthogonal_lines(X3,X1)),true),true),
inference(cp,[status(thm)],[t55,t174]) ).
cnf(t2694,plain,
true = ifeq(convergent_lines(orthogonal_through_point(X1,X2),X3),true,ifeq(unorthogonal_lines(orthogonal_through_point(X1,X2),X3),true,unorthogonal_lines(X3,X1),true),true),
inference(step,[status(thm)],[t177,t49]) ).
cnf(t2033,plain,
ifeq(convergent_lines(orthogonal_through_point(X1,X2),X3),true,ifeq(unorthogonal_lines(orthogonal_through_point(X1,X2),X3),true,unorthogonal_lines(X3,X1),true),true) = true,
inference(orient,[status(thm)],[t2694]) ).
cnf(hi2,axiom,
ifeq(convergent_lines(X0,X1),true,or(convergent_lines(X0,X2),convergent_lines(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
fof(f22,conjecture,
! [A,L] : ~ convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f22_neg,negated_conjecture,
~ ! [A,L] : ~ convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f22_nnf,plain,
? [A,L] : convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(nnf_transformation,[status(thm)],[f22_neg]) ).
fof(f22_sk,plain,
convergent_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f22_nnf]) ).
cnf(c25,plain,
convergent_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi14,negated_conjecture,
convergent_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t24,plain,
or(convergent_lines(sk1,X1),convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi14]) ).
cnf(t78,plain,
or(convergent_lines(sk1,X1),convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),X1)) = true,
inference(orient,[status(thm)],[t24]) ).
cnf(t115,plain,
true = or(false,convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1)),
inference(cp,[status(thm)],[t78,t106]) ).
cnf(t2392,plain,
true = convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),
inference(step,[status(thm)],[t115,t49]) ).
cnf(t263,plain,
convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1) = true,
inference(orient,[status(thm)],[t2392]) ).
cnf(t2040,plain,
true = ifeq(true,true,ifeq(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),true,unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)),true),true),
inference(cp,[status(thm)],[t2033,t263]) ).
cnf(t2696,plain,
true = ifeq(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),true,unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)),true),
inference(step,[status(thm)],[t2040,t47]) ).
cnf(t2050,plain,
ifeq(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),true,unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)),true) = true,
inference(orient,[status(thm)],[t2696]) ).
fof(f21,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ouo1) ).
fof(f21_nnf,plain,
! [A,L,M,N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L)
| ~ distinct_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [L,M,A,N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L)
| ~ distinct_lines(L,M) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c24,plain,
( unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t45,plain,
ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(X3,X1),or(apart_point_and_line(X3,X2),or(unorthogonal_lines(X1,X4),unorthogonal_lines(X2,X4)))),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t70,plain,
ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(X3,X1),or(apart_point_and_line(X3,X2),or(unorthogonal_lines(X1,X4),unorthogonal_lines(X2,X4)))),true) = true,
inference(orient,[status(thm)],[t45]) ).
fof(f13,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f13_nnf,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t33,plain,
ifeq(convergent_lines(X1,X2),true,or(distinct_lines(X2,X3),convergent_lines(X1,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t57,plain,
ifeq(convergent_lines(X1,X2),true,or(distinct_lines(X2,X3),convergent_lines(X1,X3)),true) = true,
inference(orient,[status(thm)],[t33]) ).
cnf(t112,plain,
true = ifeq(convergent_lines(X1,X2),true,or(distinct_lines(X2,X1),false),true),
inference(cp,[status(thm)],[t57,t106]) ).
cnf(t2406,plain,
true = ifeq(convergent_lines(X1,X2),true,distinct_lines(X2,X1),true),
inference(step,[status(thm)],[t112,t48]) ).
cnf(t337,plain,
ifeq(convergent_lines(X1,X2),true,distinct_lines(X2,X1),true) = true,
inference(orient,[status(thm)],[t2406]) ).
cnf(t338,plain,
true = ifeq(true,true,distinct_lines(orthogonal_through_point(X1,X2),X1),true),
inference(cp,[status(thm)],[t337,t302]) ).
cnf(t2407,plain,
true = distinct_lines(orthogonal_through_point(X1,X2),X1),
inference(step,[status(thm)],[t338,t47]) ).
cnf(t342,plain,
distinct_lines(orthogonal_through_point(X1,X2),X1) = true,
inference(orient,[status(thm)],[t2407]) ).
cnf(t345,plain,
true = ifeq(true,true,or(apart_point_and_line(X1,orthogonal_through_point(X2,X3)),or(apart_point_and_line(X1,X2),or(unorthogonal_lines(orthogonal_through_point(X2,X3),X4),unorthogonal_lines(X2,X4)))),true),
inference(cp,[status(thm)],[t70,t342]) ).
cnf(t2703,plain,
true = or(apart_point_and_line(X1,orthogonal_through_point(X2,X3)),or(apart_point_and_line(X1,X2),or(unorthogonal_lines(orthogonal_through_point(X2,X3),X4),unorthogonal_lines(X2,X4)))),
inference(step,[status(thm)],[t345,t47]) ).
cnf(t2098,plain,
or(apart_point_and_line(X1,orthogonal_through_point(X2,X3)),or(apart_point_and_line(X1,X2),or(unorthogonal_lines(orthogonal_through_point(X2,X3),X4),unorthogonal_lines(X2,X4)))) = true,
inference(orient,[status(thm)],[t2703]) ).
cnf(t14,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t105,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t14]) ).
fof(f8,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox/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]) ).
cnf(t26,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X1))) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t82,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X1))) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(t238,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),orthogonal_through_point(X1,X2)))),
inference(cp,[status(thm)],[t82,t231]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t187,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t2428,plain,
true = or(false,not(apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),orthogonal_through_point(X1,X2)))),
inference(step,[status(thm)],[t238,t187]) ).
cnf(t2429,plain,
true = not(apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),orthogonal_through_point(X1,X2))),
inference(step,[status(thm)],[t2428,t49]) ).
cnf(t418,plain,
not(apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),orthogonal_through_point(X1,X2))) = true,
inference(orient,[status(thm)],[t2429]) ).
cnf(t419,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),orthogonal_through_point(X1,X2)),false),
inference(cp,[status(thm)],[t105,t418]) ).
cnf(t2430,plain,
false = apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),orthogonal_through_point(X1,X2)),
inference(step,[status(thm)],[t419,t47]) ).
cnf(t420,plain,
apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),orthogonal_through_point(X1,X2)) = false,
inference(orient,[status(thm)],[t2430]) ).
cnf(t2116,plain,
true = or(false,or(apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),X1),or(unorthogonal_lines(orthogonal_through_point(X1,X2),X3),unorthogonal_lines(X1,X3)))),
inference(cp,[status(thm)],[t2098,t420]) ).
cnf(t2704,plain,
true = or(apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),X1),or(unorthogonal_lines(orthogonal_through_point(X1,X2),X3),unorthogonal_lines(X1,X3))),
inference(step,[status(thm)],[t2116,t49]) ).
fof(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox/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(t27,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X2))) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t81,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X2))) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(t239,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),X1))),
inference(cp,[status(thm)],[t81,t231]) ).
cnf(t2396,plain,
true = or(false,not(apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),X1))),
inference(step,[status(thm)],[t239,t187]) ).
cnf(t2397,plain,
true = not(apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),X1)),
inference(step,[status(thm)],[t2396,t49]) ).
cnf(t282,plain,
not(apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),X1)) = true,
inference(orient,[status(thm)],[t2397]) ).
cnf(t283,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),X1),false),
inference(cp,[status(thm)],[t105,t282]) ).
cnf(t2398,plain,
false = apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),X1),
inference(step,[status(thm)],[t283,t47]) ).
cnf(t284,plain,
apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),X1) = false,
inference(orient,[status(thm)],[t2398]) ).
cnf(t2705,plain,
true = or(false,or(unorthogonal_lines(orthogonal_through_point(X1,X2),X3),unorthogonal_lines(X1,X3))),
inference(step,[status(thm)],[t2704,t284]) ).
cnf(t2706,plain,
true = or(unorthogonal_lines(orthogonal_through_point(X1,X2),X3),unorthogonal_lines(X1,X3)),
inference(step,[status(thm)],[t2705,t49]) ).
cnf(t2145,plain,
or(unorthogonal_lines(orthogonal_through_point(X1,X2),X3),unorthogonal_lines(X1,X3)) = true,
inference(orient,[status(thm)],[t2706]) ).
cnf(t2146,plain,
true = or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X3),X1),false),
inference(cp,[status(thm)],[t2145,t174]) ).
cnf(t2707,plain,
true = unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X3),X1),
inference(step,[status(thm)],[t2146,t48]) ).
cnf(t2147,plain,
unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X3),X1) = true,
inference(orient,[status(thm)],[t2707]) ).
cnf(t2708,plain,
ifeq(true,true,unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)),true) = true,
inference(step,[status(thm)],[t2050,t2147]) ).
cnf(t2709,plain,
unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)) = true,
inference(step,[status(thm)],[t2708,t47]) ).
cnf(t2156,plain,
unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)) = true,
inference(rw,[status(thm)],[t2709]) ).
cnf(t2158,plain,
unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)) = true,
inference(orient,[status(thm)],[t2156]) ).
cnf(t2159,plain,
true = ifeq(true,true,false,true),
inference(cp,[status(thm)],[t1055,t2158]) ).
cnf(t2712,plain,
true = false,
inference(step,[status(thm)],[t2159,t47]) ).
cnf(t2168,plain,
false = true,
inference(orient,[status(thm)],[t2712]) ).
fof(f0,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/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]) ).
fof(f1,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox/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]) ).
fof(f6,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/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]) ).
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/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]) ).
fof(f14,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
fof(f14_nnf,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Y,X] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f15,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
fof(f15_nnf,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f20,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
fof(f20_nnf,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c23,plain,
~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c6,c7,c8,c9,c14,c15,c22,c23]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2168]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO222+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n014.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 11:33:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 19.77/3.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.77/3.02 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------