%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO222+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 40.02s 5.66s
% Output : Proof 40.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 16
% Syntax : Number of formulae : 132 ( 111 unt; 0 def)
% Number of atoms : 185 ( 77 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 103 ( 50 ~; 42 |; 7 &)
% ( 0 <=>; 4 =>; 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 : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 251 ( 21 sgn 79 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,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(f16_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)],[f16]) ).
fof(f16_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)],[f16_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)],[f16_sk]) ).
cnf(t36,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(t49,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)],[t36]) ).
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(t0,plain,
convergent_lines(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t103,plain,
convergent_lines(X1,X1) = false,
inference(orient,[status(thm)],[t0]) ).
cnf(t116,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)],[t49,t103]) ).
cnf(t5,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t45,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t1219,plain,
true = ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,unorthogonal_lines(X2,X1),true),true),
inference(step,[status(thm)],[t116,t45]) ).
cnf(t593,plain,
ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,unorthogonal_lines(X2,X1),true),true) = true,
inference(orient,[status(thm)],[t1219]) ).
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',apart6) ).
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(t27,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(t52,plain,
ifeq(convergent_lines(X1,X2),true,or(convergent_lines(X1,X3),convergent_lines(X2,X3)),true) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(t107,plain,
true = ifeq(convergent_lines(X1,X2),true,or(false,convergent_lines(X2,X1)),true),
inference(cp,[status(thm)],[t52,t103]) ).
cnf(t1126,plain,
true = ifeq(convergent_lines(X1,X2),true,convergent_lines(X2,X1),true),
inference(step,[status(thm)],[t107,t45]) ).
cnf(t287,plain,
ifeq(convergent_lines(X1,X2),true,convergent_lines(X2,X1),true) = true,
inference(orient,[status(thm)],[t1126]) ).
fof(f15,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
fof(f15_nnf,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c17,plain,
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t17,plain,
or(convergent_lines(X1,X2),unorthogonal_lines(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t72,plain,
or(convergent_lines(X1,X2),unorthogonal_lines(X1,X2)) = true,
inference(orient,[status(thm)],[t17]) ).
fof(f17,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
fof(f17_nnf,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [L,A] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c22,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t11,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t173,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t174,plain,
true = or(convergent_lines(orthogonal_through_point(X1,X2),X1),false),
inference(cp,[status(thm)],[t72,t173]) ).
cnf(t3,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t44,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t1109,plain,
true = convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(step,[status(thm)],[t174,t44]) ).
cnf(t234,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1) = true,
inference(orient,[status(thm)],[t1109]) ).
cnf(t288,plain,
true = ifeq(true,true,convergent_lines(X1,orthogonal_through_point(X1,X2)),true),
inference(cp,[status(thm)],[t287,t234]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t43,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t1127,plain,
true = convergent_lines(X1,orthogonal_through_point(X1,X2)),
inference(step,[status(thm)],[t288,t43]) ).
cnf(t292,plain,
convergent_lines(X1,orthogonal_through_point(X1,X2)) = true,
inference(orient,[status(thm)],[t1127]) ).
cnf(t594,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)],[t593,t292]) ).
cnf(t1220,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)],[t594,t43]) ).
cnf(t1221,plain,
true = ifeq(unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),true,false,true),
inference(step,[status(thm)],[t1220,t173]) ).
cnf(t606,plain,
ifeq(unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),true,false,true) = true,
inference(orient,[status(thm)],[t1221]) ).
cnf(c21,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t38,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(t51,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)],[t38]) ).
cnf(t176,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)],[t51,t173]) ).
cnf(t1301,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)],[t176,t45]) ).
cnf(t922,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)],[t1301]) ).
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(f20,conjecture,
! [A,L] : ~ convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f20_neg,negated_conjecture,
~ ! [A,L] : ~ convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [A,L] : convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
convergent_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f20_nnf]) ).
cnf(c25,plain,
convergent_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi18,negated_conjecture,
convergent_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t23,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,hi18]) ).
cnf(t74,plain,
or(convergent_lines(sk1,X1),convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),X1)) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t110,plain,
true = or(false,convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1)),
inference(cp,[status(thm)],[t74,t103]) ).
cnf(t1121,plain,
true = convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),
inference(step,[status(thm)],[t110,t45]) ).
cnf(t264,plain,
convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1) = true,
inference(orient,[status(thm)],[t1121]) ).
cnf(t929,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)],[t922,t264]) ).
cnf(t1303,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)],[t929,t43]) ).
cnf(t939,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)],[t1303]) ).
fof(f19,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(f19_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)],[f19]) ).
fof(f19_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)],[f19_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)],[f19_sk]) ).
cnf(t40,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(t61,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)],[t40]) ).
fof(f11,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f11_nnf,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c13,plain,
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t20,plain,
ifeq(convergent_lines(X1,X2),true,distinct_lines(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t53,plain,
ifeq(convergent_lines(X1,X2),true,distinct_lines(X1,X2),true) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t235,plain,
true = ifeq(true,true,distinct_lines(orthogonal_through_point(X1,X2),X1),true),
inference(cp,[status(thm)],[t53,t234]) ).
cnf(t1113,plain,
true = distinct_lines(orthogonal_through_point(X1,X2),X1),
inference(step,[status(thm)],[t235,t43]) ).
cnf(t251,plain,
distinct_lines(orthogonal_through_point(X1,X2),X1) = true,
inference(orient,[status(thm)],[t1113]) ).
cnf(t256,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)],[t61,t251]) ).
cnf(t1310,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)],[t256,t43]) ).
cnf(t987,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)],[t1310]) ).
fof(f18,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
fof(f18_nnf,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c23,plain,
~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t7,plain,
apart_point_and_line(X1,orthogonal_through_point(X2,X1)) = false,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t140,plain,
apart_point_and_line(X1,orthogonal_through_point(X2,X1)) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t988,plain,
true = or(false,or(apart_point_and_line(X1,X2),or(unorthogonal_lines(orthogonal_through_point(X2,X1),X3),unorthogonal_lines(X2,X3)))),
inference(cp,[status(thm)],[t987,t140]) ).
cnf(t1311,plain,
true = or(apart_point_and_line(X1,X2),or(unorthogonal_lines(orthogonal_through_point(X2,X1),X3),unorthogonal_lines(X2,X3))),
inference(step,[status(thm)],[t988,t45]) ).
cnf(t992,plain,
or(apart_point_and_line(X1,X2),or(unorthogonal_lines(orthogonal_through_point(X2,X1),X3),unorthogonal_lines(X2,X3))) = true,
inference(orient,[status(thm)],[t1311]) ).
cnf(t993,plain,
true = or(false,or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X3),unorthogonal_lines(orthogonal_through_point(X1,X2),X3))),
inference(cp,[status(thm)],[t992,t140]) ).
cnf(t1312,plain,
true = or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X3),unorthogonal_lines(orthogonal_through_point(X1,X2),X3)),
inference(step,[status(thm)],[t993,t45]) ).
cnf(t996,plain,
or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X3),unorthogonal_lines(orthogonal_through_point(X1,X2),X3)) = true,
inference(orient,[status(thm)],[t1312]) ).
cnf(t997,plain,
true = or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X1),false),
inference(cp,[status(thm)],[t996,t173]) ).
cnf(t1313,plain,
true = unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X1),
inference(step,[status(thm)],[t997,t44]) ).
cnf(t998,plain,
unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X1) = true,
inference(orient,[status(thm)],[t1313]) ).
cnf(t1314,plain,
ifeq(true,true,unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)),true) = true,
inference(step,[status(thm)],[t939,t998]) ).
cnf(t1315,plain,
unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)) = true,
inference(step,[status(thm)],[t1314,t43]) ).
cnf(t1007,plain,
unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)) = true,
inference(rw,[status(thm)],[t1315]) ).
cnf(t1009,plain,
unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)) = true,
inference(orient,[status(thm)],[t1007]) ).
cnf(t1010,plain,
true = ifeq(true,true,false,true),
inference(cp,[status(thm)],[t606,t1009]) ).
cnf(t1318,plain,
true = false,
inference(step,[status(thm)],[t1010,t43]) ).
cnf(t1019,plain,
false = true,
inference(orient,[status(thm)],[t1318]) ).
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(f12,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
fof(f12_nnf,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [Y,X] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c14,plain,
~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f13,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
fof(f13_nnf,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c15,plain,
~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c14,c15,c22,c23]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1019]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO222+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 11:39:04 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 40.02/5.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.02/5.66 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------