%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO269+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 01:17:47 PM UTC 2026
% Result : Theorem 9.72s 1.88s
% Output : Proof 9.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 21
% Syntax : Number of formulae : 133 ( 92 unt; 0 def)
% Number of atoms : 209 ( 62 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 168 ( 92 ~; 51 |; 18 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 188 ( 15 sgn 83 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9_basics) ).
fof(f18_nnf,plain,
! [L,M] :
( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [L,M] :
( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c44,plain,
( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t81,plain,
ifeq(unequally_directed_lines(X1,X2),true,ifeq(unequally_directed_lines(X1,reverse_line(X2)),true,or(left_convergent_lines(X1,X2),left_convergent_lines(X1,reverse_line(X2))),true),true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(t98,plain,
ifeq(unequally_directed_lines(X1,X2),true,ifeq(unequally_directed_lines(X1,reverse_line(X2)),true,or(left_convergent_lines(X1,X2),left_convergent_lines(X1,reverse_line(X2))),true),true) = true,
inference(orient,[status(thm)],[t81]) ).
fof(f20,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11_basics) ).
fof(f20_nnf,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c47,plain,
~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t6,plain,
left_convergent_lines(X1,X2) = false,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(t207,plain,
left_convergent_lines(X1,X2) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t1473,plain,
ifeq(unequally_directed_lines(X1,X2),true,ifeq(unequally_directed_lines(X1,reverse_line(X2)),true,or(false,left_convergent_lines(X1,reverse_line(X2))),true),true) = true,
inference(step,[status(thm)],[t98,t207]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t92,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t1474,plain,
ifeq(unequally_directed_lines(X1,X2),true,ifeq(unequally_directed_lines(X1,reverse_line(X2)),true,left_convergent_lines(X1,reverse_line(X2)),true),true) = true,
inference(step,[status(thm)],[t1473,t92]) ).
cnf(t1475,plain,
ifeq(unequally_directed_lines(X1,X2),true,ifeq(unequally_directed_lines(X1,reverse_line(X2)),true,false,true),true) = true,
inference(step,[status(thm)],[t1474,t207]) ).
cnf(t212,plain,
ifeq(unequally_directed_lines(X1,X2),true,ifeq(unequally_directed_lines(X1,reverse_line(X2)),true,false,true),true) = true,
inference(rw,[status(thm)],[t1475]) ).
cnf(t1223,plain,
ifeq(unequally_directed_lines(X1,X2),true,ifeq(unequally_directed_lines(X1,reverse_line(X2)),true,false,true),true) = true,
inference(orient,[status(thm)],[t212]) ).
fof(f15,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6_basics) ).
fof(f15_nnf,plain,
! [L,M,N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N)
| ~ unequally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [L,M,N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N)
| ~ unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c38,plain,
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t57,plain,
ifeq(unequally_directed_lines(X1,X2),true,or(unequally_directed_lines(X1,X3),unequally_directed_lines(X2,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t100,plain,
ifeq(unequally_directed_lines(X1,X2),true,or(unequally_directed_lines(X1,X3),unequally_directed_lines(X2,X3)),true) = true,
inference(orient,[status(thm)],[t57]) ).
fof(f0,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1_defns) ).
fof(f0_nnf,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t46,plain,
ifeq(unequally_directed_opposite_lines(X1,X2),true,unequally_directed_lines(X1,reverse_line(X2)),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t136,plain,
ifeq(unequally_directed_opposite_lines(X1,X2),true,unequally_directed_lines(X1,reverse_line(X2)),true) = true,
inference(orient,[status(thm)],[t46]) ).
fof(f4,axiom,
! [X,Y] :
( equally_directed_opposite_lines(X,Y)
<=> ~ unequally_directed_opposite_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a5_defns) ).
fof(f4_nnf,plain,
! [X,Y] :
( ( unequally_directed_opposite_lines(X,Y)
| equally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| ~ equally_directed_opposite_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] :
( ( unequally_directed_opposite_lines(X,Y)
| equally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| ~ equally_directed_opposite_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c9,plain,
( unequally_directed_opposite_lines(X0,X1)
| equally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t24,plain,
or(equally_directed_opposite_lines(X1,X2),unequally_directed_opposite_lines(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t163,plain,
or(equally_directed_opposite_lines(X1,X2),unequally_directed_opposite_lines(X1,X2)) = true,
inference(orient,[status(thm)],[t24]) ).
fof(f36,conjecture,
! [L] : equally_directed_opposite_lines(L,reverse_line(L)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f36_neg,negated_conjecture,
~ ! [L] : equally_directed_opposite_lines(L,reverse_line(L)),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f36_nnf,plain,
? [L] : ~ equally_directed_opposite_lines(L,reverse_line(L)),
inference(nnf_transformation,[status(thm)],[f36_neg]) ).
fof(f36_sk,plain,
~ equally_directed_opposite_lines(sk0,reverse_line(sk0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f36_nnf]) ).
cnf(c66,plain,
~ equally_directed_opposite_lines(sk0,reverse_line(sk0)),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(t12,plain,
equally_directed_opposite_lines(sk0,reverse_line(sk0)) = false,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t223,plain,
equally_directed_opposite_lines(sk0,reverse_line(sk0)) = false,
inference(orient,[status(thm)],[t12]) ).
cnf(t224,plain,
true = or(false,unequally_directed_opposite_lines(sk0,reverse_line(sk0))),
inference(cp,[status(thm)],[t163,t223]) ).
cnf(t1479,plain,
true = unequally_directed_opposite_lines(sk0,reverse_line(sk0)),
inference(step,[status(thm)],[t224,t92]) ).
cnf(t227,plain,
unequally_directed_opposite_lines(sk0,reverse_line(sk0)) = true,
inference(orient,[status(thm)],[t1479]) ).
cnf(t231,plain,
true = ifeq(true,true,unequally_directed_lines(sk0,reverse_line(reverse_line(sk0))),true),
inference(cp,[status(thm)],[t136,t227]) ).
cnf(t17,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t90,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t17]) ).
cnf(t1480,plain,
true = unequally_directed_lines(sk0,reverse_line(reverse_line(sk0))),
inference(step,[status(thm)],[t231,t90]) ).
cnf(t235,plain,
unequally_directed_lines(sk0,reverse_line(reverse_line(sk0))) = true,
inference(orient,[status(thm)],[t1480]) ).
cnf(t240,plain,
true = ifeq(true,true,or(unequally_directed_lines(sk0,X1),unequally_directed_lines(reverse_line(reverse_line(sk0)),X1)),true),
inference(cp,[status(thm)],[t100,t235]) ).
cnf(t1545,plain,
true = or(unequally_directed_lines(sk0,X1),unequally_directed_lines(reverse_line(reverse_line(sk0)),X1)),
inference(step,[status(thm)],[t240,t90]) ).
cnf(t553,plain,
or(unequally_directed_lines(sk0,X1),unequally_directed_lines(reverse_line(reverse_line(sk0)),X1)) = true,
inference(orient,[status(thm)],[t1545]) ).
cnf(t18,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t175,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t18]) ).
fof(f3,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4_defns) ).
fof(f3_nnf,plain,
! [X,Y] :
( ( unequally_directed_lines(X,Y)
| equally_directed_lines(X,Y) )
& ( ~ unequally_directed_lines(X,Y)
| ~ equally_directed_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( ( unequally_directed_lines(X,Y)
| equally_directed_lines(X,Y) )
& ( ~ unequally_directed_lines(X,Y)
| ~ equally_directed_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c6,plain,
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t36,plain,
or(not(equally_directed_lines(X1,X2)),not(unequally_directed_lines(X1,X2))) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t160,plain,
or(not(equally_directed_lines(X1,X2)),not(unequally_directed_lines(X1,X2))) = true,
inference(orient,[status(thm)],[t36]) ).
fof(f14,axiom,
! [L] : equally_directed_lines(L,L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5_basics) ).
fof(f14_nnf,plain,
! [L] : equally_directed_lines(L,L),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [L] : equally_directed_lines(L,L),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c37,plain,
equally_directed_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t4,plain,
equally_directed_lines(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(t165,plain,
equally_directed_lines(X1,X1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t166,plain,
true = or(not(true),not(unequally_directed_lines(X1,X1))),
inference(cp,[status(thm)],[t160,t165]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t191,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t1484,plain,
true = or(false,not(unequally_directed_lines(X1,X1))),
inference(step,[status(thm)],[t166,t191]) ).
cnf(t1485,plain,
true = not(unequally_directed_lines(X1,X1)),
inference(step,[status(thm)],[t1484,t92]) ).
cnf(t267,plain,
not(unequally_directed_lines(X1,X1)) = true,
inference(orient,[status(thm)],[t1485]) ).
cnf(t268,plain,
false = ifeq(true,true,unequally_directed_lines(X1,X1),false),
inference(cp,[status(thm)],[t175,t267]) ).
cnf(t1486,plain,
false = unequally_directed_lines(X1,X1),
inference(step,[status(thm)],[t268,t90]) ).
cnf(t269,plain,
unequally_directed_lines(X1,X1) = false,
inference(orient,[status(thm)],[t1486]) ).
cnf(t554,plain,
true = or(false,unequally_directed_lines(reverse_line(reverse_line(sk0)),sk0)),
inference(cp,[status(thm)],[t553,t269]) ).
cnf(t1546,plain,
true = unequally_directed_lines(reverse_line(reverse_line(sk0)),sk0),
inference(step,[status(thm)],[t554,t92]) ).
cnf(t555,plain,
unequally_directed_lines(reverse_line(reverse_line(sk0)),sk0) = true,
inference(orient,[status(thm)],[t1546]) ).
cnf(t1233,plain,
true = ifeq(true,true,ifeq(unequally_directed_lines(reverse_line(reverse_line(sk0)),reverse_line(sk0)),true,false,true),true),
inference(cp,[status(thm)],[t1223,t555]) ).
cnf(t1754,plain,
true = ifeq(unequally_directed_lines(reverse_line(reverse_line(sk0)),reverse_line(sk0)),true,false,true),
inference(step,[status(thm)],[t1233,t90]) ).
fof(f17,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8_basics) ).
fof(f17_nnf,plain,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c43,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t30,plain,
or(unequally_directed_lines(X1,X2),unequally_directed_lines(X1,reverse_line(X2))) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t154,plain,
or(unequally_directed_lines(X1,X2),unequally_directed_lines(X1,reverse_line(X2))) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(t273,plain,
true = or(unequally_directed_lines(reverse_line(X1),X1),false),
inference(cp,[status(thm)],[t154,t269]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t91,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t1489,plain,
true = unequally_directed_lines(reverse_line(X1),X1),
inference(step,[status(thm)],[t273,t91]) ).
cnf(t332,plain,
unequally_directed_lines(reverse_line(X1),X1) = true,
inference(orient,[status(thm)],[t1489]) ).
cnf(t1755,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t1754,t332]) ).
cnf(t1756,plain,
true = false,
inference(step,[status(thm)],[t1755,t90]) ).
cnf(t1260,plain,
false = true,
inference(orient,[status(thm)],[t1756]) ).
cnf(c8,plain,
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ equally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f10,axiom,
! [A] : ~ distinct_points(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1_basics) ).
fof(f10_nnf,plain,
! [A] : ~ distinct_points(A,A),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] : ~ distinct_points(A,A),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c33,plain,
~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f12,axiom,
! [L] : ~ distinct_lines(L,L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_basics) ).
fof(f12_nnf,plain,
! [L] : ~ distinct_lines(L,L),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [L] : ~ distinct_lines(L,L),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c35,plain,
~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f19,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10_basics) ).
fof(f19_nnf,plain,
! [A,L] :
( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,L] :
( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c45,plain,
~ left_apart_point(X0,X1),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(c46,plain,
~ left_apart_point(X0,reverse_line(X1)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(c48,plain,
~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f25,axiom,
! [A,B] :
( distinct_points(A,B)
=> ( ~ apart_point_and_line(B,line_connecting(A,B))
& ~ apart_point_and_line(A,line_connecting(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5_cons_objs) ).
fof(f25_nnf,plain,
! [A,B] :
( ( ~ apart_point_and_line(B,line_connecting(A,B))
& ~ apart_point_and_line(A,line_connecting(A,B)) )
| ~ distinct_points(A,B) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [A,B] :
( ( ~ apart_point_and_line(B,line_connecting(A,B))
& ~ apart_point_and_line(A,line_connecting(A,B)) )
| ~ distinct_points(A,B) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c53,plain,
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(c54,plain,
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
fof(f26,axiom,
! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( ~ apart_point_and_line(intersection_point(L,M),M)
& ~ apart_point_and_line(intersection_point(L,M),L) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6_cons_objs) ).
fof(f26_nnf,plain,
! [L,M] :
( ( ~ apart_point_and_line(intersection_point(L,M),M)
& ~ apart_point_and_line(intersection_point(L,M),L) )
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [L,M] :
( ( ~ apart_point_and_line(intersection_point(L,M),M)
& ~ apart_point_and_line(intersection_point(L,M),L) )
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c55,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(c56,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
fof(f27,axiom,
! [A,L] : ~ apart_point_and_line(A,parallel_through_point(L,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7_cons_objs) ).
fof(f27_nnf,plain,
! [A,L] : ~ apart_point_and_line(A,parallel_through_point(L,A)),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A,L] : ~ apart_point_and_line(A,parallel_through_point(L,A)),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c57,plain,
~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f28,axiom,
! [L] : ~ distinct_lines(L,reverse_line(L)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8_cons_objs) ).
fof(f28_nnf,plain,
! [L] : ~ distinct_lines(L,reverse_line(L)),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [L] : ~ distinct_lines(L,reverse_line(L)),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c58,plain,
~ distinct_lines(X0,reverse_line(X0)),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c6,c8,c33,c35,c45,c46,c47,c48,c53,c54,c55,c56,c57,c58,c66]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1260]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO269+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 11:47:02 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.72/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.72/1.88 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------