%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO251+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 01:17:43 PM UTC 2026
% Result : Theorem 4.91s 1.08s
% Output : Proof 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 70 ( 42 unt; 0 def)
% Number of atoms : 138 ( 7 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 171 ( 103 ~; 35 |; 28 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 115 ( 16 sgn 69 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,conjecture,
! [A,B,L] :
( left_apart_point(B,reverse_line(parallel_through_point(L,A)))
=> left_apart_point(A,parallel_through_point(L,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f31_neg,negated_conjecture,
~ ! [A,B,L] :
( left_apart_point(B,reverse_line(parallel_through_point(L,A)))
=> left_apart_point(A,parallel_through_point(L,B)) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f31_nnf,plain,
? [A,B,L] :
( ~ left_apart_point(A,parallel_through_point(L,B))
& left_apart_point(B,reverse_line(parallel_through_point(L,A))) ),
inference(nnf_transformation,[status(thm)],[f31_neg]) ).
fof(f31_sk,plain,
( ~ left_apart_point(sk0,parallel_through_point(sk2,sk1))
& left_apart_point(sk1,reverse_line(parallel_through_point(sk2,sk0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f31_nnf]) ).
cnf(c59,plain,
~ left_apart_point(sk0,parallel_through_point(sk2,sk1)),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(hi61,negated_conjecture,
ifeq(left_apart_point(sk0,parallel_through_point(sk2,sk1)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c59]) ).
cnf(c58,plain,
left_apart_point(sk1,reverse_line(parallel_through_point(sk2,sk0))),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(hi40,negated_conjecture,
left_apart_point(sk1,reverse_line(parallel_through_point(sk2,sk0))) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
fof(f14,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag10) ).
fof(f14_nnf,plain,
! [A,L] :
( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,L] :
( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c37,plain,
~ left_apart_point(X0,X1),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi1,axiom,
left_apart_point(X0,X1) = false,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi61,hi40,hi1]) ).
cnf(t196,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f3,axiom,
! [L,A,B] :
( before_on_line(L,A,B)
<=> ( ~ unequally_directed_lines(L,line_connecting(A,B))
& ~ ( left_apart_point(B,reverse_line(L))
| left_apart_point(B,L) )
& ~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) )
& distinct_points(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bf_def) ).
fof(f3_nnf,plain,
! [L,A,B] :
( ( unequally_directed_lines(L,line_connecting(A,B))
| left_apart_point(B,reverse_line(L))
| left_apart_point(B,L)
| left_apart_point(A,reverse_line(L))
| left_apart_point(A,L)
| ~ distinct_points(A,B)
| before_on_line(L,A,B) )
& ( ( ~ unequally_directed_lines(L,line_connecting(A,B))
& ~ left_apart_point(B,reverse_line(L))
& ~ left_apart_point(B,L)
& ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L)
& distinct_points(A,B) )
| ~ before_on_line(L,A,B) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [L,A,B] :
( ( unequally_directed_lines(L,line_connecting(A,B))
| left_apart_point(B,reverse_line(L))
| left_apart_point(B,L)
| left_apart_point(A,reverse_line(L))
| left_apart_point(A,L)
| ~ distinct_points(A,B)
| before_on_line(L,A,B) )
& ( ( ~ unequally_directed_lines(L,line_connecting(A,B))
& ~ left_apart_point(B,reverse_line(L))
& ~ left_apart_point(B,L)
& ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L)
& distinct_points(A,B) )
| ~ before_on_line(L,A,B) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c13,plain,
( ~ left_apart_point(X1,X0)
| ~ before_on_line(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(c14,plain,
( ~ left_apart_point(X1,reverse_line(X0))
| ~ before_on_line(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(c15,plain,
( ~ left_apart_point(X2,X0)
| ~ before_on_line(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(c16,plain,
( ~ left_apart_point(X2,reverse_line(X0))
| ~ before_on_line(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(c17,plain,
( ~ unequally_directed_lines(X0,line_connecting(X1,X2))
| ~ before_on_line(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f5,axiom,
! [A] : ~ distinct_points(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag1) ).
fof(f5_nnf,plain,
! [A] : ~ distinct_points(A,A),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : ~ distinct_points(A,A),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c25,plain,
~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f7,axiom,
! [L] : ~ distinct_lines(L,L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag3) ).
fof(f7_nnf,plain,
! [L] : ~ distinct_lines(L,L),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [L] : ~ distinct_lines(L,L),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c27,plain,
~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f9,axiom,
! [L] : ~ unequally_directed_lines(L,L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag5) ).
fof(f9_nnf,plain,
! [L] : ~ unequally_directed_lines(L,L),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [L] : ~ unequally_directed_lines(L,L),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c29,plain,
~ unequally_directed_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(c38,plain,
~ left_apart_point(X0,reverse_line(X1)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f15,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag11) ).
fof(f15_nnf,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c39,plain,
~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(c40,plain,
~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f20,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',oagco5) ).
fof(f20_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)],[f20]) ).
fof(f20_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)],[f20_nnf]) ).
cnf(c45,plain,
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(c46,plain,
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f21,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',oagco6) ).
fof(f21_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)],[f21]) ).
fof(f21_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)],[f21_nnf]) ).
cnf(c47,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)],[f21_sk]) ).
cnf(c48,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)],[f21_sk]) ).
fof(f22,axiom,
! [A,L] : ~ apart_point_and_line(A,parallel_through_point(L,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco7) ).
fof(f22_nnf,plain,
! [A,L] : ~ apart_point_and_line(A,parallel_through_point(L,A)),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,L] : ~ apart_point_and_line(A,parallel_through_point(L,A)),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c49,plain,
~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
fof(f23,axiom,
! [L] : ~ distinct_lines(L,reverse_line(L)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco8) ).
fof(f23_nnf,plain,
! [L] : ~ distinct_lines(L,reverse_line(L)),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [L] : ~ distinct_lines(L,reverse_line(L)),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c50,plain,
~ distinct_lines(X0,reverse_line(X0)),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
fof(f24,axiom,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco9) ).
fof(f24_nnf,plain,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c51,plain,
~ unequally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0))),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f25,axiom,
! [A,L] : ~ unequally_directed_lines(parallel_through_point(L,A),L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco10) ).
fof(f25_nnf,plain,
! [A,L] : ~ unequally_directed_lines(parallel_through_point(L,A),L),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [L,A] : ~ unequally_directed_lines(parallel_through_point(L,A),L),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c52,plain,
~ unequally_directed_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c13,c14,c15,c16,c17,c25,c27,c29,c37,c38,c39,c40,c45,c46,c47,c48,c49,c50,c51,c52,c59]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t196]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO251+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n008.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 11:42:38 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.91/1.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.91/1.08 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------