%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO178+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 : n019.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 01:17:17 PM UTC 2026
% Result : Theorem 3.31s 0.99s
% Output : Proof 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 33 unt; 0 def)
% Number of atoms : 69 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 29 ~; 11 |; 11 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 48 ( 2 sgn 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,conjecture,
! [X,Y,Z] :
( ( apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) )
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f12_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) )
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f12_nnf,plain,
? [X,Y,Z] :
( ( ~ distinct_points(Z,Y)
| ~ distinct_points(Z,X) )
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f12_neg]) ).
fof(f12_sk,plain,
( ( ~ distinct_points(sk2,sk1)
| ~ distinct_points(sk2,sk0) )
& apart_point_and_line(sk2,line_connecting(sk0,sk1))
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f12_nnf]) ).
cnf(c16,plain,
( ~ distinct_points(sk2,sk1)
| ~ distinct_points(sk2,sk0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t30,plain,
ifeq(distinct_points(sk2,sk0),true,ifeq(distinct_points(sk2,sk1),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
fof(f6,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con1) ).
fof(f6_nnf,plain,
! [X,Y,Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( distinct_points(X2,X0)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi3,axiom,
ifeq(distinct_points(X0,X1),true,ifeq(apart_point_and_line(X2,line_connecting(X0,X1)),true,distinct_points(X2,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(c14,plain,
distinct_points(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi11,negated_conjecture,
distinct_points(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(c15,plain,
apart_point_and_line(sk2,line_connecting(sk0,sk1)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,negated_conjecture,
apart_point_and_line(sk2,line_connecting(sk0,sk1)) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t7,plain,
distinct_points(sk2,sk0) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi11,hi12]) ).
cnf(t40,plain,
distinct_points(sk2,sk0) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t75,plain,
ifeq(true,true,ifeq(distinct_points(sk2,sk1),true,false,true),true) = true,
inference(step,[status(thm)],[t30,t40]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t36,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t76,plain,
ifeq(distinct_points(sk2,sk1),true,false,true) = true,
inference(step,[status(thm)],[t75,t36]) ).
cnf(c7,plain,
( distinct_points(X2,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi4,axiom,
ifeq(distinct_points(X0,X1),true,ifeq(apart_point_and_line(X2,line_connecting(X0,X1)),true,distinct_points(X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t8,plain,
distinct_points(sk2,sk1) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi11,hi12]) ).
cnf(t39,plain,
distinct_points(sk2,sk1) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t77,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t76,t39]) ).
cnf(t78,plain,
false = true,
inference(step,[status(thm)],[t77,t36]) ).
cnf(t71,plain,
false = true,
inference(orient,[status(thm)],[t78]) ).
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(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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c16]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t71]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO178+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.43 % Computer : n019.cluster.edu
% 0.10/0.43 % Model : x86_64 x86_64
% 0.10/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.43 % Memory : 8046.5625MB
% 0.10/0.43 % OS : Linux 6.8.0-71-generic
% 0.10/0.43 % CPULimit : 300
% 0.10/0.43 % WCLimit : 300
% 0.10/0.43 % DateTime : Wed Sep 23 11:18:19 UTC 2026
% 0.10/0.43 % CPUTime :
% 0.10/0.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.31/0.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.31/0.99 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------