%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO264+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 01:20:37 PM UTC 2026
% Result : Theorem 0.44s 6.29s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 37 ( 14 ~; 5 |; 13 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 26 !; 8 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( right_apart_point(X0,X1)
<=> left_apart_point(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',a2_defns) ).
fof(f20,axiom,
! [X0,X1] :
~ ( left_apart_point(X0,reverse_line(X1))
| left_apart_point(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax10_basics) ).
fof(f37,conjecture,
! [X0,X1,X2,X3] :
( left_apart_point(X2,line_connecting(X0,X1))
=> ( ( right_apart_point(X3,line_connecting(X2,X0))
& right_apart_point(X3,line_connecting(X1,X2)) )
=> left_apart_point(X3,line_connecting(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( left_apart_point(X2,line_connecting(X0,X1))
=> ( ( right_apart_point(X3,line_connecting(X2,X0))
& right_apart_point(X3,line_connecting(X1,X2)) )
=> left_apart_point(X3,line_connecting(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f53,plain,
! [X0,X1] :
( ~ left_apart_point(X0,reverse_line(X1))
& ~ left_apart_point(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f76,plain,
? [X0,X1,X2,X3] :
( left_apart_point(X2,line_connecting(X0,X1))
& right_apart_point(X3,line_connecting(X2,X0))
& right_apart_point(X3,line_connecting(X1,X2))
& ~ left_apart_point(X3,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f38]) ).
fof(f77,plain,
? [X0,X1,X2,X3] :
( left_apart_point(X2,line_connecting(X0,X1))
& right_apart_point(X3,line_connecting(X2,X0))
& right_apart_point(X3,line_connecting(X1,X2))
& ~ left_apart_point(X3,line_connecting(X0,X1)) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ( ~ right_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) )
& ( ~ left_apart_point(X0,reverse_line(X1))
| right_apart_point(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f79,plain,
( left_apart_point(sK2,line_connecting(sK0,sK1))
& right_apart_point(sK3,line_connecting(sK2,sK0))
& right_apart_point(sK3,line_connecting(sK1,sK2))
& ~ left_apart_point(sK3,line_connecting(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f77]) ).
fof(f80,plain,
! [X0,X1] :
( ~ right_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f97,plain,
! [X0,X1] : ~ left_apart_point(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f53]) ).
fof(f119,plain,
right_apart_point(sK3,line_connecting(sK2,sK0)),
inference(cnf_transformation,[],[f79]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( left_apart_point(X0,reverse_line(X1))
| ~ right_apart_point(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : ~ left_apart_point(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f97]) ).
tcf(c_89,negated_conjecture,
right_apart_point(sK3,line_connecting(sK2,sK0)),
inference(cnf_transformation,[],[f119]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] : ~ right_apart_point(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_50,c_67,c_50]) ).
tcf(c_225,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_89,c_115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO264+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.38 % Computer : n008.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Wed Sep 23 11:46:17 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 0.44/6.29 % SZS status Started for theBenchmark.p
% 0.44/6.29 % SZS status Theorem for theBenchmark.p
% 0.44/6.29
% 0.44/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.44/6.29
% 0.44/6.29 % ------ iProver source info
% 0.44/6.29
% 0.44/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.44/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.44/6.29 % git: non_committed_changes: false
% 0.44/6.29
% 0.44/6.29 % ------ Parsing...
% 0.44/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.44/6.29
% 0.44/6.29 % ------ Preprocessing...%
% 0.44/6.29
% 0.44/6.29 % SZS status Theorem for theBenchmark.p
% 0.44/6.29
% 0.44/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.44/6.29
% 0.44/6.29
%------------------------------------------------------------------------------