%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO169+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 01:20:04 PM UTC 2026
% Result : Theorem 47.49s 16.15s
% Output : CNFRefutation 47.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 48
% Syntax : Number of formulae : 290 ( 133 unt; 0 def)
% Number of atoms : 796 ( 158 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 947 ( 441 ~; 470 |; 19 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 19 con; 0-2 aty)
% Number of variables : 259 ( 0 sgn 253 !; 6 ?; 197 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ( incident(p2,X0)
& incident(p1,X0)
& incident(p3,X0) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_normal) ).
fof(f2,axiom,
( ( incident(a3,b1b2)
& incident(a2,b3b1)
& incident(a1,b2b3) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_a_in_b) ).
fof(f3,axiom,
( ( incident(b3,a1a2)
& incident(b2,a3a1)
& incident(b1,a2a3) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_b_in_a) ).
fof(f4,axiom,
( incident(b3,a1a2)
| incident(a1,b2b3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gap1) ).
fof(f5,axiom,
( incident(b1,a2a3)
| incident(a2,b3b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gap2) ).
fof(f6,axiom,
( incident(b2,a3a1)
| incident(a3,b1b2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gap3) ).
fof(f7,axiom,
incident(a1,a1a2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ia1a2) ).
fof(f8,axiom,
incident(a2,a1a2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ia2a1) ).
fof(f9,axiom,
incident(a2,a2a3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ia2a3) ).
fof(f10,axiom,
incident(a3,a2a3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ia3a2) ).
fof(f11,axiom,
incident(a3,a3a1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ia3a1) ).
fof(f12,axiom,
incident(a1,a3a1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ia1a3) ).
fof(f13,axiom,
incident(b1,b1b2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ib1b2) ).
fof(f14,axiom,
incident(b2,b1b2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ib2b1) ).
fof(f15,axiom,
incident(b2,b2b3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ib2b3) ).
fof(f16,axiom,
incident(b3,b2b3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ib3b2) ).
fof(f17,axiom,
incident(b3,b3b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ib3b1) ).
fof(f18,axiom,
incident(b1,b3b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ib1b3) ).
fof(f19,axiom,
incident(s,s1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iss1) ).
fof(f20,axiom,
incident(s,s2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iss2) ).
fof(f21,axiom,
incident(s,s3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iss3) ).
fof(f22,axiom,
incident(a1,s1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ia1s1) ).
fof(f23,axiom,
incident(a2,s2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ia2s2) ).
fof(f24,axiom,
incident(a3,s3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ia3s3) ).
fof(f25,axiom,
incident(b1,s1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ib1s1) ).
fof(f26,axiom,
incident(b2,s2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ib2s2) ).
fof(f27,axiom,
incident(b3,s3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ib3s3) ).
fof(f28,axiom,
incident(p3,a1a2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ip3a) ).
fof(f29,axiom,
incident(p3,b1b2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ip3b) ).
fof(f30,axiom,
incident(p1,a2a3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ip1a) ).
fof(f31,axiom,
incident(p1,b2b3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ip1b) ).
fof(f32,axiom,
incident(p2,a3a1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ip2a) ).
fof(f33,axiom,
incident(p2,b3b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ip2b) ).
fof(f34,axiom,
! [X0,X1] :
( incident(X0,X1)
=> point(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sort_point) ).
fof(f35,axiom,
! [X0,X1] :
( incident(X0,X1)
=> line(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sort_line) ).
fof(f36,axiom,
( a1 = a2
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_a1_a2) ).
fof(f37,axiom,
( a2 = a3
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_a2_a3) ).
fof(f38,axiom,
( a3 = a1
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_a3_a1) ).
fof(f39,axiom,
( b1 = b2
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_b1_b2) ).
fof(f40,axiom,
( b2 = b3
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_b2_b3) ).
fof(f41,axiom,
( b3 = b1
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_b3_b1) ).
fof(f42,axiom,
( a1a2 = b1b2
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not12) ).
fof(f43,axiom,
( a2a3 = b2b3
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not23) ).
fof(f44,axiom,
( a3a1 = b3b1
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not31) ).
fof(f50,axiom,
! [X0,X1,X2,X3] :
( ( incident(X1,X3)
& incident(X1,X2)
& incident(X0,X3)
& incident(X0,X2) )
=> ( X2 = X3
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique) ).
fof(f51,axiom,
! [X0,X1] :
( ( point(X1)
& point(X0) )
=> ? [X2] :
( incident(X1,X2)
& incident(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',join) ).
fof(f52,axiom,
! [X0,X1] :
( ( line(X1)
& line(X0) )
=> ? [X2] :
( incident(X2,X1)
& incident(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet) ).
fof(f53,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(f54,negated_conjecture,
~ goal,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ goal,
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ~ incident(p2,X0)
| ~ incident(p1,X0)
| ~ incident(p3,X0)
| goal ),
inference(ennf_transformation,[],[f1]) ).
fof(f57,plain,
! [X0] :
( ~ incident(p2,X0)
| ~ incident(p1,X0)
| ~ incident(p3,X0)
| goal ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
( ~ incident(a3,b1b2)
| ~ incident(a2,b3b1)
| ~ incident(a1,b2b3)
| goal ),
inference(ennf_transformation,[],[f2]) ).
fof(f59,plain,
( ~ incident(a3,b1b2)
| ~ incident(a2,b3b1)
| ~ incident(a1,b2b3)
| goal ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
( ~ incident(b3,a1a2)
| ~ incident(b2,a3a1)
| ~ incident(b1,a2a3)
| goal ),
inference(ennf_transformation,[],[f3]) ).
fof(f61,plain,
( ~ incident(b3,a1a2)
| ~ incident(b2,a3a1)
| ~ incident(b1,a2a3)
| goal ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ~ incident(X0,X1)
| point(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f63,plain,
! [X0,X1] :
( ~ incident(X0,X1)
| line(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f64,plain,
( a1 != a2
| goal ),
inference(ennf_transformation,[],[f36]) ).
fof(f65,plain,
( a2 != a3
| goal ),
inference(ennf_transformation,[],[f37]) ).
fof(f66,plain,
( a1 != a3
| goal ),
inference(ennf_transformation,[],[f38]) ).
fof(f67,plain,
( b1 != b2
| goal ),
inference(ennf_transformation,[],[f39]) ).
fof(f68,plain,
( b2 != b3
| goal ),
inference(ennf_transformation,[],[f40]) ).
fof(f69,plain,
( b1 != b3
| goal ),
inference(ennf_transformation,[],[f41]) ).
fof(f70,plain,
( b1b2 != a1a2
| goal ),
inference(ennf_transformation,[],[f42]) ).
fof(f71,plain,
( b2b3 != a2a3
| goal ),
inference(ennf_transformation,[],[f43]) ).
fof(f72,plain,
( b3b1 != a3a1
| goal ),
inference(ennf_transformation,[],[f44]) ).
fof(f80,plain,
! [X0,X1,X2,X3] :
( ~ incident(X1,X3)
| ~ incident(X1,X2)
| ~ incident(X0,X3)
| ~ incident(X0,X2)
| X2 = X3
| X0 = X1 ),
inference(ennf_transformation,[],[f50]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( ~ incident(X1,X3)
| ~ incident(X1,X2)
| ~ incident(X0,X3)
| ~ incident(X0,X2)
| X2 = X3
| X0 = X1 ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( ~ point(X1)
| ~ point(X0)
| ? [X2] :
( incident(X1,X2)
& incident(X0,X2) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f83,plain,
! [X0,X1] :
( ~ point(X1)
| ~ point(X0)
| ? [X2] :
( incident(X1,X2)
& incident(X0,X2) ) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ~ line(X1)
| ~ line(X0)
| ? [X2] :
( incident(X2,X1)
& incident(X2,X0) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f85,plain,
! [X0,X1] :
( ~ line(X1)
| ~ line(X0)
| ? [X2] :
( incident(X2,X1)
& incident(X2,X0) ) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ~ point(X1)
| ~ point(X0)
| ( incident(X1,sK0(X0,X1))
& incident(X0,sK0(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f83]) ).
fof(f87,plain,
! [X0,X1] :
( ~ line(X1)
| ~ line(X0)
| ( incident(sK1(X0,X1),X1)
& incident(sK1(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f85]) ).
fof(f88,plain,
! [X0] :
( ~ incident(p2,X0)
| ~ incident(p1,X0)
| ~ incident(p3,X0)
| goal ),
inference(cnf_transformation,[],[f57]) ).
fof(f89,plain,
( ~ incident(a3,b1b2)
| ~ incident(a2,b3b1)
| ~ incident(a1,b2b3)
| goal ),
inference(cnf_transformation,[],[f59]) ).
fof(f90,plain,
( ~ incident(b3,a1a2)
| ~ incident(b2,a3a1)
| ~ incident(b1,a2a3)
| goal ),
inference(cnf_transformation,[],[f61]) ).
fof(f91,plain,
( incident(b3,a1a2)
| incident(a1,b2b3) ),
inference(cnf_transformation,[],[f4]) ).
fof(f92,plain,
( incident(b1,a2a3)
| incident(a2,b3b1) ),
inference(cnf_transformation,[],[f5]) ).
fof(f93,plain,
( incident(b2,a3a1)
| incident(a3,b1b2) ),
inference(cnf_transformation,[],[f6]) ).
fof(f94,plain,
incident(a1,a1a2),
inference(cnf_transformation,[],[f7]) ).
fof(f95,plain,
incident(a2,a1a2),
inference(cnf_transformation,[],[f8]) ).
fof(f96,plain,
incident(a2,a2a3),
inference(cnf_transformation,[],[f9]) ).
fof(f97,plain,
incident(a3,a2a3),
inference(cnf_transformation,[],[f10]) ).
fof(f98,plain,
incident(a3,a3a1),
inference(cnf_transformation,[],[f11]) ).
fof(f99,plain,
incident(a1,a3a1),
inference(cnf_transformation,[],[f12]) ).
fof(f100,plain,
incident(b1,b1b2),
inference(cnf_transformation,[],[f13]) ).
fof(f101,plain,
incident(b2,b1b2),
inference(cnf_transformation,[],[f14]) ).
fof(f102,plain,
incident(b2,b2b3),
inference(cnf_transformation,[],[f15]) ).
fof(f103,plain,
incident(b3,b2b3),
inference(cnf_transformation,[],[f16]) ).
fof(f104,plain,
incident(b3,b3b1),
inference(cnf_transformation,[],[f17]) ).
fof(f105,plain,
incident(b1,b3b1),
inference(cnf_transformation,[],[f18]) ).
fof(f106,plain,
incident(s,s1),
inference(cnf_transformation,[],[f19]) ).
fof(f107,plain,
incident(s,s2),
inference(cnf_transformation,[],[f20]) ).
fof(f108,plain,
incident(s,s3),
inference(cnf_transformation,[],[f21]) ).
fof(f109,plain,
incident(a1,s1),
inference(cnf_transformation,[],[f22]) ).
fof(f110,plain,
incident(a2,s2),
inference(cnf_transformation,[],[f23]) ).
fof(f111,plain,
incident(a3,s3),
inference(cnf_transformation,[],[f24]) ).
fof(f112,plain,
incident(b1,s1),
inference(cnf_transformation,[],[f25]) ).
fof(f113,plain,
incident(b2,s2),
inference(cnf_transformation,[],[f26]) ).
fof(f114,plain,
incident(b3,s3),
inference(cnf_transformation,[],[f27]) ).
fof(f115,plain,
incident(p3,a1a2),
inference(cnf_transformation,[],[f28]) ).
fof(f116,plain,
incident(p3,b1b2),
inference(cnf_transformation,[],[f29]) ).
fof(f117,plain,
incident(p1,a2a3),
inference(cnf_transformation,[],[f30]) ).
fof(f118,plain,
incident(p1,b2b3),
inference(cnf_transformation,[],[f31]) ).
fof(f119,plain,
incident(p2,a3a1),
inference(cnf_transformation,[],[f32]) ).
fof(f120,plain,
incident(p2,b3b1),
inference(cnf_transformation,[],[f33]) ).
fof(f121,plain,
! [X0,X1] :
( ~ incident(X0,X1)
| point(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f122,plain,
! [X0,X1] :
( ~ incident(X0,X1)
| line(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f123,plain,
( a1 != a2
| goal ),
inference(cnf_transformation,[],[f64]) ).
fof(f124,plain,
( a2 != a3
| goal ),
inference(cnf_transformation,[],[f65]) ).
fof(f125,plain,
( a1 != a3
| goal ),
inference(cnf_transformation,[],[f66]) ).
fof(f126,plain,
( b1 != b2
| goal ),
inference(cnf_transformation,[],[f67]) ).
fof(f127,plain,
( b2 != b3
| goal ),
inference(cnf_transformation,[],[f68]) ).
fof(f128,plain,
( b1 != b3
| goal ),
inference(cnf_transformation,[],[f69]) ).
fof(f129,plain,
( b1b2 != a1a2
| goal ),
inference(cnf_transformation,[],[f70]) ).
fof(f130,plain,
( b2b3 != a2a3
| goal ),
inference(cnf_transformation,[],[f71]) ).
fof(f131,plain,
( b3b1 != a3a1
| goal ),
inference(cnf_transformation,[],[f72]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( ~ incident(X1,X3)
| ~ incident(X1,X2)
| ~ incident(X0,X3)
| ~ incident(X0,X2)
| X2 = X3
| X0 = X1 ),
inference(cnf_transformation,[],[f81]) ).
fof(f138,plain,
! [X0,X1] :
( ~ point(X1)
| ~ point(X0)
| incident(X1,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f139,plain,
! [X0,X1] :
( ~ point(X1)
| ~ point(X0)
| incident(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f140,plain,
! [X0,X1] :
( ~ line(X1)
| ~ line(X0)
| incident(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f141,plain,
! [X0,X1] :
( ~ line(X1)
| ~ line(X0)
| incident(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f142,plain,
~ goal,
inference(cnf_transformation,[],[f55]) ).
tcf(c_49,plain,
! [X0: $i] :
( goal
| ~ incident(p2,X0)
| ~ incident(p1,X0)
| ~ incident(p3,X0) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_50,plain,
( goal
| ~ incident(a3,b1b2)
| ~ incident(a2,b3b1)
| ~ incident(a1,b2b3) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_51,plain,
( goal
| ~ incident(b3,a1a2)
| ~ incident(b2,a3a1)
| ~ incident(b1,a2a3) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_52,plain,
( incident(b3,a1a2)
| incident(a1,b2b3) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_53,plain,
( incident(b1,a2a3)
| incident(a2,b3b1) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_54,plain,
( incident(b2,a3a1)
| incident(a3,b1b2) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_55,plain,
incident(a1,a1a2),
inference(cnf_transformation,[],[f94]) ).
tcf(c_56,plain,
incident(a2,a1a2),
inference(cnf_transformation,[],[f95]) ).
tcf(c_57,plain,
incident(a2,a2a3),
inference(cnf_transformation,[],[f96]) ).
tcf(c_58,plain,
incident(a3,a2a3),
inference(cnf_transformation,[],[f97]) ).
tcf(c_59,plain,
incident(a3,a3a1),
inference(cnf_transformation,[],[f98]) ).
tcf(c_60,plain,
incident(a1,a3a1),
inference(cnf_transformation,[],[f99]) ).
tcf(c_61,plain,
incident(b1,b1b2),
inference(cnf_transformation,[],[f100]) ).
tcf(c_62,plain,
incident(b2,b1b2),
inference(cnf_transformation,[],[f101]) ).
tcf(c_63,plain,
incident(b2,b2b3),
inference(cnf_transformation,[],[f102]) ).
tcf(c_64,plain,
incident(b3,b2b3),
inference(cnf_transformation,[],[f103]) ).
tcf(c_65,plain,
incident(b3,b3b1),
inference(cnf_transformation,[],[f104]) ).
tcf(c_66,plain,
incident(b1,b3b1),
inference(cnf_transformation,[],[f105]) ).
tcf(c_67,plain,
incident(s,s1),
inference(cnf_transformation,[],[f106]) ).
tcf(c_68,plain,
incident(s,s2),
inference(cnf_transformation,[],[f107]) ).
tcf(c_69,plain,
incident(s,s3),
inference(cnf_transformation,[],[f108]) ).
tcf(c_70,plain,
incident(a1,s1),
inference(cnf_transformation,[],[f109]) ).
tcf(c_71,plain,
incident(a2,s2),
inference(cnf_transformation,[],[f110]) ).
tcf(c_72,plain,
incident(a3,s3),
inference(cnf_transformation,[],[f111]) ).
tcf(c_73,plain,
incident(b1,s1),
inference(cnf_transformation,[],[f112]) ).
tcf(c_74,plain,
incident(b2,s2),
inference(cnf_transformation,[],[f113]) ).
tcf(c_75,plain,
incident(b3,s3),
inference(cnf_transformation,[],[f114]) ).
tcf(c_76,plain,
incident(p3,a1a2),
inference(cnf_transformation,[],[f115]) ).
tcf(c_77,plain,
incident(p3,b1b2),
inference(cnf_transformation,[],[f116]) ).
tcf(c_78,plain,
incident(p1,a2a3),
inference(cnf_transformation,[],[f117]) ).
tcf(c_79,plain,
incident(p1,b2b3),
inference(cnf_transformation,[],[f118]) ).
tcf(c_80,plain,
incident(p2,a3a1),
inference(cnf_transformation,[],[f119]) ).
tcf(c_81,plain,
incident(p2,b3b1),
inference(cnf_transformation,[],[f120]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( point(X0)
| ~ incident(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( line(X1)
| ~ incident(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_84,plain,
( goal
| ( a1 != a2 ) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_85,plain,
( goal
| ( a2 != a3 ) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_86,plain,
( goal
| ( a1 != a3 ) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_87,plain,
( goal
| ( b1 != b2 ) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_88,plain,
( goal
| ( b2 != b3 ) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_89,plain,
( goal
| ( b1 != b3 ) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_90,plain,
( goal
| ( b1b2 != a1a2 ) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_91,plain,
( goal
| ( b2b3 != a2a3 ) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_92,plain,
( goal
| ( b3b1 != a3a1 ) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X0 = X3 )
| ~ incident(X3,X2)
| ~ incident(X3,X1)
| ~ incident(X0,X2)
| ~ incident(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( incident(X0,sK0(X0,X1))
| ~ point(X1)
| ~ point(X0) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( incident(X1,sK0(X0,X1))
| ~ point(X1)
| ~ point(X0) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( incident(sK1(X0,X1),X0)
| ~ line(X1)
| ~ line(X0) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( incident(sK1(X0,X1),X1)
| ~ line(X1)
| ~ line(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_98,negated_conjecture,
~ goal,
inference(cnf_transformation,[],[f142]) ).
tcf(c_105,plain,
b3b1 != a3a1,
inference(global_subsumption_just,[status(thm)],[c_92,c_98,c_92]) ).
tcf(c_107,plain,
b2b3 != a2a3,
inference(global_subsumption_just,[status(thm)],[c_91,c_98,c_91]) ).
tcf(c_109,plain,
b1b2 != a1a2,
inference(global_subsumption_just,[status(thm)],[c_90,c_98,c_90]) ).
tcf(c_111,plain,
b1 != b3,
inference(global_subsumption_just,[status(thm)],[c_89,c_98,c_89]) ).
tcf(c_113,plain,
b2 != b3,
inference(global_subsumption_just,[status(thm)],[c_88,c_98,c_88]) ).
tcf(c_115,plain,
b1 != b2,
inference(global_subsumption_just,[status(thm)],[c_87,c_98,c_87]) ).
tcf(c_117,plain,
a1 != a3,
inference(global_subsumption_just,[status(thm)],[c_86,c_98,c_86]) ).
tcf(c_119,plain,
a2 != a3,
inference(global_subsumption_just,[status(thm)],[c_85,c_98,c_85]) ).
tcf(c_121,plain,
a1 != a2,
inference(global_subsumption_just,[status(thm)],[c_84,c_98,c_84]) ).
tcf(c_123,plain,
( ~ incident(b1,a2a3)
| ~ incident(b2,a3a1)
| ~ incident(b3,a1a2) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_98,c_51]) ).
tcf(c_124,plain,
( ~ incident(b3,a1a2)
| ~ incident(b2,a3a1)
| ~ incident(b1,a2a3) ),
inference(renaming,[status(thm)],[c_123]) ).
tcf(c_125,plain,
( ~ incident(a1,b2b3)
| ~ incident(a2,b3b1)
| ~ incident(a3,b1b2) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_98,c_50]) ).
tcf(c_126,plain,
( ~ incident(a3,b1b2)
| ~ incident(a2,b3b1)
| ~ incident(a1,b2b3) ),
inference(renaming,[status(thm)],[c_125]) ).
tcf(c_127,plain,
! [X0: $i] :
( ~ incident(p3,X0)
| ~ incident(p1,X0)
| ~ incident(p2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_98,c_49]) ).
tcf(c_128,plain,
! [X0: $i] :
( ~ incident(p2,X0)
| ~ incident(p1,X0)
| ~ incident(p3,X0) ),
inference(renaming,[status(thm)],[c_127]) ).
tcf(c_278,plain,
! [X0_iProver_incident_2: iProver_incident_2] :
( ~ incident(p2,X0_iProver_incident_2)
| ~ incident(p1,X0_iProver_incident_2)
| ~ incident(p3,X0_iProver_incident_2) ),
inference(subtyping,[status(esa)],[c_128]) ).
tcf(c_279,plain,
( ~ incident(a3,b1b2)
| ~ incident(a2,b3b1)
| ~ incident(a1,b2b3) ),
inference(subtyping,[status(esa)],[c_126]) ).
tcf(c_280,plain,
( ~ incident(b3,a1a2)
| ~ incident(b2,a3a1)
| ~ incident(b1,a2a3) ),
inference(subtyping,[status(esa)],[c_124]) ).
tcf(c_281,plain,
a1 != a2,
inference(subtyping,[status(esa)],[c_121]) ).
tcf(c_282,plain,
a2 != a3,
inference(subtyping,[status(esa)],[c_119]) ).
tcf(c_283,plain,
a1 != a3,
inference(subtyping,[status(esa)],[c_117]) ).
tcf(c_284,plain,
b1 != b2,
inference(subtyping,[status(esa)],[c_115]) ).
tcf(c_285,plain,
b2 != b3,
inference(subtyping,[status(esa)],[c_113]) ).
tcf(c_286,plain,
b1 != b3,
inference(subtyping,[status(esa)],[c_111]) ).
tcf(c_287,plain,
b1b2 != a1a2,
inference(subtyping,[status(esa)],[c_109]) ).
tcf(c_288,plain,
b2b3 != a2a3,
inference(subtyping,[status(esa)],[c_107]) ).
tcf(c_289,plain,
b3b1 != a3a1,
inference(subtyping,[status(esa)],[c_105]) ).
tcf(c_290,negated_conjecture,
~ goal,
inference(subtyping,[status(esa)],[c_98]) ).
tcf(c_291,plain,
! [X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( incident(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X1_iProver_incident_2)
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2) ),
inference(subtyping,[status(esa)],[c_97]) ).
tcf(c_292,plain,
! [X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( incident(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_2)
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2) ),
inference(subtyping,[status(esa)],[c_96]) ).
tcf(c_293,plain,
! [X0_iProver_incident_1: iProver_incident_1,X1_iProver_incident_1: iProver_incident_1] :
( incident(X0_iProver_incident_1,sK0(X1_iProver_incident_1,X0_iProver_incident_1))
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1) ),
inference(subtyping,[status(esa)],[c_95]) ).
tcf(c_294,plain,
! [X0_iProver_incident_1: iProver_incident_1,X1_iProver_incident_1: iProver_incident_1] :
( incident(X0_iProver_incident_1,sK0(X0_iProver_incident_1,X1_iProver_incident_1))
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1) ),
inference(subtyping,[status(esa)],[c_94]) ).
tcf(c_295,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1,X1_iProver_incident_2: iProver_incident_2] :
( ( X0_iProver_incident_2 = X1_iProver_incident_2 )
| ( X0_iProver_incident_1 = X1_iProver_incident_1 )
| ~ incident(X1_iProver_incident_1,X1_iProver_incident_2)
| ~ incident(X1_iProver_incident_1,X0_iProver_incident_2)
| ~ incident(X0_iProver_incident_1,X1_iProver_incident_2)
| ~ incident(X0_iProver_incident_1,X0_iProver_incident_2) ),
inference(subtyping,[status(esa)],[c_93]) ).
tcf(c_296,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2] :
( line(X0_iProver_incident_2)
| ~ incident(X0_iProver_incident_1,X0_iProver_incident_2) ),
inference(subtyping,[status(esa)],[c_83]) ).
tcf(c_297,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2] :
( point(X0_iProver_incident_1)
| ~ incident(X0_iProver_incident_1,X0_iProver_incident_2) ),
inference(subtyping,[status(esa)],[c_82]) ).
tcf(c_298,plain,
incident(p2,b3b1),
inference(subtyping,[status(esa)],[c_81]) ).
tcf(c_299,plain,
incident(p2,a3a1),
inference(subtyping,[status(esa)],[c_80]) ).
tcf(c_300,plain,
incident(p1,b2b3),
inference(subtyping,[status(esa)],[c_79]) ).
tcf(c_301,plain,
incident(p1,a2a3),
inference(subtyping,[status(esa)],[c_78]) ).
tcf(c_302,plain,
incident(p3,b1b2),
inference(subtyping,[status(esa)],[c_77]) ).
tcf(c_303,plain,
incident(p3,a1a2),
inference(subtyping,[status(esa)],[c_76]) ).
tcf(c_304,plain,
incident(b3,s3),
inference(subtyping,[status(esa)],[c_75]) ).
tcf(c_305,plain,
incident(b2,s2),
inference(subtyping,[status(esa)],[c_74]) ).
tcf(c_306,plain,
incident(b1,s1),
inference(subtyping,[status(esa)],[c_73]) ).
tcf(c_307,plain,
incident(a3,s3),
inference(subtyping,[status(esa)],[c_72]) ).
tcf(c_308,plain,
incident(a2,s2),
inference(subtyping,[status(esa)],[c_71]) ).
tcf(c_309,plain,
incident(a1,s1),
inference(subtyping,[status(esa)],[c_70]) ).
tcf(c_310,plain,
incident(s,s3),
inference(subtyping,[status(esa)],[c_69]) ).
tcf(c_311,plain,
incident(s,s2),
inference(subtyping,[status(esa)],[c_68]) ).
tcf(c_312,plain,
incident(s,s1),
inference(subtyping,[status(esa)],[c_67]) ).
tcf(c_313,plain,
incident(b1,b3b1),
inference(subtyping,[status(esa)],[c_66]) ).
tcf(c_314,plain,
incident(b3,b3b1),
inference(subtyping,[status(esa)],[c_65]) ).
tcf(c_315,plain,
incident(b3,b2b3),
inference(subtyping,[status(esa)],[c_64]) ).
tcf(c_316,plain,
incident(b2,b2b3),
inference(subtyping,[status(esa)],[c_63]) ).
tcf(c_317,plain,
incident(b2,b1b2),
inference(subtyping,[status(esa)],[c_62]) ).
tcf(c_318,plain,
incident(b1,b1b2),
inference(subtyping,[status(esa)],[c_61]) ).
tcf(c_319,plain,
incident(a1,a3a1),
inference(subtyping,[status(esa)],[c_60]) ).
tcf(c_320,plain,
incident(a3,a3a1),
inference(subtyping,[status(esa)],[c_59]) ).
tcf(c_321,plain,
incident(a3,a2a3),
inference(subtyping,[status(esa)],[c_58]) ).
tcf(c_322,plain,
incident(a2,a2a3),
inference(subtyping,[status(esa)],[c_57]) ).
tcf(c_323,plain,
incident(a2,a1a2),
inference(subtyping,[status(esa)],[c_56]) ).
tcf(c_324,plain,
incident(a1,a1a2),
inference(subtyping,[status(esa)],[c_55]) ).
tcf(c_325,plain,
( incident(b2,a3a1)
| incident(a3,b1b2) ),
inference(subtyping,[status(esa)],[c_54]) ).
tcf(c_326,plain,
( incident(b1,a2a3)
| incident(a2,b3b1) ),
inference(subtyping,[status(esa)],[c_53]) ).
tcf(c_327,plain,
( incident(b3,a1a2)
| incident(a1,b2b3) ),
inference(subtyping,[status(esa)],[c_52]) ).
tcf(c_2692,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2,X2_iProver_incident_2: iProver_incident_2] :
( ( X1_iProver_incident_2 = X2_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,X1_iProver_incident_2) = X0_iProver_incident_1 )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ incident(X0_iProver_incident_1,X2_iProver_incident_2)
| ~ incident(X0_iProver_incident_1,X1_iProver_incident_2)
| ~ incident(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X2_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_291,c_295]) ).
tcf(c_4704,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2,X2_iProver_incident_2: iProver_incident_2] :
( ( X0_iProver_incident_2 = X2_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,X1_iProver_incident_2) = X0_iProver_incident_1 )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ incident(X0_iProver_incident_1,X2_iProver_incident_2)
| ~ incident(X0_iProver_incident_1,X0_iProver_incident_2)
| ~ incident(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X2_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_292,c_295]) ).
tcf(c_4705,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( ( X0_iProver_incident_2 = X1_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,X1_iProver_incident_2) = X0_iProver_incident_1 )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ incident(X0_iProver_incident_1,X1_iProver_incident_2)
| ~ incident(X0_iProver_incident_1,X0_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_292,c_2692]) ).
tcf(c_5983,plain,
! [X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2,X2_iProver_incident_2: iProver_incident_2] :
( ( X1_iProver_incident_2 = X2_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,X1_iProver_incident_2) = sK1(X2_iProver_incident_2,X1_iProver_incident_2) )
| ~ line(X2_iProver_incident_2)
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ incident(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X2_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_291,c_4705]) ).
tcf(c_5984,plain,
! [X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2,X2_iProver_incident_2: iProver_incident_2] :
( ( X0_iProver_incident_2 = X2_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,X1_iProver_incident_2) = sK1(X2_iProver_incident_2,X0_iProver_incident_2) )
| ~ line(X2_iProver_incident_2)
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ incident(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X2_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_292,c_4705]) ).
tcf(c_6434,plain,
! [X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( ( X0_iProver_incident_2 = X1_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,X1_iProver_incident_2) = sK1(X1_iProver_incident_2,X0_iProver_incident_2) )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_291,c_5984]) ).
tcf(c_6530,plain,
! [X0_iProver_incident_1: iProver_incident_1] :
( ~ point(p3)
| ~ point(X0_iProver_incident_1)
| ~ incident(p2,sK0(X0_iProver_incident_1,p3))
| ~ incident(p1,sK0(X0_iProver_incident_1,p3)) ),
inference(superposition,[status(thm)],[c_293,c_278]) ).
tcf(c_6531,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1] :
( ( sK0(X0_iProver_incident_1,X1_iProver_incident_1) = X0_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,X1_iProver_incident_1)) = X1_iProver_incident_1 )
| ~ line(X0_iProver_incident_2)
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1)
| ~ incident(X1_iProver_incident_1,X0_iProver_incident_2)
| ~ line(sK0(X0_iProver_incident_1,X1_iProver_incident_1)) ),
inference(superposition,[status(thm)],[c_293,c_4705]) ).
tcf(c_6532,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1,X2_iProver_incident_1: iProver_incident_1] :
( ( X0_iProver_incident_1 = X2_iProver_incident_1 )
| ( sK0(X1_iProver_incident_1,X2_iProver_incident_1) = X0_iProver_incident_2 )
| ~ point(X2_iProver_incident_1)
| ~ point(X1_iProver_incident_1)
| ~ incident(X2_iProver_incident_1,X0_iProver_incident_2)
| ~ incident(X0_iProver_incident_1,X0_iProver_incident_2)
| ~ incident(X0_iProver_incident_1,sK0(X1_iProver_incident_1,X2_iProver_incident_1)) ),
inference(superposition,[status(thm)],[c_293,c_295]) ).
tcf(c_6533,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( ( sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)) = X0_iProver_incident_2 )
| ( sK1(sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)),X0_iProver_incident_2) = sK1(X0_iProver_incident_2,X1_iProver_incident_2) )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ line(sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2))) ),
inference(superposition,[status(thm)],[c_293,c_5984]) ).
tcf(c_6534,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( ( sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)) = X1_iProver_incident_2 )
| ( sK1(sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)),X1_iProver_incident_2) = sK1(X0_iProver_incident_2,X1_iProver_incident_2) )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ line(sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2))) ),
inference(superposition,[status(thm)],[c_293,c_5983]) ).
tcf(c_6535,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1,X1_iProver_incident_2: iProver_incident_2] :
( ( sK1(X0_iProver_incident_2,X1_iProver_incident_2) = X0_iProver_incident_1 )
| ( sK0(X1_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)) = X0_iProver_incident_2 )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X1_iProver_incident_1)
| ~ incident(X0_iProver_incident_1,X0_iProver_incident_2)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ incident(X0_iProver_incident_1,sK0(X1_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2))) ),
inference(superposition,[status(thm)],[c_293,c_4704]) ).
tcf(c_6536,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1,X1_iProver_incident_2: iProver_incident_2] :
( ( sK1(X0_iProver_incident_2,X1_iProver_incident_2) = X0_iProver_incident_1 )
| ( sK0(X1_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)) = X1_iProver_incident_2 )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X1_iProver_incident_1)
| ~ incident(X0_iProver_incident_1,X1_iProver_incident_2)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ incident(X0_iProver_incident_1,sK0(X1_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2))) ),
inference(superposition,[status(thm)],[c_293,c_2692]) ).
tcf(c_6819,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2,X2_iProver_incident_2: iProver_incident_2] :
( ( sK0(X0_iProver_incident_1,sK1(X1_iProver_incident_2,X2_iProver_incident_2)) = X1_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,sK1(X1_iProver_incident_2,X2_iProver_incident_2))) = sK1(X1_iProver_incident_2,X2_iProver_incident_2) )
| ~ line(X2_iProver_incident_2)
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X1_iProver_incident_2,X2_iProver_incident_2))
| ~ line(sK0(X0_iProver_incident_1,sK1(X1_iProver_incident_2,X2_iProver_incident_2)))
| ~ incident(sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,sK1(X1_iProver_incident_2,X2_iProver_incident_2))),X1_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_291,c_6535]) ).
tcf(c_6820,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2,X2_iProver_incident_2: iProver_incident_2] :
( ( sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)) = X0_iProver_incident_2 )
| ( sK1(sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)),X2_iProver_incident_2) = sK1(X0_iProver_incident_2,X1_iProver_incident_2) )
| ~ line(X2_iProver_incident_2)
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ line(sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)))
| ~ incident(sK1(sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)),X2_iProver_incident_2),X0_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_292,c_6535]) ).
tcf(c_6958,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( ( sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)) = X0_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2))) = sK1(X0_iProver_incident_2,X1_iProver_incident_2) )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ line(sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2))) ),
inference(superposition,[status(thm)],[c_292,c_6819]) ).
tcf(c_15933,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2,X2_iProver_incident_2: iProver_incident_2] :
( ( sK0(X0_iProver_incident_1,sK1(X1_iProver_incident_2,X2_iProver_incident_2)) = X2_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,sK1(X1_iProver_incident_2,X2_iProver_incident_2))) = sK1(X1_iProver_incident_2,X2_iProver_incident_2) )
| ~ line(X2_iProver_incident_2)
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X1_iProver_incident_2,X2_iProver_incident_2))
| ~ line(sK0(X0_iProver_incident_1,sK1(X1_iProver_incident_2,X2_iProver_incident_2)))
| ~ incident(sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,sK1(X1_iProver_incident_2,X2_iProver_incident_2))),X2_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_291,c_6536]) ).
tcf(c_15934,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2,X2_iProver_incident_2: iProver_incident_2] :
( ( sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)) = X1_iProver_incident_2 )
| ( sK1(sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)),X2_iProver_incident_2) = sK1(X0_iProver_incident_2,X1_iProver_incident_2) )
| ~ line(X2_iProver_incident_2)
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ line(sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)))
| ~ incident(sK1(sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)),X2_iProver_incident_2),X1_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_292,c_6536]) ).
tcf(c_18999,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( ( sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)) = X1_iProver_incident_2 )
| ( sK1(X1_iProver_incident_2,sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2))) = sK1(X0_iProver_incident_2,X1_iProver_incident_2) )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ line(sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2))) ),
inference(superposition,[status(thm)],[c_292,c_15933]) ).
tcf(c_24020,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1,X1_iProver_incident_2: iProver_incident_2] :
( ( sK0(X0_iProver_incident_1,X1_iProver_incident_1) = X1_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,X1_iProver_incident_1)) = X1_iProver_incident_1 )
| ~ line(X0_iProver_incident_2)
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1)
| ~ incident(X1_iProver_incident_1,X1_iProver_incident_2)
| ~ line(sK0(X0_iProver_incident_1,X1_iProver_incident_1))
| ~ incident(sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,X1_iProver_incident_1)),X1_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_291,c_6532]) ).
tcf(c_24021,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1,X1_iProver_incident_2: iProver_incident_2] :
( ( sK0(X0_iProver_incident_1,X1_iProver_incident_1) = X1_iProver_incident_2 )
| ( sK1(sK0(X0_iProver_incident_1,X1_iProver_incident_1),X0_iProver_incident_2) = X1_iProver_incident_1 )
| ~ line(X0_iProver_incident_2)
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1)
| ~ incident(X1_iProver_incident_1,X1_iProver_incident_2)
| ~ line(sK0(X0_iProver_incident_1,X1_iProver_incident_1))
| ~ incident(sK1(sK0(X0_iProver_incident_1,X1_iProver_incident_1),X0_iProver_incident_2),X1_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_292,c_6532]) ).
tcf(c_25196,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1,X2_iProver_incident_1: iProver_incident_1] :
( ( sK1(X0_iProver_incident_2,sK0(X2_iProver_incident_1,X0_iProver_incident_1)) = X0_iProver_incident_1 )
| ( sK0(X1_iProver_incident_1,sK1(X0_iProver_incident_2,sK0(X2_iProver_incident_1,X0_iProver_incident_1))) = sK0(X2_iProver_incident_1,X0_iProver_incident_1) )
| ~ line(X0_iProver_incident_2)
| ~ point(X2_iProver_incident_1)
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1)
| ~ line(sK0(X2_iProver_incident_1,X0_iProver_incident_1))
| ~ point(sK1(X0_iProver_incident_2,sK0(X2_iProver_incident_1,X0_iProver_incident_1)))
| ~ incident(X0_iProver_incident_1,sK0(X1_iProver_incident_1,sK1(X0_iProver_incident_2,sK0(X2_iProver_incident_1,X0_iProver_incident_1)))) ),
inference(superposition,[status(thm)],[c_293,c_24020]) ).
tcf(c_27051,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1] :
( ( sK0(X0_iProver_incident_1,X1_iProver_incident_1) = X0_iProver_incident_2 )
| ( sK1(sK0(X0_iProver_incident_1,X1_iProver_incident_1),X0_iProver_incident_2) = X1_iProver_incident_1 )
| ~ line(X0_iProver_incident_2)
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1)
| ~ incident(X1_iProver_incident_1,X0_iProver_incident_2)
| ~ line(sK0(X0_iProver_incident_1,X1_iProver_incident_1)) ),
inference(superposition,[status(thm)],[c_291,c_24021]) ).
tcf(c_27053,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1,X2_iProver_incident_1: iProver_incident_1] :
( ( sK1(sK0(X2_iProver_incident_1,X0_iProver_incident_1),X0_iProver_incident_2) = X0_iProver_incident_1 )
| ( sK0(X1_iProver_incident_1,sK1(sK0(X2_iProver_incident_1,X0_iProver_incident_1),X0_iProver_incident_2)) = sK0(X2_iProver_incident_1,X0_iProver_incident_1) )
| ~ line(X0_iProver_incident_2)
| ~ point(X2_iProver_incident_1)
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1)
| ~ line(sK0(X2_iProver_incident_1,X0_iProver_incident_1))
| ~ point(sK1(sK0(X2_iProver_incident_1,X0_iProver_incident_1),X0_iProver_incident_2))
| ~ incident(X0_iProver_incident_1,sK0(X1_iProver_incident_1,sK1(sK0(X2_iProver_incident_1,X0_iProver_incident_1),X0_iProver_incident_2))) ),
inference(superposition,[status(thm)],[c_293,c_24021]) ).
tcf(c_31509,plain,
! [X0_iProver_incident_1: iProver_incident_1] :
( ~ point(p3)
| ~ point(X0_iProver_incident_1)
| ~ incident(p2,sK0(p3,X0_iProver_incident_1))
| ~ incident(p1,sK0(p3,X0_iProver_incident_1)) ),
inference(superposition,[status(thm)],[c_294,c_278]) ).
tcf(c_31510,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1] :
( ( sK0(X0_iProver_incident_1,X1_iProver_incident_1) = X0_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,X1_iProver_incident_1)) = X0_iProver_incident_1 )
| ~ line(X0_iProver_incident_2)
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1)
| ~ incident(X0_iProver_incident_1,X0_iProver_incident_2)
| ~ line(sK0(X0_iProver_incident_1,X1_iProver_incident_1)) ),
inference(superposition,[status(thm)],[c_294,c_4705]) ).
tcf(c_31511,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1,X2_iProver_incident_1: iProver_incident_1] :
( ( X0_iProver_incident_1 = X1_iProver_incident_1 )
| ( sK0(X1_iProver_incident_1,X2_iProver_incident_1) = X0_iProver_incident_2 )
| ~ point(X2_iProver_incident_1)
| ~ point(X1_iProver_incident_1)
| ~ incident(X1_iProver_incident_1,X0_iProver_incident_2)
| ~ incident(X0_iProver_incident_1,X0_iProver_incident_2)
| ~ incident(X0_iProver_incident_1,sK0(X1_iProver_incident_1,X2_iProver_incident_1)) ),
inference(superposition,[status(thm)],[c_294,c_295]) ).
tcf(c_31512,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( ( sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1) = X0_iProver_incident_2 )
| ( sK1(sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1),X0_iProver_incident_2) = sK1(X0_iProver_incident_2,X1_iProver_incident_2) )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ line(sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1)) ),
inference(superposition,[status(thm)],[c_294,c_5984]) ).
tcf(c_31513,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( ( sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1) = X1_iProver_incident_2 )
| ( sK1(sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1),X1_iProver_incident_2) = sK1(X0_iProver_incident_2,X1_iProver_incident_2) )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ line(sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1)) ),
inference(superposition,[status(thm)],[c_294,c_5983]) ).
tcf(c_31514,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1,X1_iProver_incident_2: iProver_incident_2] :
( ( sK1(X0_iProver_incident_2,X1_iProver_incident_2) = X0_iProver_incident_1 )
| ( sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X1_iProver_incident_1) = X0_iProver_incident_2 )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X1_iProver_incident_1)
| ~ incident(X0_iProver_incident_1,X0_iProver_incident_2)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ incident(X0_iProver_incident_1,sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X1_iProver_incident_1)) ),
inference(superposition,[status(thm)],[c_294,c_4704]) ).
tcf(c_31515,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1,X1_iProver_incident_2: iProver_incident_2] :
( ( sK1(X0_iProver_incident_2,X1_iProver_incident_2) = X0_iProver_incident_1 )
| ( sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X1_iProver_incident_1) = X1_iProver_incident_2 )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X1_iProver_incident_1)
| ~ incident(X0_iProver_incident_1,X1_iProver_incident_2)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ incident(X0_iProver_incident_1,sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X1_iProver_incident_1)) ),
inference(superposition,[status(thm)],[c_294,c_2692]) ).
tcf(c_31516,plain,
( ~ point(p1)
| ~ point(p3)
| ~ incident(p2,sK0(p1,p3)) ),
inference(superposition,[status(thm)],[c_294,c_6530]) ).
tcf(c_31517,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1] :
( ( X0_iProver_incident_1 = X1_iProver_incident_1 )
| ( sK0(X0_iProver_incident_1,X1_iProver_incident_1) = X0_iProver_incident_2 )
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1)
| ~ incident(X1_iProver_incident_1,X0_iProver_incident_2)
| ~ incident(X0_iProver_incident_1,X0_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_294,c_6532]) ).
tcf(c_31518,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( ( sK1(X0_iProver_incident_2,X1_iProver_incident_2) = X0_iProver_incident_1 )
| ( sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)) = X1_iProver_incident_2 )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ incident(X0_iProver_incident_1,X1_iProver_incident_2)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2)) ),
inference(superposition,[status(thm)],[c_294,c_6536]) ).
tcf(c_31519,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( ( sK1(X0_iProver_incident_2,X1_iProver_incident_2) = X0_iProver_incident_1 )
| ( sK0(X0_iProver_incident_1,sK1(X0_iProver_incident_2,X1_iProver_incident_2)) = X0_iProver_incident_2 )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ incident(X0_iProver_incident_1,X0_iProver_incident_2)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2)) ),
inference(superposition,[status(thm)],[c_294,c_6535]) ).
tcf(c_31520,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1,X2_iProver_incident_1: iProver_incident_1] :
( ( sK1(X0_iProver_incident_2,sK0(X1_iProver_incident_1,X0_iProver_incident_1)) = X0_iProver_incident_1 )
| ( sK0(sK1(X0_iProver_incident_2,sK0(X1_iProver_incident_1,X0_iProver_incident_1)),X2_iProver_incident_1) = sK0(X1_iProver_incident_1,X0_iProver_incident_1) )
| ~ line(X0_iProver_incident_2)
| ~ point(X2_iProver_incident_1)
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1)
| ~ line(sK0(X1_iProver_incident_1,X0_iProver_incident_1))
| ~ point(sK1(X0_iProver_incident_2,sK0(X1_iProver_incident_1,X0_iProver_incident_1)))
| ~ incident(X0_iProver_incident_1,sK0(sK1(X0_iProver_incident_2,sK0(X1_iProver_incident_1,X0_iProver_incident_1)),X2_iProver_incident_1)) ),
inference(superposition,[status(thm)],[c_294,c_24020]) ).
tcf(c_31521,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1,X2_iProver_incident_1: iProver_incident_1] :
( ( sK1(sK0(X1_iProver_incident_1,X0_iProver_incident_1),X0_iProver_incident_2) = X0_iProver_incident_1 )
| ( sK0(sK1(sK0(X1_iProver_incident_1,X0_iProver_incident_1),X0_iProver_incident_2),X2_iProver_incident_1) = sK0(X1_iProver_incident_1,X0_iProver_incident_1) )
| ~ line(X0_iProver_incident_2)
| ~ point(X2_iProver_incident_1)
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1)
| ~ line(sK0(X1_iProver_incident_1,X0_iProver_incident_1))
| ~ point(sK1(sK0(X1_iProver_incident_1,X0_iProver_incident_1),X0_iProver_incident_2))
| ~ incident(X0_iProver_incident_1,sK0(sK1(sK0(X1_iProver_incident_1,X0_iProver_incident_1),X0_iProver_incident_2),X2_iProver_incident_1)) ),
inference(superposition,[status(thm)],[c_294,c_24021]) ).
tcf(c_31522,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1] :
( ( sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,X1_iProver_incident_1)) = X1_iProver_incident_1 )
| ( sK0(X1_iProver_incident_1,sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,X1_iProver_incident_1))) = sK0(X0_iProver_incident_1,X1_iProver_incident_1) )
| ~ line(X0_iProver_incident_2)
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1)
| ~ line(sK0(X0_iProver_incident_1,X1_iProver_incident_1))
| ~ point(sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,X1_iProver_incident_1))) ),
inference(superposition,[status(thm)],[c_294,c_25196]) ).
tcf(c_31523,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1] :
( ( sK1(sK0(X0_iProver_incident_1,X1_iProver_incident_1),X0_iProver_incident_2) = X1_iProver_incident_1 )
| ( sK0(X1_iProver_incident_1,sK1(sK0(X0_iProver_incident_1,X1_iProver_incident_1),X0_iProver_incident_2)) = sK0(X0_iProver_incident_1,X1_iProver_incident_1) )
| ~ line(X0_iProver_incident_2)
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1)
| ~ line(sK0(X0_iProver_incident_1,X1_iProver_incident_1))
| ~ point(sK1(sK0(X0_iProver_incident_1,X1_iProver_incident_1),X0_iProver_incident_2)) ),
inference(superposition,[status(thm)],[c_294,c_27053]) ).
tcf(c_33051,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1] :
( ( sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,X1_iProver_incident_1)) = X1_iProver_incident_1 )
| ( sK0(sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,X1_iProver_incident_1)),X1_iProver_incident_1) = sK0(X0_iProver_incident_1,X1_iProver_incident_1) )
| ~ line(X0_iProver_incident_2)
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1)
| ~ line(sK0(X0_iProver_incident_1,X1_iProver_incident_1))
| ~ point(sK1(X0_iProver_incident_2,sK0(X0_iProver_incident_1,X1_iProver_incident_1))) ),
inference(superposition,[status(thm)],[c_293,c_31520]) ).
tcf(c_35852,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_1: iProver_incident_1] :
( ( sK1(sK0(X0_iProver_incident_1,X1_iProver_incident_1),X0_iProver_incident_2) = X1_iProver_incident_1 )
| ( sK0(sK1(sK0(X0_iProver_incident_1,X1_iProver_incident_1),X0_iProver_incident_2),X1_iProver_incident_1) = sK0(X0_iProver_incident_1,X1_iProver_incident_1) )
| ~ line(X0_iProver_incident_2)
| ~ point(X1_iProver_incident_1)
| ~ point(X0_iProver_incident_1)
| ~ line(sK0(X0_iProver_incident_1,X1_iProver_incident_1))
| ~ point(sK1(sK0(X0_iProver_incident_1,X1_iProver_incident_1),X0_iProver_incident_2)) ),
inference(superposition,[status(thm)],[c_293,c_31521]) ).
tcf(c_47074,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2,X2_iProver_incident_2: iProver_incident_2] :
( ( sK0(sK1(X1_iProver_incident_2,X2_iProver_incident_2),X0_iProver_incident_1) = X1_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,sK0(sK1(X1_iProver_incident_2,X2_iProver_incident_2),X0_iProver_incident_1)) = sK1(X1_iProver_incident_2,X2_iProver_incident_2) )
| ~ line(X2_iProver_incident_2)
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X1_iProver_incident_2,X2_iProver_incident_2))
| ~ line(sK0(sK1(X1_iProver_incident_2,X2_iProver_incident_2),X0_iProver_incident_1))
| ~ incident(sK1(X0_iProver_incident_2,sK0(sK1(X1_iProver_incident_2,X2_iProver_incident_2),X0_iProver_incident_1)),X1_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_291,c_31514]) ).
tcf(c_47075,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2,X2_iProver_incident_2: iProver_incident_2] :
( ( sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1) = X0_iProver_incident_2 )
| ( sK1(sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1),X2_iProver_incident_2) = sK1(X0_iProver_incident_2,X1_iProver_incident_2) )
| ~ line(X2_iProver_incident_2)
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ line(sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1))
| ~ incident(sK1(sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1),X2_iProver_incident_2),X0_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_292,c_31514]) ).
tcf(c_47076,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( ( sK1(X0_iProver_incident_2,X1_iProver_incident_2) = X0_iProver_incident_1 )
| ( sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1) = X0_iProver_incident_2 )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ incident(X0_iProver_incident_1,X0_iProver_incident_2)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2)) ),
inference(superposition,[status(thm)],[c_293,c_31514]) ).
tcf(c_47730,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( ( sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1) = X0_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1)) = sK1(X0_iProver_incident_2,X1_iProver_incident_2) )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ line(sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1)) ),
inference(superposition,[status(thm)],[c_292,c_47074]) ).
tcf(c_49436,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2,X2_iProver_incident_2: iProver_incident_2] :
( ( sK0(sK1(X1_iProver_incident_2,X2_iProver_incident_2),X0_iProver_incident_1) = X2_iProver_incident_2 )
| ( sK1(X0_iProver_incident_2,sK0(sK1(X1_iProver_incident_2,X2_iProver_incident_2),X0_iProver_incident_1)) = sK1(X1_iProver_incident_2,X2_iProver_incident_2) )
| ~ line(X2_iProver_incident_2)
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X1_iProver_incident_2,X2_iProver_incident_2))
| ~ line(sK0(sK1(X1_iProver_incident_2,X2_iProver_incident_2),X0_iProver_incident_1))
| ~ incident(sK1(X0_iProver_incident_2,sK0(sK1(X1_iProver_incident_2,X2_iProver_incident_2),X0_iProver_incident_1)),X2_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_291,c_31515]) ).
tcf(c_49437,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2,X2_iProver_incident_2: iProver_incident_2] :
( ( sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1) = X1_iProver_incident_2 )
| ( sK1(sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1),X2_iProver_incident_2) = sK1(X0_iProver_incident_2,X1_iProver_incident_2) )
| ~ line(X2_iProver_incident_2)
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ line(sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1))
| ~ incident(sK1(sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1),X2_iProver_incident_2),X1_iProver_incident_2) ),
inference(superposition,[status(thm)],[c_292,c_31515]) ).
tcf(c_49438,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( ( sK1(X0_iProver_incident_2,X1_iProver_incident_2) = X0_iProver_incident_1 )
| ( sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1) = X1_iProver_incident_2 )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ incident(X0_iProver_incident_1,X1_iProver_incident_2)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2)) ),
inference(superposition,[status(thm)],[c_293,c_31515]) ).
tcf(c_50186,plain,
! [X0_iProver_incident_1: iProver_incident_1,X0_iProver_incident_2: iProver_incident_2,X1_iProver_incident_2: iProver_incident_2] :
( ( sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1) = X1_iProver_incident_2 )
| ( sK1(X1_iProver_incident_2,sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1)) = sK1(X0_iProver_incident_2,X1_iProver_incident_2) )
| ~ line(X1_iProver_incident_2)
| ~ line(X0_iProver_incident_2)
| ~ point(X0_iProver_incident_1)
| ~ point(sK1(X0_iProver_incident_2,X1_iProver_incident_2))
| ~ line(sK0(sK1(X0_iProver_incident_2,X1_iProver_incident_2),X0_iProver_incident_1)) ),
inference(superposition,[status(thm)],[c_292,c_49436]) ).
tcf(c_51612,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_50186,c_49438,c_49437,c_49436,c_47730,c_47076,c_47075,c_47074,c_35852,c_33051,c_31523,c_31522,c_31521,c_31520,c_31519,c_31518,c_31517,c_31516,c_31515,c_31514,c_31513,c_31512,c_31511,c_31510,c_31509,c_27053,c_27051,c_25196,c_24021,c_24020,c_18999,c_15934,c_15933,c_6958,c_6820,c_6819,c_6536,c_6535,c_6534,c_6533,c_6532,c_6531,c_6530,c_6434,c_5984,c_5983,c_4705,c_4704,c_2692,c_297,c_296,c_295,c_294,c_293,c_292,c_291,c_289,c_288,c_287,c_286,c_285,c_284,c_283,c_282,c_281,c_278,c_279,c_280,c_290,c_298,c_299,c_300,c_301,c_302,c_303,c_304,c_305,c_306,c_307,c_308,c_309,c_310,c_311,c_312,c_313,c_314,c_315,c_316,c_317,c_318,c_319,c_320,c_321,c_322,c_323,c_324,c_325,c_326,c_327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO169+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.59 % Computer : n014.cluster.edu
% 0.11/5.59 % Model : x86_64 x86_64
% 0.11/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59 % Memory : 8046.5625MB
% 0.11/5.59 % OS : Linux 6.8.0-71-generic
% 0.11/5.60 % CPULimit : 300
% 0.11/5.60 % WCLimit : 300
% 0.11/5.60 % DateTime : Wed Sep 23 11:14:54 UTC 2026
% 0.14/5.60 % CPUTime :
% 0.14/5.60 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.64 Running first-order theorem proving
% 0.14/5.64 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.65
% 0.14/5.65 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.65
% 0.14/5.65 % Detected problem language: tptp
% 0.14/5.66 % Proving...
% 47.49/16.15 % SZS status Started for theBenchmark.p
% 47.49/16.15 ERROR - "ProverProcess:heur/379306:2.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Z3.Error("Sort mismatch at argument #1 for function (declare-fun f_98 (s_0 s_0) Bool) supplied sort is s_121")
% 47.49/16.15 Fatal error: exception Z3.Error("Sort mismatch at argument #1 for function (declare-fun f_98 (s_0 s_0) Bool) supplied sort is s_121")
% 47.49/16.15 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 6 --comb_sup_mult 32 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground false --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs;Unflattening]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes;DemodLoopTriv;ACNormalisation]" --sup_immed_fw_main "[Subsumption;UnitSubsAndRes;Demod;LightNorm;ACNormalisation]" --sup_immed_triv "[PropSubs]" --sup_indices_passive "[]" --sup_input_bw "[SubsumptionRes]" --sup_input_fw "[SMTSubs;]" --sup_input_triv "[]" --sup_iter_deepening 1 --sup_passive_queue_type priority_queues --sup_passive_queues "[[+min_def_symb;-score;+epr];[-next_state;-conj_dist;+conj_symb]]" --sup_passive_queues_freq "[3;512]" --sup_prop_simpl_given false --sup_prop_simpl_new true --sup_restarts_mult 16 --sup_score sim_d_gen --sup_share_max_num_cl 320 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering arity_rev --sup_to_prop_solver none --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.67" --time_out_real 2.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_m9z7h2qq/1fo4lg5b 2>> /export/starexec/sandbox2/tmp/iprover_out_m9z7h2qq/1fo4lg5b_error
% 47.49/16.15 % SZS status Theorem for theBenchmark.p
% 47.49/16.15
% 47.49/16.15 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 47.49/16.15
% 47.49/16.15 % ------ iProver source info
% 47.49/16.15
% 47.49/16.15 % git: date: 2026-07-19 20:42:38 +0200
% 47.49/16.15 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 47.49/16.15 % git: non_committed_changes: false
% 47.49/16.15
% 47.49/16.15 % ------ Parsing...
% 47.49/16.15 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 47.49/16.15
% 47.49/16.15 % ------ Preprocessing...%
% 47.49/16.15
% 47.49/16.15 % ------ Preprocessing...%
% 47.49/16.15
% 47.49/16.15 % ------ Preprocessing...
% 47.49/16.15 % ------ Proving...
% 47.49/16.15 % ------ Problem Properties
% 47.49/16.15
% 47.49/16.15 %
% 47.49/16.15 % clauses 50
% 47.49/16.15 % conjectures 1
% 47.49/16.15 % EPR 46
% 47.49/16.15 % Horn 46
% 47.49/16.15 % unary 37
% 47.49/16.15 % binary 5
% 47.49/16.15 % lits 74
% 47.49/16.15 % lits eq 11
% 47.49/16.15 % fd_pure 0
% 47.49/16.15 % fd_pseudo 0
% 47.49/16.15 % fd_cond 0
% 47.49/16.15 % fd_pseudo_cond 1
% 47.49/16.15 % AC symbols 0
% 47.49/16.15
% 47.49/16.15 % ------ Input Options Time Limit: Unbounded
% 47.49/16.15
% 47.49/16.15
% 47.49/16.15 % ------
% 47.49/16.15 % Current options:
% 47.49/16.15 % ------
% 47.49/16.15
% 47.49/16.15
% 47.49/16.15 %
% 47.49/16.15
% 47.49/16.15 % ------ Proving...
% 47.49/16.15 %
% 47.49/16.15
% 47.49/16.15 % SZS status Theorem for theBenchmark.p
% 47.49/16.15
% 47.49/16.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 47.49/16.15
% 47.49/16.15
%------------------------------------------------------------------------------