%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO169+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 : Thu Sep 24 08:39:38 AM UTC 2026
% Result : Theorem 271.88s 272.19s
% Output : Proof 271.95s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(goal_normal,axiom,
! [A] :
( ( incident(ab,A)
& incident(ac,A)
& incident(bc,A)
& line_equal(A,A) )
=> goal ),
file('theBenchmark.p',goal_normal) ).
fof(t1in2,axiom,
( ( incident(c1,a2b2)
& incident(b1,a2c2)
& incident(a1,b2c2) )
=> goal ),
file('theBenchmark.p',t1in2) ).
fof(t2in1,axiom,
( ( incident(c2,a1b1)
& incident(b2,a1c1)
& incident(a2,b1c1) )
=> goal ),
file('theBenchmark.p',t2in1) ).
fof(gap_a,axiom,
( incident(b2,a1c1)
| incident(a1,b2c2) ),
file('theBenchmark.p',gap_a) ).
fof(gap_b,axiom,
( incident(c2,a1b1)
| incident(b1,a2c2) ),
file('theBenchmark.p',gap_b) ).
fof(gap_c,axiom,
( incident(a2,b1c1)
| incident(c1,a2b2) ),
file('theBenchmark.p',gap_c) ).
fof(ia1b1,axiom,
incident(a1,a1b1),
file('theBenchmark.p',ia1b1) ).
fof(ib1a1,axiom,
incident(b1,a1b1),
file('theBenchmark.p',ib1a1) ).
fof(ia2b2,axiom,
incident(a2,a2b2),
file('theBenchmark.p',ia2b2) ).
fof(ib2a2,axiom,
incident(b2,a2b2),
file('theBenchmark.p',ib2a2) ).
fof(ia1c1,axiom,
incident(a1,a1c1),
file('theBenchmark.p',ia1c1) ).
fof(ic1a1,axiom,
incident(c1,a1c1),
file('theBenchmark.p',ic1a1) ).
fof(ia2c2,axiom,
incident(a2,a2c2),
file('theBenchmark.p',ia2c2) ).
fof(ic2a2,axiom,
incident(c2,a2c2),
file('theBenchmark.p',ic2a2) ).
fof(ic1b1,axiom,
incident(c1,b1c1),
file('theBenchmark.p',ic1b1) ).
fof(ib1c1,axiom,
incident(b1,b1c1),
file('theBenchmark.p',ib1c1) ).
fof(ic2b2,axiom,
incident(c2,b2c2),
file('theBenchmark.p',ic2b2) ).
fof(ib2c2,axiom,
incident(b2,b2c2),
file('theBenchmark.p',ib2c2) ).
fof(iooa,axiom,
incident(o,oa),
file('theBenchmark.p',iooa) ).
fof(ioob,axiom,
incident(o,ob),
file('theBenchmark.p',ioob) ).
fof(iooc,axiom,
incident(o,oc),
file('theBenchmark.p',iooc) ).
fof(ia1oa,axiom,
incident(a1,oa),
file('theBenchmark.p',ia1oa) ).
fof(ia2oa,axiom,
incident(a2,oa),
file('theBenchmark.p',ia2oa) ).
fof(ib1ob,axiom,
incident(b1,ob),
file('theBenchmark.p',ib1ob) ).
fof(ib2ob,axiom,
incident(b2,ob),
file('theBenchmark.p',ib2ob) ).
fof(ic1oc,axiom,
incident(c1,oc),
file('theBenchmark.p',ic1oc) ).
fof(ic2oc,axiom,
incident(c2,oc),
file('theBenchmark.p',ic2oc) ).
fof(ibc1,axiom,
incident(bc,b1c1),
file('theBenchmark.p',ibc1) ).
fof(ibc2,axiom,
incident(bc,b2c2),
file('theBenchmark.p',ibc2) ).
fof(iac1,axiom,
incident(ac,a1c1),
file('theBenchmark.p',iac1) ).
fof(iac2,axiom,
incident(ac,a2c2),
file('theBenchmark.p',iac2) ).
fof(iab1,axiom,
incident(ab,a1b1),
file('theBenchmark.p',iab1) ).
fof(iab2,axiom,
incident(ab,a2b2),
file('theBenchmark.p',iab2) ).
fof(triangle1,axiom,
! [A] :
( ( incident(c1,A)
& incident(b1,A)
& incident(a1,A) )
=> goal ),
file('theBenchmark.p',triangle1) ).
fof(triangle2,axiom,
! [A] :
( ( incident(c2,A)
& incident(b2,A)
& incident(a2,A) )
=> goal ),
file('theBenchmark.p',triangle2) ).
fof(notaa,axiom,
( point_equal(a2,a1)
=> goal ),
file('theBenchmark.p',notaa) ).
fof(notbb,axiom,
( point_equal(b2,b1)
=> goal ),
file('theBenchmark.p',notbb) ).
fof(notcc,axiom,
( point_equal(c2,c1)
=> goal ),
file('theBenchmark.p',notcc) ).
fof(notbc,axiom,
( line_equal(b1c1,b2c2)
=> goal ),
file('theBenchmark.p',notbc) ).
fof(notac,axiom,
( line_equal(a1c1,a2c2)
=> goal ),
file('theBenchmark.p',notac) ).
fof(notab,axiom,
( line_equal(a1b1,a2b2)
=> goal ),
file('theBenchmark.p',notab) ).
fof(reflexivity_of_point_equal,axiom,
! [A,B] :
( incident(A,B)
=> point_equal(A,A) ),
file('theBenchmark.p',reflexivity_of_point_equal) ).
fof(symmetry_of_point_equal,axiom,
! [A,B] :
( point_equal(A,B)
=> point_equal(B,A) ),
file('theBenchmark.p',symmetry_of_point_equal) ).
fof(transitivity_of_point_equal,axiom,
! [A,B,C] :
( ( point_equal(B,C)
& point_equal(A,B) )
=> point_equal(A,C) ),
file('theBenchmark.p',transitivity_of_point_equal) ).
fof(reflexivity_of_line_equal,axiom,
! [A,B] :
( incident(A,B)
=> line_equal(B,B) ),
file('theBenchmark.p',reflexivity_of_line_equal) ).
fof(symmetry_of_line_equal,axiom,
! [A,B] :
( line_equal(A,B)
=> line_equal(B,A) ),
file('theBenchmark.p',symmetry_of_line_equal) ).
fof(transitivity_of_line_equal,axiom,
! [A,B,C] :
( ( line_equal(B,C)
& line_equal(A,B) )
=> line_equal(A,C) ),
file('theBenchmark.p',transitivity_of_line_equal) ).
fof(pcon,axiom,
! [A,B,C] :
( ( incident(B,C)
& point_equal(A,B) )
=> incident(A,C) ),
file('theBenchmark.p',pcon) ).
fof(lcon,axiom,
! [A,B,C] :
( ( line_equal(B,C)
& incident(A,B) )
=> incident(A,C) ),
file('theBenchmark.p',lcon) ).
fof(unique,axiom,
! [A,B,C,D] :
( ( incident(B,D)
& incident(B,C)
& incident(A,D)
& incident(A,C) )
=> ( line_equal(C,D)
| point_equal(A,B) ) ),
file('theBenchmark.p',unique) ).
fof(goal_to_be_proved,conjecture,
goal,
file('theBenchmark.p',goal_to_be_proved) ).
fof(f_1_1,plain,
! [A] :
( goal
| ~ incident(ab,A)
| ~ incident(ac,A)
| ~ incident(bc,A)
| ~ line_equal(A,A) ),
inference(fof_nnf,[status(thm)],[goal_normal]) ).
fof(f_1_2,plain,
! [U_0] :
( goal
| ~ incident(ab,U_0)
| ~ incident(ac,U_0)
| ~ incident(bc,U_0)
| ~ line_equal(U_0,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_0] :
( ~ incident(ab,U_0)
| ~ incident(ac,U_0)
| ~ incident(bc,U_0)
| ~ line_equal(U_0,U_0) )
| goal ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
! [U_0] :
( ~ incident(ab,U_0)
| ~ incident(ac,U_0)
| ~ incident(bc,U_0)
| ~ line_equal(U_0,U_0)
| goal ),
inference(definitional_conversion,[status(esa)],[f_1_3]) ).
cnf(f_1_5,plain,
( ~ incident(ab,U_0)
| ~ incident(ac,U_0)
| ~ incident(bc,U_0)
| ~ line_equal(U_0,U_0)
| goal ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
( goal
| ~ incident(c1,a2b2)
| ~ incident(b1,a2c2)
| ~ incident(a1,b2c2) ),
inference(fof_nnf,[status(thm)],[t1in2]) ).
fof(f_2_2,plain,
( goal
| ~ incident(c1,a2b2)
| ~ incident(b1,a2c2)
| ~ incident(a1,b2c2) ),
inference(definitional_conversion,[status(esa)],[f_2_1]) ).
cnf(f_2_3,plain,
( goal
| ~ incident(c1,a2b2)
| ~ incident(b1,a2c2)
| ~ incident(a1,b2c2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
( goal
| ~ incident(c2,a1b1)
| ~ incident(b2,a1c1)
| ~ incident(a2,b1c1) ),
inference(fof_nnf,[status(thm)],[t2in1]) ).
fof(f_3_2,plain,
( goal
| ~ incident(c2,a1b1)
| ~ incident(b2,a1c1)
| ~ incident(a2,b1c1) ),
inference(definitional_conversion,[status(esa)],[f_3_1]) ).
cnf(f_3_3,plain,
( goal
| ~ incident(c2,a1b1)
| ~ incident(b2,a1c1)
| ~ incident(a2,b1c1) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
( incident(b2,a1c1)
| incident(a1,b2c2) ),
inference(fof_nnf,[status(thm)],[gap_a]) ).
fof(f_4_2,plain,
( incident(b2,a1c1)
| incident(a1,b2c2) ),
inference(definitional_conversion,[status(esa)],[f_4_1]) ).
cnf(f_4_3,plain,
( incident(b2,a1c1)
| incident(a1,b2c2) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
( incident(c2,a1b1)
| incident(b1,a2c2) ),
inference(fof_nnf,[status(thm)],[gap_b]) ).
fof(f_5_2,plain,
( incident(c2,a1b1)
| incident(b1,a2c2) ),
inference(definitional_conversion,[status(esa)],[f_5_1]) ).
cnf(f_5_3,plain,
( incident(c2,a1b1)
| incident(b1,a2c2) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
( incident(a2,b1c1)
| incident(c1,a2b2) ),
inference(fof_nnf,[status(thm)],[gap_c]) ).
fof(f_6_2,plain,
( incident(a2,b1c1)
| incident(c1,a2b2) ),
inference(definitional_conversion,[status(esa)],[f_6_1]) ).
cnf(f_6_3,plain,
( incident(a2,b1c1)
| incident(c1,a2b2) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
incident(a1,a1b1),
inference(fof_nnf,[status(thm)],[ia1b1]) ).
fof(f_7_2,plain,
incident(a1,a1b1),
inference(definitional_conversion,[status(esa)],[f_7_1]) ).
cnf(f_7_3,plain,
incident(a1,a1b1),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
incident(b1,a1b1),
inference(fof_nnf,[status(thm)],[ib1a1]) ).
fof(f_8_2,plain,
incident(b1,a1b1),
inference(definitional_conversion,[status(esa)],[f_8_1]) ).
cnf(f_8_3,plain,
incident(b1,a1b1),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
incident(a2,a2b2),
inference(fof_nnf,[status(thm)],[ia2b2]) ).
fof(f_9_2,plain,
incident(a2,a2b2),
inference(definitional_conversion,[status(esa)],[f_9_1]) ).
cnf(f_9_3,plain,
incident(a2,a2b2),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
incident(b2,a2b2),
inference(fof_nnf,[status(thm)],[ib2a2]) ).
fof(f_10_2,plain,
incident(b2,a2b2),
inference(definitional_conversion,[status(esa)],[f_10_1]) ).
cnf(f_10_3,plain,
incident(b2,a2b2),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
incident(a1,a1c1),
inference(fof_nnf,[status(thm)],[ia1c1]) ).
fof(f_11_2,plain,
incident(a1,a1c1),
inference(definitional_conversion,[status(esa)],[f_11_1]) ).
cnf(f_11_3,plain,
incident(a1,a1c1),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
incident(c1,a1c1),
inference(fof_nnf,[status(thm)],[ic1a1]) ).
fof(f_12_2,plain,
incident(c1,a1c1),
inference(definitional_conversion,[status(esa)],[f_12_1]) ).
cnf(f_12_3,plain,
incident(c1,a1c1),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
incident(a2,a2c2),
inference(fof_nnf,[status(thm)],[ia2c2]) ).
fof(f_13_2,plain,
incident(a2,a2c2),
inference(definitional_conversion,[status(esa)],[f_13_1]) ).
cnf(f_13_3,plain,
incident(a2,a2c2),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
incident(c2,a2c2),
inference(fof_nnf,[status(thm)],[ic2a2]) ).
fof(f_14_2,plain,
incident(c2,a2c2),
inference(definitional_conversion,[status(esa)],[f_14_1]) ).
cnf(f_14_3,plain,
incident(c2,a2c2),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
incident(c1,b1c1),
inference(fof_nnf,[status(thm)],[ic1b1]) ).
fof(f_15_2,plain,
incident(c1,b1c1),
inference(definitional_conversion,[status(esa)],[f_15_1]) ).
cnf(f_15_3,plain,
incident(c1,b1c1),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
incident(b1,b1c1),
inference(fof_nnf,[status(thm)],[ib1c1]) ).
fof(f_16_2,plain,
incident(b1,b1c1),
inference(definitional_conversion,[status(esa)],[f_16_1]) ).
cnf(f_16_3,plain,
incident(b1,b1c1),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
incident(c2,b2c2),
inference(fof_nnf,[status(thm)],[ic2b2]) ).
fof(f_17_2,plain,
incident(c2,b2c2),
inference(definitional_conversion,[status(esa)],[f_17_1]) ).
cnf(f_17_3,plain,
incident(c2,b2c2),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
incident(b2,b2c2),
inference(fof_nnf,[status(thm)],[ib2c2]) ).
fof(f_18_2,plain,
incident(b2,b2c2),
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,plain,
incident(b2,b2c2),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
incident(o,oa),
inference(fof_nnf,[status(thm)],[iooa]) ).
fof(f_19_2,plain,
incident(o,oa),
inference(definitional_conversion,[status(esa)],[f_19_1]) ).
cnf(f_19_3,plain,
incident(o,oa),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
incident(o,ob),
inference(fof_nnf,[status(thm)],[ioob]) ).
fof(f_20_2,plain,
incident(o,ob),
inference(definitional_conversion,[status(esa)],[f_20_1]) ).
cnf(f_20_3,plain,
incident(o,ob),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
incident(o,oc),
inference(fof_nnf,[status(thm)],[iooc]) ).
fof(f_21_2,plain,
incident(o,oc),
inference(definitional_conversion,[status(esa)],[f_21_1]) ).
cnf(f_21_3,plain,
incident(o,oc),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
incident(a1,oa),
inference(fof_nnf,[status(thm)],[ia1oa]) ).
fof(f_22_2,plain,
incident(a1,oa),
inference(definitional_conversion,[status(esa)],[f_22_1]) ).
cnf(f_22_3,plain,
incident(a1,oa),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
incident(a2,oa),
inference(fof_nnf,[status(thm)],[ia2oa]) ).
fof(f_23_2,plain,
incident(a2,oa),
inference(definitional_conversion,[status(esa)],[f_23_1]) ).
cnf(f_23_3,plain,
incident(a2,oa),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
incident(b1,ob),
inference(fof_nnf,[status(thm)],[ib1ob]) ).
fof(f_24_2,plain,
incident(b1,ob),
inference(definitional_conversion,[status(esa)],[f_24_1]) ).
cnf(f_24_3,plain,
incident(b1,ob),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
incident(b2,ob),
inference(fof_nnf,[status(thm)],[ib2ob]) ).
fof(f_25_2,plain,
incident(b2,ob),
inference(definitional_conversion,[status(esa)],[f_25_1]) ).
cnf(f_25_3,plain,
incident(b2,ob),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
incident(c1,oc),
inference(fof_nnf,[status(thm)],[ic1oc]) ).
fof(f_26_2,plain,
incident(c1,oc),
inference(definitional_conversion,[status(esa)],[f_26_1]) ).
cnf(f_26_3,plain,
incident(c1,oc),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
incident(c2,oc),
inference(fof_nnf,[status(thm)],[ic2oc]) ).
fof(f_27_2,plain,
incident(c2,oc),
inference(definitional_conversion,[status(esa)],[f_27_1]) ).
cnf(f_27_3,plain,
incident(c2,oc),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
incident(bc,b1c1),
inference(fof_nnf,[status(thm)],[ibc1]) ).
fof(f_28_2,plain,
incident(bc,b1c1),
inference(definitional_conversion,[status(esa)],[f_28_1]) ).
cnf(f_28_3,plain,
incident(bc,b1c1),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
incident(bc,b2c2),
inference(fof_nnf,[status(thm)],[ibc2]) ).
fof(f_29_2,plain,
incident(bc,b2c2),
inference(definitional_conversion,[status(esa)],[f_29_1]) ).
cnf(f_29_3,plain,
incident(bc,b2c2),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
incident(ac,a1c1),
inference(fof_nnf,[status(thm)],[iac1]) ).
fof(f_30_2,plain,
incident(ac,a1c1),
inference(definitional_conversion,[status(esa)],[f_30_1]) ).
cnf(f_30_3,plain,
incident(ac,a1c1),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
incident(ac,a2c2),
inference(fof_nnf,[status(thm)],[iac2]) ).
fof(f_31_2,plain,
incident(ac,a2c2),
inference(definitional_conversion,[status(esa)],[f_31_1]) ).
cnf(f_31_3,plain,
incident(ac,a2c2),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
incident(ab,a1b1),
inference(fof_nnf,[status(thm)],[iab1]) ).
fof(f_32_2,plain,
incident(ab,a1b1),
inference(definitional_conversion,[status(esa)],[f_32_1]) ).
cnf(f_32_3,plain,
incident(ab,a1b1),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
incident(ab,a2b2),
inference(fof_nnf,[status(thm)],[iab2]) ).
fof(f_33_2,plain,
incident(ab,a2b2),
inference(definitional_conversion,[status(esa)],[f_33_1]) ).
cnf(f_33_3,plain,
incident(ab,a2b2),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A] :
( goal
| ~ incident(c1,A)
| ~ incident(b1,A)
| ~ incident(a1,A) ),
inference(fof_nnf,[status(thm)],[triangle1]) ).
fof(f_34_2,plain,
! [U_1] :
( goal
| ~ incident(c1,U_1)
| ~ incident(b1,U_1)
| ~ incident(a1,U_1) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_1] :
( ~ incident(c1,U_1)
| ~ incident(b1,U_1)
| ~ incident(a1,U_1) )
| goal ),
inference(miniscope,[status(thm)],[f_34_2]) ).
fof(f_34_4,plain,
! [U_1] :
( ~ incident(c1,U_1)
| ~ incident(b1,U_1)
| ~ incident(a1,U_1)
| goal ),
inference(definitional_conversion,[status(esa)],[f_34_3]) ).
cnf(f_34_5,plain,
( ~ incident(c1,U_1)
| ~ incident(b1,U_1)
| ~ incident(a1,U_1)
| goal ),
inference(clausify,[status(thm)],[f_34_4]) ).
fof(f_35_1,plain,
! [A] :
( goal
| ~ incident(c2,A)
| ~ incident(b2,A)
| ~ incident(a2,A) ),
inference(fof_nnf,[status(thm)],[triangle2]) ).
fof(f_35_2,plain,
! [U_2] :
( goal
| ~ incident(c2,U_2)
| ~ incident(b2,U_2)
| ~ incident(a2,U_2) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_2] :
( ~ incident(c2,U_2)
| ~ incident(b2,U_2)
| ~ incident(a2,U_2) )
| goal ),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
! [U_2] :
( ~ incident(c2,U_2)
| ~ incident(b2,U_2)
| ~ incident(a2,U_2)
| goal ),
inference(definitional_conversion,[status(esa)],[f_35_3]) ).
cnf(f_35_5,plain,
( ~ incident(c2,U_2)
| ~ incident(b2,U_2)
| ~ incident(a2,U_2)
| goal ),
inference(clausify,[status(thm)],[f_35_4]) ).
fof(f_36_1,plain,
( goal
| ~ point_equal(a2,a1) ),
inference(fof_nnf,[status(thm)],[notaa]) ).
fof(f_36_2,plain,
( goal
| ~ point_equal(a2,a1) ),
inference(definitional_conversion,[status(esa)],[f_36_1]) ).
cnf(f_36_3,plain,
( goal
| ~ point_equal(a2,a1) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
( goal
| ~ point_equal(b2,b1) ),
inference(fof_nnf,[status(thm)],[notbb]) ).
fof(f_37_2,plain,
( goal
| ~ point_equal(b2,b1) ),
inference(definitional_conversion,[status(esa)],[f_37_1]) ).
cnf(f_37_3,plain,
( goal
| ~ point_equal(b2,b1) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
( goal
| ~ point_equal(c2,c1) ),
inference(fof_nnf,[status(thm)],[notcc]) ).
fof(f_38_2,plain,
( goal
| ~ point_equal(c2,c1) ),
inference(definitional_conversion,[status(esa)],[f_38_1]) ).
cnf(f_38_3,plain,
( goal
| ~ point_equal(c2,c1) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
( goal
| ~ line_equal(b1c1,b2c2) ),
inference(fof_nnf,[status(thm)],[notbc]) ).
fof(f_39_2,plain,
( goal
| ~ line_equal(b1c1,b2c2) ),
inference(definitional_conversion,[status(esa)],[f_39_1]) ).
cnf(f_39_3,plain,
( goal
| ~ line_equal(b1c1,b2c2) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
( goal
| ~ line_equal(a1c1,a2c2) ),
inference(fof_nnf,[status(thm)],[notac]) ).
fof(f_40_2,plain,
( goal
| ~ line_equal(a1c1,a2c2) ),
inference(definitional_conversion,[status(esa)],[f_40_1]) ).
cnf(f_40_3,plain,
( goal
| ~ line_equal(a1c1,a2c2) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
( goal
| ~ line_equal(a1b1,a2b2) ),
inference(fof_nnf,[status(thm)],[notab]) ).
fof(f_41_2,plain,
( goal
| ~ line_equal(a1b1,a2b2) ),
inference(definitional_conversion,[status(esa)],[f_41_1]) ).
cnf(f_41_3,plain,
( goal
| ~ line_equal(a1b1,a2b2) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [A,B] :
( point_equal(A,A)
| ~ incident(A,B) ),
inference(fof_nnf,[status(thm)],[reflexivity_of_point_equal]) ).
fof(f_42_2,plain,
! [U_4,U_3] :
( point_equal(U_4,U_4)
| ~ incident(U_4,U_3) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_4] :
( ! [U_3] : ~ incident(U_4,U_3)
| point_equal(U_4,U_4) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
! [U_3,U_4] :
( ~ incident(U_4,U_3)
| point_equal(U_4,U_4) ),
inference(definitional_conversion,[status(esa)],[f_42_3]) ).
cnf(f_42_5,plain,
( ~ incident(U_4,U_3)
| point_equal(U_4,U_4) ),
inference(clausify,[status(thm)],[f_42_4]) ).
fof(f_43_1,plain,
! [A,B] :
( point_equal(B,A)
| ~ point_equal(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_of_point_equal]) ).
fof(f_43_2,plain,
! [U_6,U_5] :
( point_equal(U_5,U_6)
| ~ point_equal(U_6,U_5) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_5,U_6] :
( point_equal(U_5,U_6)
| ~ point_equal(U_6,U_5) ),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
( point_equal(U_5,U_6)
| ~ point_equal(U_6,U_5) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A,B,C] :
( point_equal(A,C)
| ~ point_equal(B,C)
| ~ point_equal(A,B) ),
inference(fof_nnf,[status(thm)],[transitivity_of_point_equal]) ).
fof(f_44_2,plain,
! [U_9,U_8,U_7] :
( point_equal(U_9,U_7)
| ~ point_equal(U_8,U_7)
| ~ point_equal(U_9,U_8) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_7,U_8,U_9] :
( point_equal(U_9,U_7)
| ~ point_equal(U_8,U_7)
| ~ point_equal(U_9,U_8) ),
inference(definitional_conversion,[status(esa)],[f_44_2]) ).
cnf(f_44_4,plain,
( point_equal(U_9,U_7)
| ~ point_equal(U_8,U_7)
| ~ point_equal(U_9,U_8) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A,B] :
( line_equal(B,B)
| ~ incident(A,B) ),
inference(fof_nnf,[status(thm)],[reflexivity_of_line_equal]) ).
fof(f_45_2,plain,
! [U_11,U_10] :
( line_equal(U_10,U_10)
| ~ incident(U_11,U_10) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_11,U_10] :
( line_equal(U_10,U_10)
| ~ incident(U_11,U_10) ),
inference(definitional_conversion,[status(esa)],[f_45_2]) ).
cnf(f_45_4,plain,
( line_equal(U_10,U_10)
| ~ incident(U_11,U_10) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [A,B] :
( line_equal(B,A)
| ~ line_equal(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_of_line_equal]) ).
fof(f_46_2,plain,
! [U_13,U_12] :
( line_equal(U_12,U_13)
| ~ line_equal(U_13,U_12) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_12,U_13] :
( line_equal(U_12,U_13)
| ~ line_equal(U_13,U_12) ),
inference(definitional_conversion,[status(esa)],[f_46_2]) ).
cnf(f_46_4,plain,
( line_equal(U_12,U_13)
| ~ line_equal(U_13,U_12) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [A,B,C] :
( line_equal(A,C)
| ~ line_equal(B,C)
| ~ line_equal(A,B) ),
inference(fof_nnf,[status(thm)],[transitivity_of_line_equal]) ).
fof(f_47_2,plain,
! [U_16,U_15,U_14] :
( line_equal(U_16,U_14)
| ~ line_equal(U_15,U_14)
| ~ line_equal(U_16,U_15) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_14,U_15,U_16] :
( line_equal(U_16,U_14)
| ~ line_equal(U_15,U_14)
| ~ line_equal(U_16,U_15) ),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
( line_equal(U_16,U_14)
| ~ line_equal(U_15,U_14)
| ~ line_equal(U_16,U_15) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [A,B,C] :
( incident(A,C)
| ~ incident(B,C)
| ~ point_equal(A,B) ),
inference(fof_nnf,[status(thm)],[pcon]) ).
fof(f_48_2,plain,
! [U_19,U_18,U_17] :
( incident(U_19,U_17)
| ~ incident(U_18,U_17)
| ~ point_equal(U_19,U_18) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_19,U_17,U_18] :
( incident(U_19,U_17)
| ~ incident(U_18,U_17)
| ~ point_equal(U_19,U_18) ),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
( incident(U_19,U_17)
| ~ incident(U_18,U_17)
| ~ point_equal(U_19,U_18) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [A,B,C] :
( incident(A,C)
| ~ line_equal(B,C)
| ~ incident(A,B) ),
inference(fof_nnf,[status(thm)],[lcon]) ).
fof(f_49_2,plain,
! [U_22,U_21,U_20] :
( incident(U_22,U_20)
| ~ line_equal(U_21,U_20)
| ~ incident(U_22,U_21) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_22,U_20,U_21] :
( incident(U_22,U_20)
| ~ line_equal(U_21,U_20)
| ~ incident(U_22,U_21) ),
inference(definitional_conversion,[status(esa)],[f_49_2]) ).
cnf(f_49_4,plain,
( incident(U_22,U_20)
| ~ line_equal(U_21,U_20)
| ~ incident(U_22,U_21) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [A,B,C,D] :
( line_equal(C,D)
| point_equal(A,B)
| ~ incident(B,D)
| ~ incident(B,C)
| ~ incident(A,D)
| ~ incident(A,C) ),
inference(fof_nnf,[status(thm)],[unique]) ).
fof(f_50_2,plain,
! [U_26,U_25,U_24,U_23] :
( line_equal(U_24,U_23)
| point_equal(U_26,U_25)
| ~ incident(U_25,U_23)
| ~ incident(U_25,U_24)
| ~ incident(U_26,U_23)
| ~ incident(U_26,U_24) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_24,U_23,U_25,U_26] :
( line_equal(U_24,U_23)
| point_equal(U_26,U_25)
| ~ incident(U_25,U_23)
| ~ incident(U_25,U_24)
| ~ incident(U_26,U_23)
| ~ incident(U_26,U_24) ),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
( line_equal(U_24,U_23)
| point_equal(U_26,U_25)
| ~ incident(U_25,U_23)
| ~ incident(U_25,U_24)
| ~ incident(U_26,U_23)
| ~ incident(U_26,U_24) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,negated_conjecture,
~ goal,
inference(negate,[status(cth)],[goal_to_be_proved]) ).
fof(f_51_2,negated_conjecture,
~ goal,
inference(definitional_conversion,[status(esa)],[f_51_1]) ).
cnf(f_51_3,negated_conjecture,
~ goal,
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO169+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 07:36:18 UTC 2026
% 0.12/0.36 % CPUTime :
% 271.88/272.19 % SZS status Theorem for theBenchmark
% 271.88/272.19 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------