%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO204+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 01:20:19 PM UTC 2026
% Result : Theorem 0.95s 0.96s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 76 ( 20 unt; 2 def)
% Number of atoms : 229 ( 2 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 195 ( 76 ~; 97 |; 11 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 110 !; 6 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X1,X2)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart4) ).
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( ( distinct_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq1) ).
fof(f31,axiom,
! [X0,X1] :
( equal_points(X0,X1)
<=> ~ distinct_points(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax1) ).
fof(f32,axiom,
! [X0,X1] :
( equal_lines(X0,X1)
<=> ~ distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax2) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( equal_points(X1,X2)
& distinct_points(X0,X1) )
=> ( equal_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( equal_points(X1,X2)
& distinct_points(X0,X1) )
=> ( equal_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
=> equal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f39,plain,
! [X0,X1] :
( equal_points(X0,X1)
=> ~ distinct_points(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(flattening,[],[f40]) ).
fof(f46,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f47,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(ennf_transformation,[],[f12]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(flattening,[],[f52]) ).
fof(f78,plain,
! [X0,X1] :
( ~ equal_points(X0,X1)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f79,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f80,plain,
? [X0,X1,X2] :
( equal_points(X1,X2)
& distinct_points(X0,X1)
& ( ~ equal_lines(line_connecting(X0,X1),line_connecting(X0,X2))
| ~ distinct_points(X0,X2) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f81,plain,
? [X0,X1,X2] :
( equal_points(X1,X2)
& distinct_points(X0,X1)
& ( ~ equal_lines(line_connecting(X0,X1),line_connecting(X0,X2))
| ~ distinct_points(X0,X2) ) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
( equal_points(sK1,sK2)
& distinct_points(sK0,sK1)
& ( ~ equal_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ distinct_points(sK0,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f81]) ).
fof(f83,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f86,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f89,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f90,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f93,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f119,plain,
! [X0,X1] :
( ~ equal_points(X0,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f120,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f121,plain,
equal_points(sK1,sK2),
inference(cnf_transformation,[],[f82]) ).
fof(f122,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f82]) ).
fof(f123,plain,
( ~ equal_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ distinct_points(sK0,sK2) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_49,plain,
! [X0: $i] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f83]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X1,X0)
| ~ apart_point_and_line(X0,line_connecting(X1,X0)) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ~ equal_points(X0,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_87,negated_conjecture,
( ~ distinct_points(sK0,sK2)
| ~ equal_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_88,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f122]) ).
tcf(c_89,negated_conjecture,
equal_points(sK1,sK2),
inference(cnf_transformation,[],[f121]) ).
tcf(c_301,plain,
~ distinct_points(sK1,sK2),
inference(resolution,[status(thm)],[c_85,c_89]) ).
tcf(c_306,plain,
( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ distinct_points(sK0,sK2) ),
inference(resolution,[status(thm)],[c_86,c_87]) ).
tcf(c_473,definition,
iPr_def_10 = line_connecting(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_474,definition,
iPr_def_11 = line_connecting(sK0,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_475,plain,
( distinct_lines(iPr_def_10,iPr_def_11)
| ~ distinct_points(sK0,sK2) ),
inference(demodulation,[status(thm)],[c_306,c_474,c_473]) ).
tcf(c_476,plain,
~ distinct_points(sK1,sK2),
inference(demodulation,[status(thm)],[c_301]) ).
tcf(c_477,negated_conjecture,
distinct_points(sK0,sK1),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_934,plain,
! [X0: $i] :
( distinct_points(sK1,X0)
| distinct_points(sK0,X0) ),
inference(superposition,[status(thm)],[c_477,c_52]) ).
tcf(c_943,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK1,X1)
| distinct_points(sK0,X0)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_934,c_52]) ).
tcf(c_944,plain,
distinct_points(sK0,sK2),
inference(superposition,[status(thm)],[c_934,c_476]) ).
tcf(c_948,plain,
distinct_lines(iPr_def_10,iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_475,c_944]) ).
tcf(c_1182,plain,
( ~ apart_point_and_line(sK0,iPr_def_10)
| ~ distinct_points(sK0,sK1) ),
inference(superposition,[status(thm)],[c_473,c_55]) ).
tcf(c_1183,plain,
( ~ apart_point_and_line(sK0,iPr_def_11)
| ~ distinct_points(sK0,sK2) ),
inference(superposition,[status(thm)],[c_474,c_55]) ).
tcf(c_1184,plain,
~ apart_point_and_line(sK0,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_1183,c_944]) ).
tcf(c_1185,plain,
~ apart_point_and_line(sK0,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1182,c_477]) ).
tcf(c_1190,plain,
( ~ apart_point_and_line(sK1,iPr_def_10)
| ~ distinct_points(sK0,sK1) ),
inference(superposition,[status(thm)],[c_473,c_56]) ).
tcf(c_1191,plain,
( ~ apart_point_and_line(sK2,iPr_def_11)
| ~ distinct_points(sK0,sK2) ),
inference(superposition,[status(thm)],[c_474,c_56]) ).
tcf(c_1192,plain,
~ apart_point_and_line(sK2,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_1191,c_944]) ).
tcf(c_1193,plain,
~ apart_point_and_line(sK1,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1190,c_477]) ).
tcf(c_1290,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| ~ distinct_points(sK0,sK1)
| ~ distinct_lines(X0,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1705,plain,
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK0,iPr_def_11)
| apart_point_and_line(sK0,iPr_def_10)
| ~ distinct_lines(iPr_def_10,iPr_def_11)
| ~ distinct_points(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_1290]) ).
tcf(c_3355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_943,c_59]) ).
tcf(c_4322,plain,
! [X0: $i] :
( apart_point_and_line(X0,iPr_def_11)
| distinct_points(sK1,X0)
| ~ apart_point_and_line(sK1,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_4805,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(X1,iPr_def_11)
| apart_point_and_line(X1,iPr_def_10)
| apart_point_and_line(X0,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK1,X1)
| distinct_points(sK0,X0) ),
inference(superposition,[status(thm)],[c_948,c_3355]) ).
tcf(c_6109,plain,
! [X0: $i] :
( apart_point_and_line(sK0,iPr_def_11)
| apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(X0,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK1,X0) ),
inference(superposition,[status(thm)],[c_4805,c_49]) ).
tcf(c_6112,plain,
! [X0: $i] :
( apart_point_and_line(X0,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6109,c_1184,c_1185]) ).
tcf(c_6119,plain,
! [X0: $i] :
( apart_point_and_line(X0,iPr_def_11)
| distinct_points(sK1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_6112,c_88,c_948,c_1185,c_1184,c_1193,c_1705,c_4322]) ).
tcf(c_6128,plain,
apart_point_and_line(sK2,iPr_def_11),
inference(superposition,[status(thm)],[c_6119,c_476]) ).
tcf(c_6129,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6128,c_1192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO204+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Wed Sep 23 11:27:51 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.33
% 0.04/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.04/0.33
% 0.04/0.33 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 0.95/0.96 % SZS status Started for theBenchmark.p
% 0.95/0.96 % SZS status Theorem for theBenchmark.p
% 0.95/0.96
% 0.95/0.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.95/0.96
% 0.95/0.96 % ------ iProver source info
% 0.95/0.96
% 0.95/0.96 % git: date: 2026-07-19 20:42:38 +0200
% 0.95/0.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.95/0.96 % git: non_committed_changes: false
% 0.95/0.96
% 0.95/0.96 % ------ Parsing...
% 0.95/0.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.95/0.96
% 0.95/0.96 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.95/0.96
% 0.95/0.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.95/0.96
% 0.95/0.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.95/0.96 % ------ Proving...
% 0.95/0.96 % ------ Problem Properties
% 0.95/0.96
% 0.95/0.96 %
% 0.95/0.96 % clauses 33
% 0.95/0.96 % conjectures 1
% 0.95/0.96 % EPR 23
% 0.95/0.96 % Horn 17
% 0.95/0.96 % unary 11
% 0.95/0.96 % binary 7
% 0.95/0.96 % lits 81
% 0.95/0.96 % lits eq 2
% 0.95/0.96 % fd_pure 0
% 0.95/0.96 % fd_pseudo 0
% 0.95/0.96 % fd_cond 0
% 0.95/0.96 % fd_pseudo_cond 0
% 0.95/0.96 % AC symbols 0
% 0.95/0.96
% 0.95/0.96 % ------ Schedule dynamic 5 is on
% 0.95/0.96
% 0.95/0.96 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.95/0.96
% 0.95/0.96
% 0.95/0.96 % ------
% 0.95/0.96 % Current options:
% 0.95/0.96 % ------
% 0.95/0.96
% 0.95/0.96
% 0.95/0.96 %
% 0.95/0.96
% 0.95/0.96 % ------ Proving...
% 0.95/0.96 %
% 0.95/0.96
% 0.95/0.96 % SZS status Theorem for theBenchmark.p
% 0.95/0.96
% 0.95/0.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.95/0.96
% 0.95/0.96
%------------------------------------------------------------------------------