%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO217+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 : n013.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 01:20:24 PM UTC 2026
% Result : Theorem 2.42s 1.25s
% Output : CNFRefutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 17 unt; 0 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 100 ( 40 ~; 45 |; 9 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 85 ( 0 sgn 79 !; 6 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| distinct_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(f33,axiom,
! [X0,X1] :
( parallel_lines(X0,X1)
<=> ~ convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a3) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( parallel_lines(X0,X2)
& parallel_lines(X0,X1) )
=> parallel_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( parallel_lines(X0,X2)
& parallel_lines(X0,X1) )
=> parallel_lines(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(flattening,[],[f40]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f76,plain,
? [X0,X1,X2] :
( parallel_lines(X0,X2)
& parallel_lines(X0,X1)
& ~ parallel_lines(X1,X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2] :
( parallel_lines(X0,X2)
& parallel_lines(X0,X1)
& ~ parallel_lines(X1,X2) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ( ~ parallel_lines(X0,X1)
| ~ convergent_lines(X0,X1) )
& ( convergent_lines(X0,X1)
| parallel_lines(X0,X1) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f79,plain,
( parallel_lines(sK0,sK2)
& parallel_lines(sK0,sK1)
& ~ parallel_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f77]) ).
fof(f81,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f82,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f94,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f116,plain,
! [X0,X1] :
( ~ parallel_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f117,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| parallel_lines(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f118,plain,
parallel_lines(sK0,sK2),
inference(cnf_transformation,[],[f79]) ).
fof(f119,plain,
parallel_lines(sK0,sK1),
inference(cnf_transformation,[],[f79]) ).
fof(f120,plain,
~ parallel_lines(sK1,sK2),
inference(cnf_transformation,[],[f79]) ).
tcf(c_50,plain,
! [X0: $i] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f81]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f82]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( parallel_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( ~ parallel_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_87,negated_conjecture,
~ parallel_lines(sK1,sK2),
inference(cnf_transformation,[],[f120]) ).
tcf(c_88,negated_conjecture,
parallel_lines(sK0,sK1),
inference(cnf_transformation,[],[f119]) ).
tcf(c_89,negated_conjecture,
parallel_lines(sK0,sK2),
inference(cnf_transformation,[],[f118]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( convergent_lines(X0,X1)
| parallel_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_85]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( parallel_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_109]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] :
( ~ parallel_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_63,c_86]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i,X2: $i] :
( parallel_lines(X2,X0)
| convergent_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_62,c_110]) ).
tcf(c_729,plain,
~ distinct_lines(sK0,sK1),
inference(resolution,[status(thm)],[c_113,c_88]) ).
tcf(c_741,plain,
~ distinct_lines(sK0,sK2),
inference(resolution,[status(thm)],[c_113,c_89]) ).
tcf(c_1761,negated_conjecture,
~ parallel_lines(sK1,sK2),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_1782,plain,
~ convergent_lines(sK1,sK1),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_1783,plain,
! [X0: $i] :
( ~ parallel_lines(sK1,X0)
| ~ convergent_lines(sK1,X0) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_1784,plain,
( ~ parallel_lines(sK1,sK0)
| ~ convergent_lines(sK1,sK0) ),
inference(instantiation,[status(thm)],[c_1783]) ).
tcf(c_1790,plain,
! [X0: $i,X1: $i] :
( parallel_lines(sK1,X0)
| convergent_lines(sK1,X1)
| distinct_lines(X0,X1) ),
inference(instantiation,[status(thm)],[c_191]) ).
tcf(c_2035,plain,
! [X0: $i] :
( convergent_lines(sK1,sK1)
| parallel_lines(sK1,X0)
| distinct_lines(X0,sK1) ),
inference(instantiation,[status(thm)],[c_1790]) ).
tcf(c_2036,plain,
( parallel_lines(sK1,sK0)
| convergent_lines(sK1,sK1)
| distinct_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_2035]) ).
tcf(c_2095,plain,
! [X0: $i] :
( convergent_lines(sK1,X0)
| distinct_lines(sK2,X0) ),
inference(superposition,[status(thm)],[c_191,c_1761]) ).
tcf(c_2282,plain,
! [X0: $i,X1: $i] :
( convergent_lines(sK1,X0)
| distinct_lines(sK2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2095,c_53]) ).
tcf(c_2421,plain,
! [X0: $i] :
( convergent_lines(sK1,X0)
| distinct_lines(X0,sK2) ),
inference(superposition,[status(thm)],[c_2282,c_50]) ).
tcf(c_2445,plain,
( convergent_lines(sK1,sK0)
| distinct_lines(sK0,sK2) ),
inference(instantiation,[status(thm)],[c_2421]) ).
tcf(c_2446,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2445,c_2036,c_1784,c_1782,c_741,c_729]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO217+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Wed Sep 23 11:31:42 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.39 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 2.42/1.25 % SZS status Started for theBenchmark.p
% 2.42/1.25 % SZS status Theorem for theBenchmark.p
% 2.42/1.25
% 2.42/1.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.42/1.25
% 2.42/1.25 % ------ iProver source info
% 2.42/1.25
% 2.42/1.25 % git: date: 2026-07-19 20:42:38 +0200
% 2.42/1.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.42/1.25 % git: non_committed_changes: false
% 2.42/1.25
% 2.42/1.25 % ------ Parsing...
% 2.42/1.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.42/1.25
% 2.42/1.25 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe_e sf_s rm: 11 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.42/1.25
% 2.42/1.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.42/1.25 % ------ Proving...
% 2.42/1.25 % ------ Problem Properties
% 2.42/1.25
% 2.42/1.25 %
% 2.42/1.25 % clauses 22
% 2.42/1.25 % conjectures 3
% 2.42/1.25 % EPR 20
% 2.42/1.25 % Horn 10
% 2.42/1.25 % unary 7
% 2.42/1.25 % binary 4
% 2.42/1.25 % lits 52
% 2.42/1.25 % lits eq 0
% 2.42/1.25 % fd_pure 0
% 2.42/1.25 % fd_pseudo 0
% 2.42/1.25 % fd_cond 0
% 2.42/1.25 % fd_pseudo_cond 0
% 2.42/1.25 % AC symbols 0
% 2.42/1.25
% 2.42/1.25 % ------ Schedule dynamic 5 is on
% 2.42/1.25
% 2.42/1.25 % ------ no equalities: superposition off
% 2.42/1.25
% 2.42/1.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.42/1.25
% 2.42/1.25
% 2.42/1.25 % ------
% 2.42/1.25 % Current options:
% 2.42/1.25 % ------
% 2.42/1.25
% 2.42/1.25
% 2.42/1.25 %
% 2.42/1.25
% 2.42/1.25 % ------ Proving...
% 2.42/1.25 %
% 2.42/1.25
% 2.42/1.25 % SZS status Theorem for theBenchmark.p
% 2.42/1.25
% 2.42/1.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.42/1.25
% 2.42/1.25
%------------------------------------------------------------------------------