%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO087+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 01:19:50 PM UTC 2026
% Result : Theorem 3.16s 1.17s
% Output : CNFRefutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 17 unt; 0 def)
% Number of atoms : 186 ( 2 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 216 ( 84 ~; 75 |; 47 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 100 !; 11 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X1)
=> incident_c(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',part_of_defn) ).
fof(f4,axiom,
! [X0,X1] :
( inner_point(X0,X1)
<=> ( ~ end_point(X0,X1)
& incident_c(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',inner_point_defn) ).
fof(f5,axiom,
! [X0,X1,X2] :
( meet(X0,X1,X2)
<=> ( ! [X3] :
( ( incident_c(X3,X2)
& incident_c(X3,X1) )
=> ( end_point(X3,X2)
& end_point(X3,X1) ) )
& incident_c(X0,X2)
& incident_c(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',meet_defn) ).
fof(f10,axiom,
! [X0] :
? [X1] : inner_point(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',c3) ).
fof(f17,conjecture,
! [X0,X1] :
( part_of(X0,X1)
=> ~ ? [X2] : meet(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_9) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( part_of(X0,X1)
=> ~ ? [X2] : meet(X2,X0,X1) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f21,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( ~ incident_c(X2,X1)
| incident_c(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f24,plain,
! [X0,X1,X2] :
( meet(X0,X1,X2)
<=> ( ! [X3] :
( ~ incident_c(X3,X2)
| ~ incident_c(X3,X1)
| ( end_point(X3,X2)
& end_point(X3,X1) ) )
& incident_c(X0,X2)
& incident_c(X0,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f25,plain,
! [X0,X1,X2] :
( meet(X0,X1,X2)
<=> ( ! [X3] :
( ~ incident_c(X3,X2)
| ~ incident_c(X3,X1)
| ( end_point(X3,X2)
& end_point(X3,X1) ) )
& incident_c(X0,X2)
& incident_c(X0,X1) ) ),
inference(flattening,[],[f24]) ).
fof(f40,plain,
? [X0,X1] :
( part_of(X0,X1)
& ? [X2] : meet(X2,X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f41,plain,
! [X0,X1] :
( ( ~ part_of(X1,X0)
| ! [X2] :
( ~ incident_c(X2,X1)
| incident_c(X2,X0) ) )
& ( ? [X2] :
( incident_c(X2,X1)
& ~ incident_c(X2,X0) )
| part_of(X1,X0) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f42,plain,
! [X0,X1] :
( ( ~ part_of(X1,X0)
| ! [X3] :
( ~ incident_c(X3,X1)
| incident_c(X3,X0) ) )
& ( ? [X2] :
( incident_c(X2,X1)
& ~ incident_c(X2,X0) )
| part_of(X1,X0) ) ),
inference(rectify,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ( ~ part_of(X1,X0)
| ! [X3] :
( ~ incident_c(X3,X1)
| incident_c(X3,X0) ) )
& ( ( incident_c(sK0(X0,X1),X1)
& ~ incident_c(sK0(X0,X1),X0) )
| part_of(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f42]) ).
fof(f52,plain,
! [X0,X1] :
( ( ~ inner_point(X0,X1)
| ( ~ end_point(X0,X1)
& incident_c(X0,X1) ) )
& ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| inner_point(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f53,plain,
! [X0,X1] :
( ( ~ inner_point(X0,X1)
| ( ~ end_point(X0,X1)
& incident_c(X0,X1) ) )
& ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| inner_point(X0,X1) ) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( ~ meet(X0,X1,X2)
| ( ! [X3] :
( ~ incident_c(X3,X2)
| ~ incident_c(X3,X1)
| ( end_point(X3,X2)
& end_point(X3,X1) ) )
& incident_c(X0,X2)
& incident_c(X0,X1) ) )
& ( ? [X3] :
( incident_c(X3,X2)
& incident_c(X3,X1)
& ( ~ end_point(X3,X2)
| ~ end_point(X3,X1) ) )
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X1)
| meet(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( ~ meet(X0,X1,X2)
| ( ! [X3] :
( ~ incident_c(X3,X2)
| ~ incident_c(X3,X1)
| ( end_point(X3,X2)
& end_point(X3,X1) ) )
& incident_c(X0,X2)
& incident_c(X0,X1) ) )
& ( ? [X3] :
( incident_c(X3,X2)
& incident_c(X3,X1)
& ( ~ end_point(X3,X2)
| ~ end_point(X3,X1) ) )
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X1)
| meet(X0,X1,X2) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( ~ meet(X0,X1,X2)
| ( ! [X4] :
( ~ incident_c(X4,X2)
| ~ incident_c(X4,X1)
| ( end_point(X4,X2)
& end_point(X4,X1) ) )
& incident_c(X0,X2)
& incident_c(X0,X1) ) )
& ( ? [X3] :
( incident_c(X3,X2)
& incident_c(X3,X1)
& ( ~ end_point(X3,X2)
| ~ end_point(X3,X1) ) )
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X1)
| meet(X0,X1,X2) ) ),
inference(rectify,[],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( ~ meet(X0,X1,X2)
| ( ! [X4] :
( ~ incident_c(X4,X2)
| ~ incident_c(X4,X1)
| ( end_point(X4,X2)
& end_point(X4,X1) ) )
& incident_c(X0,X2)
& incident_c(X0,X1) ) )
& ( ( incident_c(sK4(X1,X2),X2)
& incident_c(sK4(X1,X2),X1)
& ( ~ end_point(sK4(X1,X2),X2)
| ~ end_point(sK4(X1,X2),X1) ) )
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X1)
| meet(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X1,X2))],[f56]) ).
fof(f60,plain,
! [X0] : inner_point(sK7(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f10]) ).
fof(f67,plain,
( part_of(sK13,sK14)
& meet(sK15,sK13,sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15)],[f40]) ).
fof(f68,plain,
! [X3,X0,X1] :
( ~ part_of(X1,X0)
| ~ incident_c(X3,X1)
| incident_c(X3,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f69,plain,
! [X0,X1] :
( incident_c(sK0(X0,X1),X1)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f70,plain,
! [X0,X1] :
( ~ incident_c(sK0(X0,X1),X0)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f85,plain,
! [X0,X1] :
( ~ inner_point(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f86,plain,
! [X0,X1] :
( ~ inner_point(X0,X1)
| incident_c(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f89,plain,
! [X2,X0,X1,X4] :
( ~ meet(X0,X1,X2)
| ~ incident_c(X4,X2)
| ~ incident_c(X4,X1)
| end_point(X4,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f99,plain,
! [X0] : inner_point(sK7(X0),X0),
inference(cnf_transformation,[],[f60]) ).
fof(f109,plain,
part_of(sK13,sK14),
inference(cnf_transformation,[],[f67]) ).
fof(f110,plain,
meet(sK15,sK13,sK14),
inference(cnf_transformation,[],[f67]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( part_of(X1,X0)
| ~ incident_c(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( part_of(X1,X0)
| incident_c(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(X2,X1)
| ~ incident_c(X2,X0)
| ~ part_of(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( incident_c(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ~ inner_point(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( end_point(X3,X1)
| ~ incident_c(X3,X2)
| ~ incident_c(X3,X1)
| ~ meet(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_80,plain,
! [X0: $i] : inner_point(sK7(X0),X0),
inference(cnf_transformation,[],[f99]) ).
tcf(c_90,negated_conjecture,
meet(sK15,sK13,sK14),
inference(cnf_transformation,[],[f110]) ).
tcf(c_91,negated_conjecture,
part_of(sK13,sK14),
inference(cnf_transformation,[],[f109]) ).
tcf(c_723,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ end_point(X1,X2)
| ( X0 != X2 )
| ( sK7(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_80]) ).
tcf(c_724,plain,
! [X0: $i] : ~ end_point(sK7(X0),X0),
inference(unflattening,[status(thm)],[c_723]) ).
tcf(c_725,plain,
~ end_point(sK7(sK13),sK13),
inference(instantiation,[status(thm)],[c_724]) ).
tcf(c_745,negated_conjecture,
part_of(sK13,sK14),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_746,negated_conjecture,
meet(sK15,sK13,sK14),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_1420,plain,
! [X0: $i] : incident_c(sK7(X0),X0),
inference(superposition,[status(thm)],[c_80,c_67]) ).
tcf(c_1484,plain,
! [X0: $i] : part_of(X0,X0),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_1591,plain,
! [X0: $i,X1: $i] :
( incident_c(sK7(X0),X1)
| ~ part_of(X0,X1) ),
inference(superposition,[status(thm)],[c_1420,c_51]) ).
tcf(c_1802,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(sK7(X0),X2)
| ~ part_of(X1,X2)
| ~ part_of(X0,X1) ),
inference(superposition,[status(thm)],[c_1591,c_51]) ).
tcf(c_2127,plain,
! [X0: $i] :
( incident_c(sK7(sK13),X0)
| ~ part_of(sK14,X0) ),
inference(superposition,[status(thm)],[c_745,c_1802]) ).
tcf(c_2276,plain,
! [X0: $i] :
( end_point(X0,sK13)
| ~ incident_c(X0,sK14)
| ~ incident_c(X0,sK13) ),
inference(superposition,[status(thm)],[c_746,c_74]) ).
tcf(c_2307,plain,
( end_point(sK7(sK13),sK13)
| ~ incident_c(sK7(sK13),sK14) ),
inference(superposition,[status(thm)],[c_1420,c_2276]) ).
tcf(c_2395,plain,
~ incident_c(sK7(sK13),sK14),
inference(global_subsumption_just,[status(thm)],[c_2307,c_725,c_2307]) ).
tcf(c_2399,plain,
~ part_of(sK14,sK14),
inference(superposition,[status(thm)],[c_2127,c_2395]) ).
tcf(c_2400,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2399,c_1484]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO087+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 10:51:55 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 3.16/1.17 % SZS status Started for theBenchmark.p
% 3.16/1.17 % SZS status Theorem for theBenchmark.p
% 3.16/1.17
% 3.16/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.16/1.17
% 3.16/1.17 % ------ iProver source info
% 3.16/1.17
% 3.16/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 3.16/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.16/1.17 % git: non_committed_changes: false
% 3.16/1.17
% 3.16/1.17 % ------ Parsing...
% 3.16/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.16/1.17
% 3.16/1.17 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.16/1.17
% 3.16/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.16/1.17
% 3.16/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.16/1.17 % ------ Proving...
% 3.16/1.17 % ------ Problem Properties
% 3.16/1.17
% 3.16/1.17 %
% 3.16/1.17 % clauses 43
% 3.16/1.17 % conjectures 2
% 3.16/1.17 % EPR 15
% 3.16/1.17 % Horn 27
% 3.16/1.17 % unary 3
% 3.16/1.17 % binary 16
% 3.16/1.17 % lits 131
% 3.16/1.17 % lits eq 12
% 3.16/1.17 % fd_pure 0
% 3.16/1.17 % fd_pseudo 0
% 3.16/1.17 % fd_cond 0
% 3.16/1.17 % fd_pseudo_cond 7
% 3.16/1.17 % AC symbols 0
% 3.16/1.17
% 3.16/1.17 % ------ Schedule dynamic 5 is on
% 3.16/1.17
% 3.16/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.16/1.17
% 3.16/1.17
% 3.16/1.17 % ------
% 3.16/1.17 % Current options:
% 3.16/1.17 % ------
% 3.16/1.17
% 3.16/1.17
% 3.16/1.17 %
% 3.16/1.17
% 3.16/1.17 % ------ Proving...
% 3.16/1.17 %
% 3.16/1.17
% 3.16/1.17 % SZS status Theorem for theBenchmark.p
% 3.16/1.17
% 3.16/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.16/1.17
%------------------------------------------------------------------------------