%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO093+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 : n019.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 01:19:52 PM UTC 2026
% Result : Theorem 3.48s 6.11s
% Output : CNFRefutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 59 ( 14 unt; 0 def)
% Number of atoms : 198 ( 21 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 211 ( 72 ~; 86 |; 45 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 132 ( 0 sgn 119 !; 13 ?; 40 :)
% 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(f2,axiom,
! [X0,X1,X2] :
( X0 = sum(X1,X2)
<=> ! [X3] :
( incident_c(X3,X0)
<=> ( incident_c(X3,X2)
| incident_c(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',sum_defn) ).
fof(f8,axiom,
! [X0,X1] :
( ( X1 != X0
& part_of(X1,X0) )
=> open(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',c1) ).
fof(f17,conjecture,
! [X0,X1,X2,X3] :
( ( meet(X3,X1,X2)
& part_of(X2,X0)
& part_of(X1,X0)
& open(X0) )
=> open(sum(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proposition_2_14_2) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( meet(X3,X1,X2)
& part_of(X2,X0)
& part_of(X1,X0)
& open(X0) )
=> open(sum(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1,X2,X3] :
( meet(X3,X1,X2)
& part_of(X2,X0)
& part_of(X1,X0)
& open(X0)
& ~ open(sum(X1,X2)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
? [X0,X1,X2,X3] :
( meet(X3,X1,X2)
& part_of(X2,X0)
& part_of(X1,X0)
& open(X0)
& ~ open(sum(X1,X2)) ),
inference(flattening,[],[f19]) ).
fof(f26,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( ~ incident_c(X2,X1)
| incident_c(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f29,plain,
! [X0,X1] :
( X0 = X1
| ~ part_of(X1,X0)
| open(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f30,plain,
! [X0,X1] :
( X0 = X1
| ~ part_of(X1,X0)
| open(X1) ),
inference(flattening,[],[f29]) ).
fof(f35,plain,
( meet(sK3,sK1,sK2)
& part_of(sK2,sK0)
& part_of(sK1,sK0)
& open(sK0)
& ~ open(sum(sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f20]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) != X0
| ! [X3] :
( ( ~ incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| incident_c(X3,X0) ) ) )
& ( ? [X3] :
( ( incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ~ incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) ) )
| X0 = sum(X1,X2) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) != X0
| ! [X3] :
( ( ~ incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| incident_c(X3,X0) ) ) )
& ( ? [X3] :
( ( incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ~ incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) ) )
| X0 = sum(X1,X2) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) != X0
| ! [X4] :
( ( ~ incident_c(X4,X0)
| incident_c(X4,X2)
| incident_c(X4,X1) )
& ( ( ~ incident_c(X4,X2)
& ~ incident_c(X4,X1) )
| incident_c(X4,X0) ) ) )
& ( ? [X3] :
( ( incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ~ incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) ) )
| X0 = sum(X1,X2) ) ),
inference(rectify,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) != X0
| ! [X4] :
( ( ~ incident_c(X4,X0)
| incident_c(X4,X2)
| incident_c(X4,X1) )
& ( ( ~ incident_c(X4,X2)
& ~ incident_c(X4,X1) )
| incident_c(X4,X0) ) ) )
& ( ( ( incident_c(sK5(X0,X1,X2),X0)
| incident_c(sK5(X0,X1,X2),X2)
| incident_c(sK5(X0,X1,X2),X1) )
& ( ~ incident_c(sK5(X0,X1,X2),X0)
| ( ~ incident_c(sK5(X0,X1,X2),X2)
& ~ incident_c(sK5(X0,X1,X2),X1) ) ) )
| X0 = sum(X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f40]) ).
fof(f46,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,[],[f26]) ).
fof(f47,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,[],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ( ~ part_of(X1,X0)
| ! [X3] :
( ~ incident_c(X3,X1)
| incident_c(X3,X0) ) )
& ( ( incident_c(sK8(X0,X1),X1)
& ~ incident_c(sK8(X0,X1),X0) )
| part_of(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f47]) ).
fof(f60,plain,
part_of(sK2,sK0),
inference(cnf_transformation,[],[f35]) ).
fof(f61,plain,
part_of(sK1,sK0),
inference(cnf_transformation,[],[f35]) ).
fof(f62,plain,
open(sK0),
inference(cnf_transformation,[],[f35]) ).
fof(f63,plain,
~ open(sum(sK1,sK2)),
inference(cnf_transformation,[],[f35]) ).
fof(f65,plain,
! [X2,X0,X1,X4] :
( sum(X1,X2) != X0
| ~ incident_c(X4,X0)
| incident_c(X4,X2)
| incident_c(X4,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f66,plain,
! [X2,X0,X1,X4] :
( sum(X1,X2) != X0
| ~ incident_c(X4,X2)
| incident_c(X4,X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f67,plain,
! [X2,X0,X1,X4] :
( sum(X1,X2) != X0
| ~ incident_c(X4,X1)
| incident_c(X4,X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f80,plain,
! [X3,X0,X1] :
( ~ part_of(X1,X0)
| ~ incident_c(X3,X1)
| incident_c(X3,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f81,plain,
! [X0,X1] :
( incident_c(sK8(X0,X1),X1)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f82,plain,
! [X0,X1] :
( ~ incident_c(sK8(X0,X1),X0)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f90,plain,
! [X0,X1] :
( X0 = X1
| ~ part_of(X1,X0)
| open(X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f98,plain,
! [X2,X1,X4] :
( ~ incident_c(X4,X1)
| incident_c(X4,sum(X1,X2)) ),
inference(equality_resolution,[],[f67]) ).
fof(f99,plain,
! [X2,X1,X4] :
( ~ incident_c(X4,X2)
| incident_c(X4,sum(X1,X2)) ),
inference(equality_resolution,[],[f66]) ).
fof(f100,plain,
! [X2,X1,X4] :
( ~ incident_c(X4,sum(X1,X2))
| incident_c(X4,X2)
| incident_c(X4,X1) ),
inference(equality_resolution,[],[f65]) ).
tcf(c_49,negated_conjecture,
~ open(sum(sK1,sK2)),
inference(cnf_transformation,[],[f63]) ).
tcf(c_50,negated_conjecture,
open(sK0),
inference(cnf_transformation,[],[f62]) ).
tcf(c_51,negated_conjecture,
part_of(sK1,sK0),
inference(cnf_transformation,[],[f61]) ).
tcf(c_52,negated_conjecture,
part_of(sK2,sK0),
inference(cnf_transformation,[],[f60]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(X0,sum(X1,X2))
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(X0,sum(X2,X1))
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(X0,X2)
| incident_c(X0,X1)
| ~ incident_c(X0,sum(X1,X2)) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( part_of(X1,X0)
| ~ incident_c(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( part_of(X1,X0)
| incident_c(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(X2,X1)
| ~ incident_c(X2,X0)
| ~ part_of(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( open(X0)
| ( X0 = X1 )
| ~ part_of(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_1593,plain,
! [X0: $i,X1: $i,X2: $i] :
( part_of(X2,sum(X0,X1))
| ~ incident_c(sK8(sum(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_58,c_70]) ).
tcf(c_1655,plain,
! [X0: $i] :
( incident_c(X0,sK0)
| ~ incident_c(X0,sK1) ),
inference(superposition,[status(thm)],[c_51,c_72]) ).
tcf(c_1656,plain,
! [X0: $i] :
( incident_c(X0,sK0)
| ~ incident_c(X0,sK2) ),
inference(superposition,[status(thm)],[c_52,c_72]) ).
tcf(c_3085,plain,
! [X0: $i,X1: $i] : part_of(X0,sum(X0,X1)),
inference(superposition,[status(thm)],[c_71,c_1593]) ).
tcf(c_3100,plain,
! [X0: $i,X1: $i] :
( open(X0)
| ( sum(X0,X1) = X0 ) ),
inference(superposition,[status(thm)],[c_3085,c_80]) ).
tcf(c_3164,plain,
! [X0: $i] : sum(sum(sK1,sK2),X0) = sum(sK1,sK2),
inference(superposition,[status(thm)],[c_3100,c_49]) ).
tcf(c_3315,plain,
! [X0: $i,X1: $i] :
( incident_c(X0,sum(sK1,sK2))
| ~ incident_c(X0,X1) ),
inference(superposition,[status(thm)],[c_3164,c_59]) ).
tcf(c_3833,plain,
! [X0: $i,X1: $i] :
( part_of(X1,X0)
| incident_c(sK8(X0,X1),sum(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_71,c_3315]) ).
tcf(c_4156,plain,
! [X0: $i,X1: $i] :
( part_of(X1,X0)
| incident_c(sK8(X0,X1),sK2)
| incident_c(sK8(X0,X1),sK1) ),
inference(superposition,[status(thm)],[c_3833,c_60]) ).
tcf(c_6432,plain,
! [X0: $i,X1: $i] :
( part_of(X1,X0)
| incident_c(sK8(X0,X1),sK0)
| incident_c(sK8(X0,X1),sK1) ),
inference(superposition,[status(thm)],[c_4156,c_1656]) ).
tcf(c_6569,plain,
! [X0: $i,X1: $i] :
( part_of(X1,X0)
| incident_c(sK8(X0,X1),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6432,c_1655]) ).
tcf(c_6579,plain,
! [X0: $i] : part_of(X0,sK0),
inference(superposition,[status(thm)],[c_6569,c_70]) ).
tcf(c_7520,plain,
! [X0: $i] :
( open(X0)
| ( X0 = sK0 ) ),
inference(superposition,[status(thm)],[c_6579,c_80]) ).
tcf(c_7537,plain,
sum(sK1,sK2) = sK0,
inference(superposition,[status(thm)],[c_7520,c_49]) ).
tcf(c_7558,plain,
~ open(sK0),
inference(demodulation,[status(thm)],[c_49,c_7537]) ).
tcf(c_7559,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7558,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO093+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/5.38 % Computer : n019.cluster.edu
% 0.08/5.38 % Model : x86_64 x86_64
% 0.08/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.38 % Memory : 8046.5625MB
% 0.08/5.38 % OS : Linux 6.8.0-71-generic
% 0.08/5.38 % CPULimit : 300
% 0.08/5.38 % WCLimit : 300
% 0.08/5.38 % DateTime : Wed Sep 23 10:49:56 UTC 2026
% 0.08/5.38 % CPUTime :
% 0.08/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 3.48/6.11 % SZS status Started for theBenchmark.p
% 3.48/6.11 % SZS status Theorem for theBenchmark.p
% 3.48/6.11
% 3.48/6.11 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.48/6.11
% 3.48/6.11 % ------ iProver source info
% 3.48/6.11
% 3.48/6.11 % git: date: 2026-07-19 20:42:38 +0200
% 3.48/6.11 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.48/6.11 % git: non_committed_changes: false
% 3.48/6.11
% 3.48/6.11 % ------ Parsing...
% 3.48/6.11 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.48/6.11
% 3.48/6.11 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.48/6.11
% 3.48/6.11 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.48/6.11
% 3.48/6.11 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.48/6.11 % ------ Proving...
% 3.48/6.11 % ------ Problem Properties
% 3.48/6.11
% 3.48/6.11 %
% 3.48/6.11 % clauses 39
% 3.48/6.11 % conjectures 5
% 3.48/6.11 % EPR 15
% 3.48/6.11 % Horn 25
% 3.48/6.11 % unary 5
% 3.48/6.11 % binary 12
% 3.48/6.11 % lits 118
% 3.48/6.11 % lits eq 11
% 3.48/6.11 % fd_pure 0
% 3.48/6.11 % fd_pseudo 0
% 3.48/6.11 % fd_cond 0
% 3.48/6.11 % fd_pseudo_cond 7
% 3.48/6.11 % AC symbols 0
% 3.48/6.11
% 3.48/6.11 % ------ Schedule dynamic 5 is on
% 3.48/6.11
% 3.48/6.11 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.48/6.11
% 3.48/6.11
% 3.48/6.11 % ------
% 3.48/6.11 % Current options:
% 3.48/6.11 % ------
% 3.48/6.11
% 3.48/6.11
% 3.48/6.11 %
% 3.48/6.11
% 3.48/6.11 % ------ Proving...
% 3.48/6.11 %
% 3.48/6.11
% 3.48/6.11 % SZS status Theorem for theBenchmark.p
% 3.48/6.11
% 3.48/6.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.48/6.11
% 3.48/6.11
%------------------------------------------------------------------------------