%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO082+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 01:19:49 PM UTC 2026
% Result : Theorem 3.47s 1.28s
% Output : CNFRefutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 112 ( 32 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 111 ( 40 ~; 47 |; 16 &)
% ( 3 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 52 !; 8 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X1)
=> incident_c(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',part_of_defn) ).
fof(f16,axiom,
! [X0,X1] :
( ! [X2] :
( incident_c(X2,X0)
<=> incident_c(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',c9) ).
fof(f17,conjecture,
! [X0,X1] :
( ( part_of(X1,X0)
& part_of(X0,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_antisymmetry) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( part_of(X1,X0)
& part_of(X0,X1) )
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1] :
( part_of(X1,X0)
& part_of(X0,X1)
& X0 != X1 ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
? [X0,X1] :
( part_of(X1,X0)
& part_of(X0,X1)
& X0 != X1 ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X2] :
( incident_c(X2,X0)
<~> incident_c(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( ~ incident_c(X2,X1)
| incident_c(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f34,plain,
( part_of(sK1,sK0)
& part_of(sK0,sK1)
& sK0 != sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
fof(f35,plain,
! [X0,X1] :
( ? [X2] :
( ( incident_c(X2,X0)
| incident_c(X2,X1) )
& ( ~ incident_c(X2,X0)
| ~ incident_c(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X0,X1] :
( ( ( incident_c(sK2(X0,X1),X0)
| incident_c(sK2(X0,X1),X1) )
& ( ~ incident_c(sK2(X0,X1),X0)
| ~ incident_c(sK2(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f35]) ).
fof(f42,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,[],[f29]) ).
fof(f43,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,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ( ~ part_of(X1,X0)
| ! [X3] :
( ~ incident_c(X3,X1)
| incident_c(X3,X0) ) )
& ( ( incident_c(sK6(X0,X1),X1)
& ~ incident_c(sK6(X0,X1),X0) )
| part_of(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f43]) ).
fof(f59,plain,
part_of(sK1,sK0),
inference(cnf_transformation,[],[f34]) ).
fof(f60,plain,
part_of(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f61,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f34]) ).
fof(f62,plain,
! [X0,X1] :
( incident_c(sK2(X0,X1),X0)
| incident_c(sK2(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f63,plain,
! [X0,X1] :
( ~ incident_c(sK2(X0,X1),X0)
| ~ incident_c(sK2(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f76,plain,
! [X3,X0,X1] :
( ~ part_of(X1,X0)
| ~ incident_c(X3,X1)
| incident_c(X3,X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_49,negated_conjecture,
sK0 != sK1,
inference(cnf_transformation,[],[f61]) ).
tcf(c_50,negated_conjecture,
part_of(sK0,sK1),
inference(cnf_transformation,[],[f60]) ).
tcf(c_51,negated_conjecture,
part_of(sK1,sK0),
inference(cnf_transformation,[],[f59]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ incident_c(sK2(X0,X1),X1)
| ~ incident_c(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( incident_c(sK2(X0,X1),X1)
| incident_c(sK2(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(X2,X1)
| ~ incident_c(X2,X0)
| ~ part_of(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_972,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_974,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_982,plain,
sK0 = sK0,
inference(instantiation,[status(thm)],[c_972]) ).
tcf(c_1702,plain,
! [X0: $i] :
( incident_c(X0,sK1)
| ~ incident_c(X0,sK0) ),
inference(superposition,[status(thm)],[c_50,c_68]) ).
tcf(c_1703,plain,
! [X0: $i] :
( incident_c(X0,sK0)
| ~ incident_c(X0,sK1) ),
inference(superposition,[status(thm)],[c_51,c_68]) ).
tcf(c_1917,plain,
! [X0: $i] :
( incident_c(sK2(X0,sK0),sK1)
| incident_c(sK2(X0,sK0),X0)
| ( X0 = sK0 ) ),
inference(superposition,[status(thm)],[c_53,c_1702]) ).
tcf(c_1922,plain,
! [X0: $i] :
( incident_c(sK2(sK1,X0),sK0)
| incident_c(sK2(sK1,X0),X0)
| ( X0 = sK1 ) ),
inference(superposition,[status(thm)],[c_53,c_1703]) ).
tcf(c_1953,plain,
( incident_c(sK2(sK1,sK0),sK0)
| ( sK0 = sK1 ) ),
inference(instantiation,[status(thm)],[c_1922]) ).
tcf(c_1957,plain,
! [X0: $i] :
( ( sK0 = sK1 )
| ( sK1 != X0 )
| ( sK0 != X0 ) ),
inference(instantiation,[status(thm)],[c_974]) ).
tcf(c_1958,plain,
( ( sK0 = sK1 )
| ( sK1 != sK0 )
| ( sK0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_1957]) ).
tcf(c_2157,plain,
! [X0: $i] :
( ( sK1 = X0 )
| ~ incident_c(sK2(sK1,X0),sK1)
| ~ incident_c(sK2(sK1,X0),X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_2158,plain,
( ( sK1 = sK0 )
| ~ incident_c(sK2(sK1,sK0),sK1)
| ~ incident_c(sK2(sK1,sK0),sK0) ),
inference(instantiation,[status(thm)],[c_2157]) ).
tcf(c_2304,plain,
( incident_c(sK2(sK1,sK0),sK1)
| ( sK0 = sK1 ) ),
inference(equality_factoring,[status(thm)],[c_1917]) ).
tcf(c_2306,plain,
incident_c(sK2(sK1,sK0),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_2304,c_49]) ).
tcf(c_2322,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2306,c_2158,c_1958,c_1953,c_982,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO082+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Wed Sep 23 10:51:19 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.40 Running first-order theorem proving
% 0.03/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.41
% 0.03/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.41
% 0.03/0.41 % Detected problem language: tptp
% 0.03/0.42 % Proving...
% 3.47/1.28 % SZS status Started for theBenchmark.p
% 3.47/1.28 % SZS status Theorem for theBenchmark.p
% 3.47/1.28
% 3.47/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.47/1.28
% 3.47/1.28 % ------ iProver source info
% 3.47/1.28
% 3.47/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.47/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.47/1.28 % git: non_committed_changes: false
% 3.47/1.28
% 3.47/1.28 % ------ Parsing...
% 3.47/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.47/1.28
% 3.47/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.47/1.28
% 3.47/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.47/1.28
% 3.47/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.47/1.28 % ------ Proving...
% 3.47/1.28 % ------ Problem Properties
% 3.47/1.28
% 3.47/1.28 %
% 3.47/1.28 % clauses 40
% 3.47/1.28 % conjectures 3
% 3.47/1.28 % EPR 15
% 3.47/1.28 % Horn 26
% 3.47/1.28 % unary 4
% 3.47/1.28 % binary 14
% 3.47/1.28 % lits 121
% 3.47/1.28 % lits eq 12
% 3.47/1.28 % fd_pure 0
% 3.47/1.28 % fd_pseudo 0
% 3.47/1.28 % fd_cond 0
% 3.47/1.28 % fd_pseudo_cond 6
% 3.47/1.28 % AC symbols 0
% 3.47/1.28
% 3.47/1.28 % ------ Schedule dynamic 5 is on
% 3.47/1.28
% 3.47/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.47/1.28
% 3.47/1.28
% 3.47/1.28 % ------
% 3.47/1.28 % Current options:
% 3.47/1.28 % ------
% 3.47/1.28
% 3.47/1.28
% 3.47/1.28 %
% 3.47/1.28
% 3.47/1.28 % ------ Proving...
% 3.47/1.28 %
% 3.47/1.28
% 3.47/1.28 % SZS status Theorem for theBenchmark.p
% 3.47/1.28
% 3.47/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.47/1.28
% 3.47/1.28
%------------------------------------------------------------------------------