%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG089+1 : TPTP v9.3.1. Released v4.0.0.
% 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 02:38:48 PM UTC 2026
% Result : Theorem 2.80s 1.19s
% Output : CNFRefutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 91 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 93 ( 35 ~; 31 |; 15 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f25,axiom,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(f26,axiom,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElementOf0(xx,sdtpldt1(xI,xJ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
fof(f27,axiom,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).
fof(f30,conjecture,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f31,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f36,plain,
! [X0] :
( aIdeal0(X0)
=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f37,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(ennf_transformation,[],[f31]) ).
fof(f38,plain,
! [X0] :
( ~ aIdeal0(X0)
| ( ! [X1] :
( ~ aElementOf0(X1,X0)
| ( ! [X3] :
( ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f68,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f25]) ).
fof(f69,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f25]) ).
fof(f70,plain,
aElement0(xz),
inference(cnf_transformation,[],[f26]) ).
fof(f74,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f27]) ).
fof(f75,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f27]) ).
fof(f81,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(cnf_transformation,[],[f37]) ).
fof(f82,plain,
! [X3,X0,X1] :
( ~ aIdeal0(X0)
| ~ aElementOf0(X1,X0)
| ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X1),X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_49,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f69]) ).
tcf(c_50,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_53,plain,
aElement0(xz),
inference(cnf_transformation,[],[f70]) ).
tcf(c_54,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f75]) ).
tcf(c_55,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_62,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtasdt0(X2,X0),X1)
| ~ aElement0(X2)
| ~ aIdeal0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_608,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2)
| ~ aElementOf0(X1,X0)
| ( X0 != xI ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_65]) ).
tcf(c_609,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X1,X0),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xI) ),
inference(unflattening,[status(thm)],[c_608]) ).
tcf(c_637,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2)
| ~ aElementOf0(X1,X0)
| ( X0 != xJ ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_65]) ).
tcf(c_638,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xJ) ),
inference(unflattening,[status(thm)],[c_637]) ).
tcf(c_2184,plain,
! [X0: $i] :
( aElementOf0(sdtasdt0(xz,X0),xI)
| ~ aElement0(xz)
| ~ aElementOf0(X0,xI) ),
inference(instantiation,[status(thm)],[c_609]) ).
tcf(c_2252,plain,
! [X0: $i] :
( aElementOf0(sdtasdt0(xz,X0),xJ)
| ~ aElement0(xz)
| ~ aElementOf0(X0,xJ) ),
inference(instantiation,[status(thm)],[c_638]) ).
tcf(c_3838,plain,
( aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElement0(xz)
| ~ aElementOf0(xk,xI) ),
inference(instantiation,[status(thm)],[c_2184]) ).
tcf(c_3925,plain,
( aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElement0(xz)
| ~ aElementOf0(xl,xJ) ),
inference(instantiation,[status(thm)],[c_2252]) ).
tcf(c_3926,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3925,c_3838,c_62,c_54,c_55,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG089+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 08:15:37 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 2.80/1.19 % SZS status Started for theBenchmark.p
% 2.80/1.19 % SZS status Theorem for theBenchmark.p
% 2.80/1.19
% 2.80/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.80/1.19
% 2.80/1.19 % ------ iProver source info
% 2.80/1.19
% 2.80/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 2.80/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.80/1.19 % git: non_committed_changes: false
% 2.80/1.19
% 2.80/1.19 % ------ Parsing...
% 2.80/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.80/1.19
% 2.80/1.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 2.80/1.19
% 2.80/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.80/1.19
% 2.80/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.80/1.19 % ------ Proving...
% 2.80/1.19 % ------ Problem Properties
% 2.80/1.19
% 2.80/1.19 %
% 2.80/1.19 % clauses 42
% 2.80/1.19 % conjectures 1
% 2.80/1.19 % EPR 9
% 2.80/1.19 % Horn 36
% 2.80/1.19 % unary 13
% 2.80/1.19 % binary 2
% 2.80/1.19 % lits 118
% 2.80/1.19 % lits eq 16
% 2.80/1.19 % fd_pure 0
% 2.80/1.19 % fd_pseudo 0
% 2.80/1.19 % fd_cond 0
% 2.80/1.19 % fd_pseudo_cond 5
% 2.80/1.19 % AC symbols 0
% 2.80/1.19
% 2.80/1.19 % ------ Schedule dynamic 5 is on
% 2.80/1.19
% 2.80/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.80/1.19
% 2.80/1.19
% 2.80/1.19 % ------
% 2.80/1.19 % Current options:
% 2.80/1.19 % ------
% 2.80/1.19
% 2.80/1.19
% 2.80/1.19 %
% 2.80/1.19
% 2.80/1.19 % ------ Proving...
% 2.80/1.19 %
% 2.80/1.19
% 2.80/1.19 % SZS status Theorem for theBenchmark.p
% 2.80/1.19
% 2.80/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.80/1.19
% 2.80/1.19
%------------------------------------------------------------------------------