%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG088+1 : 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 : n015.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 1.97s 1.48s
% Output : CNFRefutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 17 unt; 2 def)
% Number of atoms : 101 ( 6 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 89 ( 34 ~; 28 |; 15 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?; 13 :)
% 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/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f25,axiom,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
fof(f27,axiom,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__934) ).
fof(f28,axiom,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__967) ).
fof(f29,conjecture,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f30,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f34,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(f35,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,[],[f34]) ).
fof(f65,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,[],[f35]) ).
fof(f66,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(ennf_transformation,[],[f30]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ aIdeal0(X0)
| ~ aElementOf0(X1,X0)
| ~ aElementOf0(X2,X0)
| aElementOf0(sdtpldt0(X1,X2),X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f131,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f25]) ).
fof(f132,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f25]) ).
fof(f137,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f27]) ).
fof(f138,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f27]) ).
fof(f140,plain,
aElementOf0(xn,xJ),
inference(cnf_transformation,[],[f28]) ).
fof(f141,plain,
aElementOf0(xm,xI),
inference(cnf_transformation,[],[f28]) ).
fof(f142,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtpldt0(X0,X2),X1)
| ~ aIdeal0(X1)
| ~ aElementOf0(X2,X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_99,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f132]) ).
tcf(c_100,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_104,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f138]) ).
tcf(c_105,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_107,plain,
aElementOf0(xm,xI),
inference(cnf_transformation,[],[f141]) ).
tcf(c_108,plain,
aElementOf0(xn,xJ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_110,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_911,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0)
| ~ aElementOf0(X1,X0)
| ( X0 != xI ) ),
inference(resolution_lifted,[status(thm)],[c_97,c_99]) ).
tcf(c_912,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI) ),
inference(unflattening,[status(thm)],[c_911]) ).
tcf(c_935,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0)
| ~ aElementOf0(X1,X0)
| ( X0 != xJ ) ),
inference(resolution_lifted,[status(thm)],[c_97,c_100]) ).
tcf(c_936,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtpldt0(X0,X1),xJ)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xJ) ),
inference(unflattening,[status(thm)],[c_935]) ).
tcf(c_1598,definition,
iPr_def_10 = sdtpldt0(xk,xm),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1599,definition,
iPr_def_11 = sdtpldt0(xl,xn),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1600,negated_conjecture,
( ~ aElementOf0(iPr_def_11,xJ)
| ~ aElementOf0(iPr_def_10,xI) ),
inference(demodulation,[status(thm)],[c_110,c_1599,c_1598]) ).
tcf(c_2484,plain,
( aElementOf0(iPr_def_10,xI)
| ~ aElementOf0(xm,xI)
| ~ aElementOf0(xk,xI) ),
inference(superposition,[status(thm)],[c_1598,c_912]) ).
tcf(c_2485,plain,
aElementOf0(iPr_def_10,xI),
inference(forward_subsumption_resolution,[status(thm)],[c_2484,c_107,c_104]) ).
tcf(c_2486,plain,
~ aElementOf0(iPr_def_11,xJ),
inference(backward_subsumption_resolution,[status(thm)],[c_1600,c_2485]) ).
tcf(c_2523,plain,
( aElementOf0(iPr_def_11,xJ)
| ~ aElementOf0(xn,xJ)
| ~ aElementOf0(xl,xJ) ),
inference(superposition,[status(thm)],[c_1599,c_936]) ).
tcf(c_2524,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2523,c_2486,c_108,c_105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG088+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.57 % Computer : n015.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Thu Sep 24 08:12:56 UTC 2026
% 0.11/0.57 % CPUTime :
% 0.11/0.57 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.60 Running first-order theorem proving
% 0.11/0.60 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
% 0.11/0.62
% 0.11/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.62
% 0.11/0.62 % Detected problem language: tptp
% 0.14/0.63 % Proving...
% 1.97/1.48 % SZS status Started for theBenchmark.p
% 1.97/1.48 % SZS status Theorem for theBenchmark.p
% 1.97/1.48
% 1.97/1.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.97/1.48
% 1.97/1.48 % ------ iProver source info
% 1.97/1.48
% 1.97/1.48 % git: date: 2026-07-19 20:42:38 +0200
% 1.97/1.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.97/1.48 % git: non_committed_changes: false
% 1.97/1.48
% 1.97/1.48 % ------ Parsing...
% 1.97/1.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.97/1.48
% 1.97/1.48 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 1.97/1.48
% 1.97/1.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.97/1.48
% 1.97/1.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.97/1.48 % ------ Proving...
% 1.97/1.48 % ------ Problem Properties
% 1.97/1.48
% 1.97/1.48 %
% 1.97/1.48 % clauses 64
% 1.97/1.48 % conjectures 1
% 1.97/1.48 % EPR 13
% 1.97/1.48 % Horn 55
% 1.97/1.48 % unary 16
% 1.97/1.48 % binary 13
% 1.97/1.48 % lits 183
% 1.97/1.48 % lits eq 35
% 1.97/1.48 % fd_pure 0
% 1.97/1.48 % fd_pseudo 0
% 1.97/1.48 % fd_cond 1
% 1.97/1.48 % fd_pseudo_cond 8
% 1.97/1.48 % AC symbols 0
% 1.97/1.48
% 1.97/1.48 % ------ Schedule dynamic 5 is on
% 1.97/1.48
% 1.97/1.48 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.97/1.48
% 1.97/1.48
% 1.97/1.48 % ------
% 1.97/1.48 % Current options:
% 1.97/1.48 % ------
% 1.97/1.48
% 1.97/1.48
% 1.97/1.48 %
% 1.97/1.48
% 1.97/1.48 % ------ Proving...
% 1.97/1.48 %
% 1.97/1.48
% 1.97/1.48 % SZS status Theorem for theBenchmark.p
% 1.97/1.48
% 1.97/1.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.97/1.48
% 1.97/1.48
%------------------------------------------------------------------------------