%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG089+2 : 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 : n008.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 3.72s 11.34s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 11 unt; 2 def)
% Number of atoms : 121 ( 9 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 110 ( 27 ~; 22 |; 49 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 26 !; 8 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
( aIdeal0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) )
& ! [X1] :
( aElementOf0(X1,xJ)
=> aElementOf0(sdtpldt0(X0,X1),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
fof(f26,axiom,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xy
& aElementOf0(X1,xJ)
& aElementOf0(X0,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xx
& aElementOf0(X1,xJ)
& aElementOf0(X0,xI) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__901) ).
fof(f27,axiom,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__934) ).
fof(f30,conjecture,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
file('/export/starexec/sandbox/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(f36,plain,
( aIdeal0(xJ)
& ! [X3] :
( aElementOf0(X3,xJ)
=> ( ! [X5] :
( aElement0(X5)
=> aElementOf0(sdtasdt0(X5,X3),xJ) )
& ! [X4] :
( aElementOf0(X4,xJ)
=> aElementOf0(sdtpldt0(X3,X4),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
inference(rectify,[],[f25]) ).
fof(f37,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [X2,X3] :
( xy = sdtpldt0(X2,X3)
& aElementOf0(X3,xJ)
& aElementOf0(X2,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xx
& aElementOf0(X1,xJ)
& aElementOf0(X0,xI) ) ),
inference(rectify,[],[f26]) ).
fof(f69,plain,
( aIdeal0(xJ)
& ! [X3] :
( ~ aElementOf0(X3,xJ)
| ( ! [X5] :
( ~ aElement0(X5)
| aElementOf0(sdtasdt0(X5,X3),xJ) )
& ! [X4] :
( ~ aElementOf0(X4,xJ)
| aElementOf0(sdtpldt0(X3,X4),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X0] :
( ~ aElementOf0(X0,xI)
| ( ! [X2] :
( ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X0),xI) )
& ! [X1] :
( ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
inference(ennf_transformation,[],[f36]) ).
fof(f70,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(ennf_transformation,[],[f31]) ).
fof(f85,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& xy = sdtpldt0(sK12,sK13)
& aElementOf0(sK13,xJ)
& aElementOf0(sK12,xI)
& aElementOf0(xx,sdtpldt1(xI,xJ))
& xx = sdtpldt0(sK10,sK11)
& aElementOf0(sK11,xJ)
& aElementOf0(sK10,xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13)],[f37]) ).
fof(f137,plain,
! [X3,X5] :
( ~ aElementOf0(X3,xJ)
| ~ aElement0(X5)
| aElementOf0(sdtasdt0(X5,X3),xJ) ),
inference(cnf_transformation,[],[f69]) ).
fof(f141,plain,
! [X2,X0] :
( ~ aElementOf0(X0,xI)
| ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X0),xI) ),
inference(cnf_transformation,[],[f69]) ).
fof(f144,plain,
aElement0(xz),
inference(cnf_transformation,[],[f85]) ).
fof(f154,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f27]) ).
fof(f155,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f27]) ).
fof(f161,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X1,X0),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xJ) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_115,plain,
aElement0(xz),
inference(cnf_transformation,[],[f144]) ).
tcf(c_116,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f155]) ).
tcf(c_117,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_124,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_2951,definition,
iPr_def_10 = sdtasdt0(xz,xk),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2952,definition,
iPr_def_11 = sdtasdt0(xz,xl),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2953,negated_conjecture,
( ~ aElementOf0(iPr_def_11,xJ)
| ~ aElementOf0(iPr_def_10,xI) ),
inference(demodulation,[status(thm)],[c_124,c_2952,c_2951]) ).
tcf(c_4450,plain,
( aElementOf0(iPr_def_10,xI)
| ~ aElement0(xz)
| ~ aElementOf0(xk,xI) ),
inference(superposition,[status(thm)],[c_2951,c_101]) ).
tcf(c_4483,plain,
aElementOf0(iPr_def_10,xI),
inference(forward_subsumption_resolution,[status(thm)],[c_4450,c_115,c_116]) ).
tcf(c_4497,plain,
( aElementOf0(iPr_def_11,xJ)
| ~ aElement0(xz)
| ~ aElementOf0(xl,xJ) ),
inference(superposition,[status(thm)],[c_2952,c_105]) ).
tcf(c_4523,plain,
aElementOf0(iPr_def_11,xJ),
inference(forward_subsumption_resolution,[status(thm)],[c_4497,c_115,c_117]) ).
tcf(c_4531,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4523,c_4483,c_2953]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG089+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/10.38 % Computer : n008.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Thu Sep 24 08:10:36 UTC 2026
% 0.09/10.39 % CPUTime :
% 0.09/10.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/10.45 Running first-order theorem proving
% 0.14/10.45 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
% 0.14/10.47
% 0.14/10.47 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.47
% 0.14/10.47 % Detected problem language: tptp
% 0.14/10.49 % Proving...
% 3.72/11.34 % SZS status Started for theBenchmark.p
% 3.72/11.34 % SZS status Theorem for theBenchmark.p
% 3.72/11.34
% 3.72/11.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.72/11.34
% 3.72/11.34 % ------ iProver source info
% 3.72/11.34
% 3.72/11.34 % git: date: 2026-07-19 20:42:38 +0200
% 3.72/11.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.72/11.34 % git: non_committed_changes: false
% 3.72/11.34
% 3.72/11.34 % ------ Parsing...
% 3.72/11.34 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.72/11.34
% 3.72/11.34 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.72/11.34
% 3.72/11.34 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.72/11.34
% 3.72/11.34 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.72/11.34 % ------ Proving...
% 3.72/11.34 % ------ Problem Properties
% 3.72/11.34
% 3.72/11.34 %
% 3.72/11.34 % clauses 72
% 3.72/11.34 % conjectures 1
% 3.72/11.34 % EPR 17
% 3.72/11.34 % Horn 63
% 3.72/11.34 % unary 24
% 3.72/11.34 % binary 13
% 3.72/11.34 % lits 191
% 3.72/11.34 % lits eq 37
% 3.72/11.34 % fd_pure 0
% 3.72/11.34 % fd_pseudo 0
% 3.72/11.34 % fd_cond 1
% 3.72/11.34 % fd_pseudo_cond 8
% 3.72/11.34 % AC symbols 0
% 3.72/11.34
% 3.72/11.34 % ------ Schedule dynamic 5 is on
% 3.72/11.34
% 3.72/11.34 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.72/11.34
% 3.72/11.34
% 3.72/11.34 % ------
% 3.72/11.34 % Current options:
% 3.72/11.34 % ------
% 3.72/11.34
% 3.72/11.34
% 3.72/11.34 %
% 3.72/11.34
% 3.72/11.34 % ------ Proving...
% 3.72/11.34 %
% 3.72/11.34
% 3.72/11.34 % SZS status Theorem for theBenchmark.p
% 3.72/11.34
% 3.72/11.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.72/11.34
% 3.72/11.34
%------------------------------------------------------------------------------