%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG099+2 : 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 : n012.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 02:38:56 PM UTC 2026
% Result : Theorem 1.84s 0.98s
% Output : CNFRefutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 30 unt; 2 def)
% Number of atoms : 166 ( 6 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 155 ( 58 ~; 49 |; 32 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 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 : 9 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 50 !; 2 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f28,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/sandbox2/benchmark/theBenchmark.p',m__1205) ).
fof(f30,axiom,
( aElement0(xy)
& aElement0(xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1217) ).
fof(f31,axiom,
( sdtpldt0(xa,xb) = sz10
& aElementOf0(xb,xJ)
& aElementOf0(xa,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1294) ).
fof(f32,axiom,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1319) ).
fof(f33,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1332) ).
fof(f34,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1409) ).
fof(f35,conjecture,
? [X0] :
( ( sdteqdtlpzmzozddtrp0(X0,xy,xJ)
| aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ) )
& ( sdteqdtlpzmzozddtrp0(X0,xx,xI)
| aElementOf0(sdtpldt0(X0,smndt0(xx)),xI) )
& aElement0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f36,negated_conjecture,
~ ? [X0] :
( ( sdteqdtlpzmzozddtrp0(X0,xy,xJ)
| aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ) )
& ( sdteqdtlpzmzozddtrp0(X0,xx,xI)
| aElementOf0(sdtpldt0(X0,smndt0(xx)),xI) )
& aElement0(X0) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f41,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,[],[f28]) ).
fof(f43,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f44,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f46,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f45]) ).
fof(f64,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f78,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,[],[f41]) ).
fof(f80,plain,
! [X0] :
( ( ~ sdteqdtlpzmzozddtrp0(X0,xy,xJ)
& ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ) )
| ( ~ sdteqdtlpzmzozddtrp0(X0,xx,xI)
& ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f104,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f105,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f124,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f163,plain,
aSet0(xJ),
inference(cnf_transformation,[],[f78]) ).
fof(f167,plain,
aSet0(xI),
inference(cnf_transformation,[],[f78]) ).
fof(f172,plain,
aElement0(xy),
inference(cnf_transformation,[],[f30]) ).
fof(f173,plain,
aElement0(xx),
inference(cnf_transformation,[],[f30]) ).
fof(f175,plain,
aElementOf0(xb,xJ),
inference(cnf_transformation,[],[f31]) ).
fof(f176,plain,
aElementOf0(xa,xI),
inference(cnf_transformation,[],[f31]) ).
fof(f177,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(cnf_transformation,[],[f32]) ).
fof(f178,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(cnf_transformation,[],[f33]) ).
fof(f179,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(cnf_transformation,[],[f34]) ).
fof(f183,plain,
! [X0] :
( ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_108,plain,
aSet0(xI),
inference(cnf_transformation,[],[f167]) ).
tcf(c_112,plain,
aSet0(xJ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_120,plain,
aElement0(xx),
inference(cnf_transformation,[],[f173]) ).
tcf(c_121,plain,
aElement0(xy),
inference(cnf_transformation,[],[f172]) ).
tcf(c_122,plain,
aElementOf0(xa,xI),
inference(cnf_transformation,[],[f176]) ).
tcf(c_123,plain,
aElementOf0(xb,xJ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_125,plain,
sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) = xw,
inference(cnf_transformation,[],[f177]) ).
tcf(c_126,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(cnf_transformation,[],[f178]) ).
tcf(c_127,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_128,negated_conjecture,
! [X0: $i] :
( ~ aElement0(X0)
| ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_3393,definition,
iPr_def_10 = smndt0(xy),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3394,definition,
iPr_def_11 = smndt0(xx),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3398,negated_conjecture,
! [X0: $i] :
( ~ aElement0(X0)
| ~ aElementOf0(sdtpldt0(X0,iPr_def_11),xI)
| ~ aElementOf0(sdtpldt0(X0,iPr_def_10),xJ) ),
inference(demodulation,[status(thm)],[c_128]) ).
tcf(c_4586,plain,
aElementOf0(sdtpldt0(xw,iPr_def_11),xI),
inference(light_normalisation,[status(thm)],[c_126,c_3394]) ).
tcf(c_4594,plain,
aElementOf0(sdtpldt0(xw,iPr_def_10),xJ),
inference(light_normalisation,[status(thm)],[c_127,c_3393]) ).
tcf(c_4595,plain,
( ~ aElement0(xw)
| ~ aElementOf0(sdtpldt0(xw,iPr_def_11),xI) ),
inference(superposition,[status(thm)],[c_4594,c_3398]) ).
tcf(c_4599,plain,
~ aElement0(xw),
inference(forward_subsumption_resolution,[status(thm)],[c_4595,c_4586]) ).
tcf(c_4734,plain,
( aElement0(xa)
| ~ aSet0(xI) ),
inference(superposition,[status(thm)],[c_122,c_72]) ).
tcf(c_4735,plain,
( aElement0(xb)
| ~ aSet0(xJ) ),
inference(superposition,[status(thm)],[c_123,c_72]) ).
tcf(c_4738,plain,
aElement0(xb),
inference(forward_subsumption_resolution,[status(thm)],[c_4735,c_112]) ).
tcf(c_4739,plain,
aElement0(xa),
inference(forward_subsumption_resolution,[status(thm)],[c_4734,c_108]) ).
tcf(c_4767,plain,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(superposition,[status(thm)],[c_125,c_52]) ).
tcf(c_4785,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4767,c_4599]) ).
tcf(c_4889,plain,
( ~ aElement0(xa)
| ~ aElement0(xy)
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(superposition,[status(thm)],[c_53,c_4785]) ).
tcf(c_4890,plain,
~ aElement0(sdtasdt0(xx,xb)),
inference(forward_subsumption_resolution,[status(thm)],[c_4889,c_4739,c_121]) ).
tcf(c_4895,plain,
( ~ aElement0(xb)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_53,c_4890]) ).
tcf(c_4896,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4895,c_4738,c_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG099+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 08:13:40 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.34 % Proving...
% 1.84/0.98 % SZS status Started for theBenchmark.p
% 1.84/0.98 % SZS status Theorem for theBenchmark.p
% 1.84/0.98
% 1.84/0.98 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.84/0.98
% 1.84/0.98 % ------ iProver source info
% 1.84/0.98
% 1.84/0.98 % git: date: 2026-07-19 20:42:38 +0200
% 1.84/0.98 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.84/0.98 % git: non_committed_changes: false
% 1.84/0.98
% 1.84/0.98 % ------ Parsing...
% 1.84/0.98 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.84/0.98
% 1.84/0.98 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.84/0.98
% 1.84/0.98 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.84/0.98
% 1.84/0.98 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.84/0.98 % ------ Proving...
% 1.84/0.98 % ------ Problem Properties
% 1.84/0.98
% 1.84/0.98 %
% 1.84/0.98 % clauses 84
% 1.84/0.98 % conjectures 4
% 1.84/0.98 % EPR 15
% 1.84/0.98 % Horn 71
% 1.84/0.98 % unary 17
% 1.84/0.98 % binary 17
% 1.84/0.98 % lits 247
% 1.84/0.98 % lits eq 36
% 1.84/0.98 % fd_pure 0
% 1.84/0.98 % fd_pseudo 0
% 1.84/0.98 % fd_cond 1
% 1.84/0.98 % fd_pseudo_cond 8
% 1.84/0.98 % AC symbols 0
% 1.84/0.98
% 1.84/0.98 % ------ Schedule dynamic 5 is on
% 1.84/0.98
% 1.84/0.98 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.84/0.98
% 1.84/0.98
% 1.84/0.98 % ------
% 1.84/0.98 % Current options:
% 1.84/0.98 % ------
% 1.84/0.98
% 1.84/0.98
% 1.84/0.98 %
% 1.84/0.98
% 1.84/0.98 % ------ Proving...
% 1.84/0.98 %
% 1.84/0.98
% 1.84/0.98 % SZS status Theorem for theBenchmark.p
% 1.84/0.98
% 1.84/0.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.84/0.98
% 1.84/0.98
%------------------------------------------------------------------------------