%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG123+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 : 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 02:39:14 PM UTC 2026
% Result : Theorem 7.18s 12.29s
% Output : CNFRefutation 7.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 17 unt; 0 def)
% Number of atoms : 111 ( 4 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 128 ( 46 ~; 42 |; 31 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 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 : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 35 !; 9 ?; 4 :)
% 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(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f52,axiom,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2690) ).
fof(f53,axiom,
aElementOf0(xb,xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2699) ).
fof(f54,axiom,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2718) ).
fof(f55,conjecture,
aElementOf0(xr,xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f56,negated_conjecture,
~ aElementOf0(xr,xI),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f60,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(f64,plain,
~ aElementOf0(xr,xI),
inference(flattening,[],[f56]) ).
fof(f95,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,[],[f60]) ).
fof(f132,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) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ( ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) )
| ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f95]) ).
fof(f133,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) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ( ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) )
| ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(flattening,[],[f132]) ).
fof(f134,plain,
! [X0] :
( ( ~ aIdeal0(X0)
| ( ! [X4] :
( ~ aElementOf0(X4,X0)
| ( ! [X6] :
( ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),X0) )
& ! [X5] :
( ~ aElementOf0(X5,X0)
| aElementOf0(sdtpldt0(X4,X5),X0) ) ) )
& aSet0(X0) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ( ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) )
| ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(rectify,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ( ~ aIdeal0(X0)
| ( ! [X4] :
( ~ aElementOf0(X4,X0)
| ( ! [X6] :
( ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),X0) )
& ! [X5] :
( ~ aElementOf0(X5,X0)
| aElementOf0(sdtpldt0(X4,X5),X0) ) ) )
& aSet0(X0) ) )
& ( ( aElementOf0(sK10(X0),X0)
& ( ( aElement0(sK12(X0))
& ~ aElementOf0(sdtasdt0(sK12(X0),sK10(X0)),X0) )
| ( aElementOf0(sK11(X0),X0)
& ~ aElementOf0(sdtpldt0(sK10(X0),sK11(X0)),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X1,sK10(X0)),skolemize(X2,sK11(X0)),skolemize(X3,sK12(X0))],[f134]) ).
fof(f204,plain,
! [X0,X4,X5] :
( ~ aIdeal0(X0)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X5,X0)
| aElementOf0(sdtpldt0(X4,X5),X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f252,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f42]) ).
fof(f273,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[],[f52]) ).
fof(f274,plain,
aElementOf0(xb,xI),
inference(cnf_transformation,[],[f53]) ).
fof(f275,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(cnf_transformation,[],[f54]) ).
fof(f276,plain,
~ aElementOf0(xr,xI),
inference(cnf_transformation,[],[f64]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtpldt0(X0,X2),X1)
| ~ aIdeal0(X1)
| ~ aElementOf0(X2,X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_144,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f252]) ).
tcf(c_166,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[],[f273]) ).
tcf(c_167,plain,
aElementOf0(xb,xI),
inference(cnf_transformation,[],[f274]) ).
tcf(c_168,plain,
sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = xr,
inference(cnf_transformation,[],[f275]) ).
tcf(c_169,negated_conjecture,
~ aElementOf0(xr,xI),
inference(cnf_transformation,[],[f276]) ).
tcf(c_6042,plain,
! [X0: $i] :
( aElementOf0(xr,X0)
| ~ aIdeal0(X0)
| ~ aElementOf0(xb,X0)
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),X0) ),
inference(superposition,[status(thm)],[c_168,c_102]) ).
tcf(c_6117,plain,
( aElementOf0(xr,xI)
| ~ aIdeal0(xI)
| ~ aElementOf0(xb,xI) ),
inference(superposition,[status(thm)],[c_166,c_6042]) ).
tcf(c_6118,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6117,c_169,c_167,c_144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG123+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/11.01 % Computer : n008.cluster.edu
% 0.10/11.01 % Model : x86_64 x86_64
% 0.10/11.01 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/11.01 % Memory : 8046.5625MB
% 0.10/11.01 % OS : Linux 6.8.0-71-generic
% 0.10/11.01 % CPULimit : 300
% 0.10/11.01 % WCLimit : 300
% 0.10/11.01 % DateTime : Thu Sep 24 08:22:25 UTC 2026
% 0.10/11.01 % CPUTime :
% 0.10/11.01 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/11.05 Running first-order theorem proving
% 0.14/11.05 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
% 0.14/11.06
% 0.14/11.06 % ======== iProver multi-core TPTP/SMT =========
% 0.14/11.06
% 0.14/11.07 % Detected problem language: tptp
% 0.14/11.08 % Proving...
% 7.18/12.29 % SZS status Started for theBenchmark.p
% 7.18/12.29 % SZS status Theorem for theBenchmark.p
% 7.18/12.29
% 7.18/12.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.18/12.29
% 7.18/12.29 % ------ iProver source info
% 7.18/12.29
% 7.18/12.29 % git: date: 2026-07-19 20:42:38 +0200
% 7.18/12.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.18/12.29 % git: non_committed_changes: false
% 7.18/12.29
% 7.18/12.29 % ------ Parsing...
% 7.18/12.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.18/12.29
% 7.18/12.29 % ------ 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 %
% 7.18/12.29
% 7.18/12.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.18/12.29
% 7.18/12.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.18/12.29 % ------ Proving...
% 7.18/12.29 % ------ Problem Properties
% 7.18/12.29
% 7.18/12.29 %
% 7.18/12.29 % clauses 116
% 7.18/12.29 % conjectures 1
% 7.18/12.29 % EPR 30
% 7.18/12.29 % Horn 92
% 7.18/12.29 % unary 31
% 7.18/12.29 % binary 16
% 7.18/12.29 % lits 359
% 7.18/12.29 % lits eq 54
% 7.18/12.29 % fd_pure 0
% 7.18/12.29 % fd_pseudo 0
% 7.18/12.29 % fd_cond 5
% 7.18/12.29 % fd_pseudo_cond 11
% 7.18/12.29 % AC symbols 0
% 7.18/12.29
% 7.18/12.29 % ------ Input Options Time Limit: Unbounded
% 7.18/12.29
% 7.18/12.29
% 7.18/12.29 % ------
% 7.18/12.29 % Current options:
% 7.18/12.29 % ------
% 7.18/12.29
% 7.18/12.29
% 7.18/12.29 %
% 7.18/12.29
% 7.18/12.29 % ------ Proving...
% 7.18/12.29 %
% 7.18/12.29
% 7.18/12.29 % SZS status Theorem for theBenchmark.p
% 7.18/12.29
% 7.18/12.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.18/12.29
% 7.18/12.29
%------------------------------------------------------------------------------