%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG112+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 : n011.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 02:39:11 PM UTC 2026
% Result : Theorem 21.24s 3.75s
% Output : CNFRefutation 21.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 11 unt; 0 def)
% Number of atoms : 190 ( 97 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 226 ( 94 ~; 97 |; 28 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 47 !; 8 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f16,axiom,
! [X0] :
( aElement0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(f17,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X1 = sz00
| X0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCancel) ).
fof(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f44,axiom,
? [X0] :
( X0 != sz00
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2228) ).
fof(f45,axiom,
! [X0] :
( ( X0 != sz00
& aElementOf0(X0,xI) )
=> ? [X1] :
( ! [X2] :
( ( X2 != sz00
& aElementOf0(X2,xI) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) )
& X1 != sz00
& aElementOf0(X1,xI) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2351) ).
fof(f46,conjecture,
? [X0] :
( ! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& X0 != sz00
& aElementOf0(X0,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ? [X0] :
( ! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& X0 != sz00
& aElementOf0(X0,xI) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f75,plain,
! [X0] :
( ~ aElement0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(ennf_transformation,[],[f17]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(flattening,[],[f76]) ).
fof(f105,plain,
! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| ? [X1] :
( ! [X2] :
( sz00 = X2
| ~ aElementOf0(X2,xI)
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) )
& X1 != sz00
& aElementOf0(X1,xI) ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f106,plain,
! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| ? [X1] :
( ! [X2] :
( sz00 = X2
| ~ aElementOf0(X2,xI)
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) )
& X1 != sz00
& aElementOf0(X1,xI) ) ),
inference(flattening,[],[f105]) ).
fof(f107,plain,
! [X0] :
( ? [X1] :
( X1 != sz00
& aElementOf0(X1,xI)
& iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(ennf_transformation,[],[f47]) ).
fof(f108,plain,
! [X0] :
( ? [X1] :
( X1 != sz00
& aElementOf0(X1,xI)
& iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(flattening,[],[f107]) ).
fof(f145,plain,
( sz00 != sK22
& aElementOf0(sK22,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X0,sK22)],[f44]) ).
fof(f146,plain,
! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| ( ! [X2] :
( sz00 = X2
| ~ aElementOf0(X2,xI)
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(sK23)) )
& sz00 != sK23
& aElementOf0(sK23,xI) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X1,sK23)],[f106]) ).
fof(f147,plain,
! [X0] :
( ( sz00 != sK24(X0)
& aElementOf0(sK24(X0),xI)
& iLess0(sbrdtbr0(sK24(X0)),sbrdtbr0(X0)) )
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(X1,sK24(X0))],[f108]) ).
fof(f148,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f167,plain,
! [X0] :
( ~ aElement0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f169,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f77]) ).
fof(f243,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f42]) ).
fof(f249,plain,
sz00 != sK22,
inference(cnf_transformation,[],[f145]) ).
fof(f250,plain,
aElementOf0(sK22,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f145]) ).
fof(f251,plain,
! [X2,X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| sz00 = X2
| ~ aElementOf0(X2,xI)
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(sK23)) ),
inference(cnf_transformation,[],[f146]) ).
fof(f252,plain,
! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| sz00 != sK23 ),
inference(cnf_transformation,[],[f146]) ).
fof(f253,plain,
! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| aElementOf0(sK23,xI) ),
inference(cnf_transformation,[],[f146]) ).
fof(f254,plain,
! [X0] :
( sz00 != sK24(X0)
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f147]) ).
fof(f255,plain,
! [X0] :
( aElementOf0(sK24(X0),xI)
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f147]) ).
fof(f256,plain,
! [X0] :
( iLess0(sbrdtbr0(sK24(X0)),sbrdtbr0(X0))
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_49,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f148]) ).
tcf(c_69,plain,
! [X0: $i] :
( ( sdtasdt0(sz00,X0) = sz00 )
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( X0 = sz00 )
| ~ aElement0(X1)
| ~ aElement0(X0)
| ( sdtasdt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_145,plain,
sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
inference(cnf_transformation,[],[f243]) ).
tcf(c_150,plain,
aElementOf0(sK22,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f250]) ).
tcf(c_151,negated_conjecture,
sz00 != sK22,
inference(cnf_transformation,[],[f249]) ).
tcf(c_152,plain,
! [X0: $i] :
( aElementOf0(sK23,xI)
| ( X0 = sz00 )
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f253]) ).
tcf(c_153,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aElementOf0(X0,xI)
| ( sz00 != sK23 ) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( X0 = sz00 )
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK23)) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_155,negated_conjecture,
! [X0: $i] :
( iLess0(sbrdtbr0(sK24(X0)),sbrdtbr0(X0))
| ( X0 = sz00 )
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f256]) ).
tcf(c_156,negated_conjecture,
! [X0: $i] :
( aElementOf0(sK24(X0),xI)
| ( X0 = sz00 )
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f255]) ).
tcf(c_157,negated_conjecture,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aElementOf0(X0,xI)
| ( sK24(X0) != sz00 ) ),
inference(cnf_transformation,[],[f254]) ).
tcf(c_165,plain,
( ( sdtasdt0(sz00,sz00) = sz00 )
| ~ aElement0(sz00) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_220,plain,
( ( sz00 = sz00 )
| ~ aElement0(sz00)
| ( sdtasdt0(sz00,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_383,plain,
! [X0: $i] :
( ( sz00 = sK22 )
| ( sK22 != X0 )
| ( sz00 != X0 ) ),
inference(instantiation,[status(thm)],[c_289]) ).
tcf(c_384,plain,
( ( sz00 = sK22 )
| ( sK22 != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_383]) ).
tcf(c_420,plain,
aElementOf0(sK22,xI),
inference(superposition,[status(thm)],[c_145,c_150]) ).
tcf(c_529,plain,
( ( sK22 = sz00 )
| ~ aElementOf0(sK22,xI)
| ( sz00 != sK23 ) ),
inference(instantiation,[status(thm)],[c_153]) ).
tcf(c_530,plain,
( aElementOf0(sK23,xI)
| ( sK22 = sz00 )
| ~ aElementOf0(sK22,xI) ),
inference(instantiation,[status(thm)],[c_152]) ).
tcf(c_1339,plain,
! [X0: $i] :
( ( sK22 = sz00 )
| ( X0 = sz00 )
| ~ aElementOf0(sK22,xI)
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK23)) ),
inference(instantiation,[status(thm)],[c_154]) ).
tcf(c_1400,plain,
! [X0: $i] :
( ( sz00 = sK23 )
| ( sK23 != X0 )
| ( sz00 != X0 ) ),
inference(instantiation,[status(thm)],[c_289]) ).
tcf(c_1401,plain,
( ( sz00 = sK23 )
| ( sK23 != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_1400]) ).
tcf(c_6713,plain,
( iLess0(sbrdtbr0(sK24(sK23)),sbrdtbr0(sK23))
| ( sK23 = sz00 )
| ~ aElementOf0(sK23,xI) ),
inference(instantiation,[status(thm)],[c_155]) ).
tcf(c_6714,plain,
( ( sK23 = sz00 )
| ~ aElementOf0(sK23,xI)
| ( sK24(sK23) != sz00 ) ),
inference(instantiation,[status(thm)],[c_157]) ).
tcf(c_6715,plain,
( aElementOf0(sK24(sK23),xI)
| ( sK23 = sz00 )
| ~ aElementOf0(sK23,xI) ),
inference(instantiation,[status(thm)],[c_156]) ).
tcf(c_11194,plain,
( ( sK22 = sz00 )
| ( sK24(sK23) = sz00 )
| ~ aElementOf0(sK22,xI)
| ~ aElementOf0(sK24(sK23),xI)
| ~ iLess0(sbrdtbr0(sK24(sK23)),sbrdtbr0(sK23)) ),
inference(instantiation,[status(thm)],[c_1339]) ).
tcf(c_11195,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11194,c_6713,c_6714,c_6715,c_1401,c_529,c_530,c_420,c_384,c_220,c_165,c_151,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG112+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.39 % Computer : n011.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Thu Sep 24 08:17:43 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 0.10/0.44
% 0.10/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.44
% 0.10/0.44 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 21.24/3.75 % SZS status Started for theBenchmark.p
% 21.24/3.75 % SZS status Theorem for theBenchmark.p
% 21.24/3.75
% 21.24/3.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.24/3.75
% 21.24/3.75 % ------ iProver source info
% 21.24/3.75
% 21.24/3.75 % git: date: 2026-07-19 20:42:38 +0200
% 21.24/3.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.24/3.75 % git: non_committed_changes: false
% 21.24/3.75
% 21.24/3.75 % ------ Parsing...
% 21.24/3.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 21.24/3.75
% 21.24/3.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e %
% 21.24/3.75
% 21.24/3.75 % ------ Preprocessing...%
% 21.24/3.75
% 21.24/3.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 21.24/3.75 % ------ Proving...
% 21.24/3.75 % ------ Problem Properties
% 21.24/3.75
% 21.24/3.75 %
% 21.24/3.75 % clauses 109
% 21.24/3.75 % conjectures 6
% 21.24/3.75 % EPR 23
% 21.24/3.75 % Horn 81
% 21.24/3.75 % unary 14
% 21.24/3.75 % binary 17
% 21.24/3.75 % lits 378
% 21.24/3.75 % lits eq 57
% 21.24/3.75 % fd_pure 0
% 21.24/3.75 % fd_pseudo 0
% 21.24/3.75 % fd_cond 10
% 21.24/3.75 % fd_pseudo_cond 11
% 21.24/3.75 % AC symbols 0
% 21.24/3.75
% 21.24/3.75 % ------ Input Options Time Limit: Unbounded
% 21.24/3.75
% 21.24/3.75
% 21.24/3.75 % ------
% 21.24/3.75 % Current options:
% 21.24/3.75 % ------
% 21.24/3.75
% 21.24/3.75
% 21.24/3.75 %
% 21.24/3.75
% 21.24/3.75 % ------ Proving...
% 21.24/3.75 %
% 21.24/3.75
% 21.24/3.75 % SZS status Theorem for theBenchmark.p
% 21.24/3.75
% 21.24/3.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.24/3.75
% 21.24/3.75
%------------------------------------------------------------------------------