%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG123+4 : 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 : n003.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 3.76s 1.23s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 203 ( 50 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 227 ( 56 ~; 52 |; 104 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 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 : 21 ( 21 usr; 12 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 54 !; 34 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xb))
<=> ? [X1] :
( sdtasdt0(xb,X1) = X0
& aElement0(X1) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
& 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__2174) ).
fof(f52,axiom,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = smndt0(sdtasdt0(xq,xu))
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2690) ).
fof(f53,axiom,
( aElementOf0(xb,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xb
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) )
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xb
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2699) ).
fof(f54,axiom,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2718) ).
fof(f55,conjecture,
( aElementOf0(xr,xI)
| ? [X0,X1] :
( sdtpldt0(X0,X1) = xr
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f56,negated_conjecture,
~ ( aElementOf0(xr,xI)
| ? [X0,X1] :
( sdtpldt0(X0,X1) = xr
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f65,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X7] :
( aElementOf0(X7,xI)
<=> ? [X8,X9] :
( sdtpldt0(X8,X9) = X7
& aElementOf0(X9,slsdtgt0(xb))
& aElementOf0(X8,slsdtgt0(xa)) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xb))
<=> ? [X6] :
( sdtasdt0(xb,X6) = X5
& aElement0(X6) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xa))
<=> ? [X4] :
( sdtasdt0(xa,X4) = X3
& aElement0(X4) ) )
& 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,[],[f42]) ).
fof(f71,plain,
( aElementOf0(xb,xI)
& ? [X2,X3] :
( xb = sdtpldt0(X2,X3)
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) )
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xb
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(rectify,[],[f53]) ).
fof(f124,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X7] :
( aElementOf0(X7,xI)
<=> ? [X8,X9] :
( sdtpldt0(X8,X9) = X7
& aElementOf0(X9,slsdtgt0(xb))
& aElementOf0(X8,slsdtgt0(xa)) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xb))
<=> ? [X6] :
( sdtasdt0(xb,X6) = X5
& aElement0(X6) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xa))
<=> ? [X4] :
( sdtasdt0(xa,X4) = X3
& aElement0(X4) ) )
& 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,[],[f65]) ).
fof(f129,plain,
( ~ aElementOf0(xr,xI)
& ! [X0,X1] :
( sdtpldt0(X0,X1) != xr
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f177,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X7] :
( ( ~ aElementOf0(X7,xI)
| ? [X8,X9] :
( sdtpldt0(X8,X9) = X7
& aElementOf0(X9,slsdtgt0(xb))
& aElementOf0(X8,slsdtgt0(xa)) ) )
& ( ! [X8,X9] :
( sdtpldt0(X8,X9) != X7
| ~ aElementOf0(X9,slsdtgt0(xb))
| ~ aElementOf0(X8,slsdtgt0(xa)) )
| aElementOf0(X7,xI) ) )
& ! [X5] :
( ( ~ aElementOf0(X5,slsdtgt0(xb))
| ? [X6] :
( sdtasdt0(xb,X6) = X5
& aElement0(X6) ) )
& ( ! [X6] :
( sdtasdt0(xb,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,slsdtgt0(xb)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xa))
| ? [X4] :
( sdtasdt0(xa,X4) = X3
& aElement0(X4) ) )
& ( ! [X4] :
( sdtasdt0(xa,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xa)) ) )
& 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(nnf_transformation,[],[f124]) ).
fof(f178,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X9] :
( ( ~ aElementOf0(X9,xI)
| ? [X12,X13] :
( sdtpldt0(X12,X13) = X9
& aElementOf0(X13,slsdtgt0(xb))
& aElementOf0(X12,slsdtgt0(xa)) ) )
& ( ! [X10,X11] :
( sdtpldt0(X10,X11) != X9
| ~ aElementOf0(X11,slsdtgt0(xb))
| ~ aElementOf0(X10,slsdtgt0(xa)) )
| aElementOf0(X9,xI) ) )
& ! [X6] :
( ( ~ aElementOf0(X6,slsdtgt0(xb))
| ? [X8] :
( sdtasdt0(xb,X8) = X6
& aElement0(X8) ) )
& ( ! [X7] :
( sdtasdt0(xb,X7) != X6
| ~ aElement0(X7) )
| aElementOf0(X6,slsdtgt0(xb)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xa))
| ? [X5] :
( sdtasdt0(xa,X5) = X3
& aElement0(X5) ) )
& ( ! [X4] :
( sdtasdt0(xa,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xa)) ) )
& 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,[],[f177]) ).
fof(f179,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X9] :
( ( ~ aElementOf0(X9,xI)
| ( sdtpldt0(sK30(X9),sK31(X9)) = X9
& aElementOf0(sK31(X9),slsdtgt0(xb))
& aElementOf0(sK30(X9),slsdtgt0(xa)) ) )
& ( ! [X10,X11] :
( sdtpldt0(X10,X11) != X9
| ~ aElementOf0(X11,slsdtgt0(xb))
| ~ aElementOf0(X10,slsdtgt0(xa)) )
| aElementOf0(X9,xI) ) )
& ! [X6] :
( ( ~ aElementOf0(X6,slsdtgt0(xb))
| ( sdtasdt0(xb,sK29(X6)) = X6
& aElement0(sK29(X6)) ) )
& ( ! [X7] :
( sdtasdt0(xb,X7) != X6
| ~ aElement0(X7) )
| aElementOf0(X6,slsdtgt0(xb)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xa))
| ( sdtasdt0(xa,sK28(X3)) = X3
& aElement0(sK28(X3)) ) )
& ( ! [X4] :
( sdtasdt0(xa,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xa)) ) )
& 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(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29,sK30,sK31]),skolemize(X5,sK28(X3)),skolemize(X8,sK29(X6)),skolemize(X12,sK30(X9)),skolemize(X13,sK31(X9))],[f178]) ).
fof(f189,plain,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
& smndt0(sdtasdt0(xq,xu)) = sdtpldt0(sK46,sK47)
& aElementOf0(sK47,slsdtgt0(xb))
& aElementOf0(sK46,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46,sK47]),skolemize(X0,sK46),skolemize(X1,sK47)],[f52]) ).
fof(f190,plain,
( aElementOf0(xb,xI)
& xb = sdtpldt0(sK50,sK51)
& aElementOf0(sK51,slsdtgt0(xb))
& aElementOf0(sK50,slsdtgt0(xa))
& xb = sdtpldt0(sK48,sK49)
& aElementOf0(sK49,slsdtgt0(xb))
& aElementOf0(sK48,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48,sK49,sK50,sK51]),skolemize(X0,sK48),skolemize(X1,sK49),skolemize(X2,sK50),skolemize(X3,sK51)],[f71]) ).
fof(f318,plain,
! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ),
inference(cnf_transformation,[],[f179]) ).
fof(f369,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[],[f189]) ).
fof(f370,plain,
smndt0(sdtasdt0(xq,xu)) = sdtpldt0(sK46,sK47),
inference(cnf_transformation,[],[f189]) ).
fof(f373,plain,
aElementOf0(xb,xI),
inference(cnf_transformation,[],[f190]) ).
fof(f380,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(cnf_transformation,[],[f54]) ).
fof(f381,plain,
~ aElementOf0(xr,xI),
inference(cnf_transformation,[],[f129]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f318]) ).
tcf(c_229,plain,
smndt0(sdtasdt0(xq,xu)) = sdtpldt0(sK46,sK47),
inference(cnf_transformation,[],[f370]) ).
tcf(c_230,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[],[f369]) ).
tcf(c_237,plain,
aElementOf0(xb,xI),
inference(cnf_transformation,[],[f373]) ).
tcf(c_238,plain,
sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = xr,
inference(cnf_transformation,[],[f380]) ).
tcf(c_240,negated_conjecture,
~ aElementOf0(xr,xI),
inference(cnf_transformation,[],[f381]) ).
tcf(c_1392,plain,
sdtpldt0(sdtpldt0(sK46,sK47),xb) = xr,
inference(demodulation,[status(thm)],[c_238,c_229]) ).
tcf(c_1393,plain,
aElementOf0(sdtpldt0(sK46,sK47),xI),
inference(demodulation,[status(thm)],[c_230,c_229]) ).
tcf(c_7848,negated_conjecture,
~ aElementOf0(xr,xI),
inference(demodulation,[status(thm)],[c_240]) ).
tcf(c_13001,plain,
( aElementOf0(xr,xI)
| ~ aElementOf0(xb,xI)
| ~ aElementOf0(sdtpldt0(sK46,sK47),xI) ),
inference(superposition,[status(thm)],[c_1392,c_164]) ).
tcf(c_13038,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13001,c_7848,c_237,c_1393]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG123+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.42 % Computer : n003.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Thu Sep 24 08:23:51 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.45 Running first-order theorem proving
% 0.15/0.45 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
% 0.21/0.46
% 0.21/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.21/0.46
% 0.21/0.46 % Detected problem language: tptp
% 0.21/0.47 % Proving...
% 3.76/1.23 % SZS status Started for theBenchmark.p
% 3.76/1.23 % SZS status Theorem for theBenchmark.p
% 3.76/1.23
% 3.76/1.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.76/1.23
% 3.76/1.23 % ------ iProver source info
% 3.76/1.23
% 3.76/1.23 % git: date: 2026-07-19 20:42:38 +0200
% 3.76/1.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.76/1.23 % git: non_committed_changes: false
% 3.76/1.23
% 3.76/1.23 % ------ Parsing...
% 3.76/1.23 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.76/1.23
% 3.76/1.23 % ------ Preprocessing... sup_sim: 3 sf_s rm: 2 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 %
% 3.76/1.23
% 3.76/1.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.76/1.23
% 3.76/1.23 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.76/1.23 % ------ Proving...
% 3.76/1.23 % ------ Problem Properties
% 3.76/1.23
% 3.76/1.23 %
% 3.76/1.23 % clauses 181
% 3.76/1.23 % conjectures 2
% 3.76/1.23 % EPR 49
% 3.76/1.23 % Horn 154
% 3.76/1.23 % unary 68
% 3.76/1.23 % binary 33
% 3.76/1.23 % lits 465
% 3.76/1.23 % lits eq 79
% 3.76/1.23 % fd_pure 0
% 3.76/1.23 % fd_pseudo 0
% 3.76/1.23 % fd_cond 5
% 3.76/1.23 % fd_pseudo_cond 11
% 3.76/1.23 % AC symbols 0
% 3.76/1.23
% 3.76/1.23 % ------ Schedule dynamic 5 is on
% 3.76/1.23
% 3.76/1.23 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.76/1.23
% 3.76/1.23
% 3.76/1.23 % ------
% 3.76/1.23 % Current options:
% 3.76/1.23 % ------
% 3.76/1.23
% 3.76/1.23
% 3.76/1.23 %
% 3.76/1.23
% 3.76/1.23 % ------ Proving...
% 3.76/1.23 %
% 3.76/1.23
% 3.76/1.23 % SZS status Theorem for theBenchmark.p
% 3.76/1.23
% 3.76/1.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.76/1.23
%------------------------------------------------------------------------------