%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG124+4 : 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 : n026.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 3.59s 1.20s
% Output : CNFRefutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 87 ( 32 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 99 ( 32 ~; 22 |; 43 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 13 !; 14 ?; 1 :)
% Comments :
%------------------------------------------------------------------------------
fof(f45,axiom,
( ! [X0] :
( ( X0 != sz00
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xu
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).
fof(f50,axiom,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2666) ).
fof(f51,axiom,
xr != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2673) ).
fof(f55,axiom,
( aElementOf0(xr,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xr
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2729) ).
fof(f69,plain,
( ! [X2] :
( ( sz00 != X2
& ( aElementOf0(X2,xI)
| ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xu
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(rectify,[],[f45]) ).
fof(f127,plain,
( ! [X2] :
( sz00 = X2
| ( ~ aElementOf0(X2,xI)
& ! [X3,X4] :
( sdtpldt0(X3,X4) != X2
| ~ aElementOf0(X4,slsdtgt0(xb))
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xu
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f128,plain,
( ! [X2] :
( sz00 = X2
| ( ~ aElementOf0(X2,xI)
& ! [X3,X4] :
( sdtpldt0(X3,X4) != X2
| ~ aElementOf0(X4,slsdtgt0(xb))
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xu
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(flattening,[],[f127]) ).
fof(f185,plain,
( ! [X2] :
( sz00 = X2
| ( ~ aElementOf0(X2,xI)
& ! [X3,X4] :
( sdtpldt0(X3,X4) != X2
| ~ aElementOf0(X4,slsdtgt0(xb))
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& xu = sdtpldt0(sK41,sK42)
& aElementOf0(sK42,slsdtgt0(xb))
& aElementOf0(sK41,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41,sK42]),skolemize(X0,sK41),skolemize(X1,sK42)],[f128]) ).
fof(f192,plain,
( aElementOf0(xr,xI)
& xr = sdtpldt0(sK52,sK53)
& aElementOf0(sK53,slsdtgt0(xb))
& aElementOf0(sK52,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52,sK53]),skolemize(X0,sK52),skolemize(X1,sK53)],[f55]) ).
fof(f345,plain,
! [X2] :
( sz00 = X2
| ~ aElementOf0(X2,xI)
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) ),
inference(cnf_transformation,[],[f185]) ).
fof(f366,plain,
( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| sz00 = xr ),
inference(cnf_transformation,[],[f50]) ).
fof(f370,plain,
sz00 != xr,
inference(cnf_transformation,[],[f51]) ).
fof(f383,plain,
aElementOf0(xr,xI),
inference(cnf_transformation,[],[f192]) ).
tcf(c_207,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) ),
inference(cnf_transformation,[],[f345]) ).
tcf(c_225,plain,
( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| ( sz00 = xr ) ),
inference(cnf_transformation,[],[f366]) ).
tcf(c_226,plain,
sz00 != xr,
inference(cnf_transformation,[],[f370]) ).
tcf(c_242,plain,
aElementOf0(xr,xI),
inference(cnf_transformation,[],[f383]) ).
tcf(c_509,plain,
iLess0(sbrdtbr0(xr),sbrdtbr0(xu)),
inference(global_subsumption_just,[status(thm)],[c_225,c_226,c_225]) ).
tcf(c_1431,plain,
( ( sz00 = xr )
| ~ aElementOf0(xr,xI) ),
inference(superposition,[status(thm)],[c_509,c_207]) ).
tcf(c_1432,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1431,c_226,c_242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG124+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 08:24:38 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 3.59/1.20 % SZS status Started for theBenchmark.p
% 3.59/1.20 % SZS status Theorem for theBenchmark.p
% 3.59/1.20
% 3.59/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.59/1.20
% 3.59/1.20 % ------ iProver source info
% 3.59/1.20
% 3.59/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.59/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.59/1.20 % git: non_committed_changes: false
% 3.59/1.20
% 3.59/1.20 % ------ Parsing...
% 3.59/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.59/1.20 % ------ Proving...
% 3.59/1.20 % ------ Problem Properties
% 3.59/1.20
% 3.59/1.20 %
% 3.59/1.20 % clauses 195
% 3.59/1.20 % conjectures 1
% 3.59/1.20 % EPR 56
% 3.59/1.20 % Horn 167
% 3.59/1.20 % unary 68
% 3.59/1.20 % binary 42
% 3.59/1.20 % lits 504
% 3.59/1.20 % lits eq 80
% 3.59/1.20 % fd_pure 0
% 3.59/1.20 % fd_pseudo 0
% 3.59/1.20 % fd_cond 5
% 3.59/1.20 % fd_pseudo_cond 11
% 3.59/1.20 % AC symbols 0
% 3.59/1.20
% 3.59/1.20 % ------ Input Options Time Limit: Unbounded
% 3.59/1.20
% 3.59/1.20
% 3.59/1.20 % ------
% 3.59/1.20 % Current options:
% 3.59/1.20 % ------
% 3.59/1.20
% 3.59/1.20
% 3.59/1.20 %
% 3.59/1.20
% 3.59/1.20 % ------ Proving...
% 3.59/1.20 %
% 3.59/1.20
% 3.59/1.20 % ------ Proving...
% 3.59/1.20 %
% 3.59/1.20
% 3.59/1.20 % ------ Proving...
% 3.59/1.20 %
% 3.59/1.20
% 3.59/1.20 % SZS status Theorem for theBenchmark.p
% 3.59/1.20
% 3.59/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.66/1.20
% 2.66/1.20
%------------------------------------------------------------------------------