%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM624+3 : 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 : n002.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 02:26:17 PM UTC 2026
% Result : Theorem 3.58s 1.20s
% Output : CNFRefutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 18 unt; 0 def)
% Number of atoms : 109 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 110 ( 43 ~; 31 |; 26 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 30 !; 9 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).
fof(f103,axiom,
( xp = szmzizndt0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(xp,X0) )
& aElementOf0(xp,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(f105,axiom,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).
fof(f114,axiom,
( ? [X0] :
( sdtlpdtrp0(xe,X0) = xx
& aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& aElementOf0(xx,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5365) ).
fof(f116,axiom,
! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5401) ).
fof(f119,axiom,
( aElementOf0(xx,xQ)
& aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5481) ).
fof(f120,axiom,
( ~ ~ ? [X0] : aElementOf0(X0,sdtlpdtrp0(xN,xm))
& ~ ~ ? [X0] : aElementOf0(X0,xQ)
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
=> aElementOf0(X0,szNzAzT0) )
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5518) ).
fof(f121,conjecture,
xp = xx,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f122,negated_conjecture,
xp != xx,
inference(negated_conjecture,[status(cth)],[f121]) ).
fof(f145,plain,
( ~ ~ ? [X3] : aElementOf0(X3,sdtlpdtrp0(xN,xm))
& ~ ~ ? [X2] : aElementOf0(X2,xQ)
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xm))
=> aElementOf0(X1,szNzAzT0) )
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,szNzAzT0) ) ),
inference(rectify,[],[f120]) ).
fof(f146,plain,
( ? [X3] : aElementOf0(X3,sdtlpdtrp0(xN,xm))
& ? [X2] : aElementOf0(X2,xQ)
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xm))
=> aElementOf0(X1,szNzAzT0) )
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f145]) ).
fof(f147,plain,
xp != xx,
inference(flattening,[],[f122]) ).
fof(f189,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f35]) ).
fof(f190,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f189]) ).
fof(f281,plain,
( xp = szmzizndt0(xQ)
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(xp,X0) )
& aElementOf0(xp,xQ) ),
inference(ennf_transformation,[],[f103]) ).
fof(f285,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,X0) ),
inference(ennf_transformation,[],[f116]) ).
fof(f288,plain,
( ? [X3] : aElementOf0(X3,sdtlpdtrp0(xN,xm))
& ? [X2] : aElementOf0(X2,xQ)
& ! [X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xm))
| aElementOf0(X1,szNzAzT0) )
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f146]) ).
fof(f473,plain,
( xx = sdtlpdtrp0(xe,sK73)
& aElementOf0(sK73,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xx,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(X0,sK73)],[f114]) ).
fof(f475,plain,
( aElementOf0(sK76,sdtlpdtrp0(xN,xm))
& aElementOf0(sK75,xQ)
& ! [X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xm))
| aElementOf0(X1,szNzAzT0) )
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75,sK76]),skolemize(X2,sK75),skolemize(X3,sK76)],[f288]) ).
fof(f536,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f190]) ).
fof(f884,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(xp,X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f893,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f105]) ).
fof(f914,plain,
aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[],[f473]) ).
fof(f917,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f923,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f119]) ).
fof(f924,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f119]) ).
fof(f928,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f475]) ).
fof(f929,plain,
xp != xx,
inference(cnf_transformation,[],[f147]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f536]) ).
tcf(c_457,plain,
! [X0: $i] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f884]) ).
tcf(c_466,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f893]) ).
tcf(c_485,plain,
aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[],[f914]) ).
tcf(c_490,plain,
! [X0: $i] :
( sdtlseqdt0(xx,X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xm)) ),
inference(cnf_transformation,[],[f917]) ).
tcf(c_496,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f924]) ).
tcf(c_497,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f923]) ).
tcf(c_498,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f928]) ).
tcf(c_502,negated_conjecture,
xp != xx,
inference(cnf_transformation,[],[f929]) ).
tcf(c_553,plain,
sdtlseqdt0(xx,xp),
inference(superposition,[status(thm)],[c_496,c_490]) ).
tcf(c_587,plain,
sdtlseqdt0(xp,xx),
inference(superposition,[status(thm)],[c_497,c_457]) ).
tcf(c_594,plain,
aElementOf0(xp,szNzAzT0),
inference(superposition,[status(thm)],[c_466,c_498]) ).
tcf(c_785,plain,
( ( xp = xx )
| ~ sdtlseqdt0(xx,xp)
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(xp,szNzAzT0) ),
inference(superposition,[status(thm)],[c_587,c_109]) ).
tcf(c_786,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_785,c_594,c_553,c_502,c_485]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM624+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n002.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 05:01:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 3.58/1.20 % SZS status Started for theBenchmark.p
% 3.58/1.20 % SZS status Theorem for theBenchmark.p
% 3.58/1.20
% 3.58/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.58/1.20
% 3.58/1.20 % ------ iProver source info
% 3.58/1.20
% 3.58/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.58/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.58/1.20 % git: non_committed_changes: false
% 3.58/1.20
% 3.58/1.20 % ------ Parsing...
% 3.58/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.58/1.20 % ------ Proving...
% 3.58/1.20 % ------ Problem Properties
% 3.58/1.20
% 3.58/1.20 %
% 3.58/1.20 % clauses 454
% 3.58/1.20 % conjectures 1
% 3.58/1.20 % EPR 96
% 3.58/1.20 % Horn 369
% 3.58/1.20 % unary 86
% 3.58/1.20 % binary 131
% 3.58/1.20 % lits 1348
% 3.58/1.20 % lits eq 179
% 3.58/1.20 % fd_pure 0
% 3.58/1.20 % fd_pseudo 0
% 3.58/1.20 % fd_cond 11
% 3.58/1.20 % fd_pseudo_cond 47
% 3.58/1.20 % AC symbols 0
% 3.58/1.20
% 3.58/1.20 % ------ Input Options Time Limit: Unbounded
% 3.58/1.20
% 3.58/1.20
% 3.58/1.20 % ------
% 3.58/1.20 % Current options:
% 3.58/1.20 % ------
% 3.58/1.20
% 3.58/1.20
% 3.58/1.20 %
% 3.58/1.20
% 3.58/1.20 % ------ Proving...
% 3.58/1.20 %
% 3.58/1.20
% 3.58/1.20 % ------ Proving...
% 3.58/1.20 %
% 3.58/1.20
% 3.58/1.20 % SZS status Theorem for theBenchmark.p
% 3.58/1.20
% 3.58/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.75/1.20
% 2.75/1.20
%------------------------------------------------------------------------------