%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM621+3 : 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 : n020.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 02:26:16 PM UTC 2026
% Result : Theorem 27.25s 9.58s
% Output : CNFRefutation 27.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 60 ( 24 unt; 2 def)
% Number of atoms : 154 ( 26 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 133 ( 48 ~; 41 |; 33 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 36 !; 1 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(f91,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
& aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).
fof(f101,axiom,
( aSubsetOf0(xQ,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).
fof(f103,axiom,
( xp = szmzizndt0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(xp,X0) )
& aElementOf0(xp,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
fof(f105,axiom,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5173) ).
fof(f111,axiom,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,szDzozmdt0(xd)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).
fof(f113,axiom,
( aElementOf0(xx,xP)
& xx != szmzizndt0(xQ)
& aElementOf0(xx,xQ)
& aElement0(xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5348) ).
fof(f114,axiom,
( ? [X0] :
( sdtlpdtrp0(xe,X0) = xx
& aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& aElementOf0(xx,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5365) ).
fof(f116,axiom,
! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5401) ).
fof(f118,conjecture,
( ( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> aElementOf0(X0,sdtlpdtrp0(xN,xm)) ) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f119,negated_conjecture,
~ ( ( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> aElementOf0(X0,sdtlpdtrp0(xN,xm)) ) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(negated_conjecture,[status(cth)],[f118]) ).
fof(f183,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f35]) ).
fof(f184,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f183]) ).
fof(f264,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
& aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
inference(ennf_transformation,[],[f91]) ).
fof(f273,plain,
( aSubsetOf0(xQ,szNzAzT0)
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f101]) ).
fof(f275,plain,
( xp = szmzizndt0(xQ)
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(xp,X0) )
& aElementOf0(xp,xQ) ),
inference(ennf_transformation,[],[f103]) ).
fof(f279,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,X0) ),
inference(ennf_transformation,[],[f116]) ).
fof(f281,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
& ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
| aElementOf0(X0,sdtlpdtrp0(xN,xm)) )
& ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(ennf_transformation,[],[f119]) ).
fof(f282,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
& ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
| aElementOf0(X0,sdtlpdtrp0(xN,xm)) )
& ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(flattening,[],[f281]) ).
fof(f467,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(f529,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f184]) ).
fof(f820,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f264]) ).
fof(f870,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f876,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f275]) ).
fof(f877,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(xp,X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f886,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f105]) ).
fof(f895,plain,
xp = sdtlpdtrp0(xe,xn),
inference(cnf_transformation,[],[f111]) ).
fof(f896,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f902,plain,
szmzizndt0(xQ) != xx,
inference(cnf_transformation,[],[f113]) ).
fof(f903,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f113]) ).
fof(f907,plain,
aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[],[f467]) ).
fof(f910,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f915,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
| aElementOf0(X0,sdtlpdtrp0(xN,xm)) ),
inference(cnf_transformation,[],[f282]) ).
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,[],[f529]) ).
tcf(c_400,plain,
! [X0: $i] :
( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f820]) ).
tcf(c_449,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f870]) ).
tcf(c_457,plain,
! [X0: $i] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f877]) ).
tcf(c_458,plain,
szmzizndt0(xQ) = xp,
inference(cnf_transformation,[],[f876]) ).
tcf(c_466,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f886]) ).
tcf(c_478,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f896]) ).
tcf(c_479,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(cnf_transformation,[],[f895]) ).
tcf(c_482,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f903]) ).
tcf(c_483,plain,
szmzizndt0(xQ) != xx,
inference(cnf_transformation,[],[f902]) ).
tcf(c_485,plain,
aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[],[f907]) ).
tcf(c_490,plain,
! [X0: $i] :
( sdtlseqdt0(xx,X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xm)) ),
inference(cnf_transformation,[],[f910]) ).
tcf(c_495,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) ),
inference(cnf_transformation,[],[f915]) ).
tcf(c_3436,plain,
xp != xx,
inference(light_normalisation,[status(thm)],[c_483,c_458]) ).
tcf(c_26427,definition,
iPr_def_10 = sdtlpdtrp0(xN,xn),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_26428,definition,
iPr_def_11 = sdtlpdtrp0(xN,xm),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_26432,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,iPr_def_11)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_495]) ).
tcf(c_31915,plain,
aElementOf0(xp,szNzAzT0),
inference(superposition,[status(thm)],[c_466,c_449]) ).
tcf(c_31930,plain,
sdtlseqdt0(xp,xx),
inference(superposition,[status(thm)],[c_482,c_457]) ).
tcf(c_32384,plain,
! [X0: $i] :
( sdtlseqdt0(xx,X0)
| ~ aElementOf0(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_490,c_26428]) ).
tcf(c_32937,plain,
( aElementOf0(sdtlpdtrp0(xe,xn),iPr_def_10)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(superposition,[status(thm)],[c_26427,c_400]) ).
tcf(c_32944,plain,
( aElementOf0(xp,iPr_def_10)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(light_normalisation,[status(thm)],[c_32937,c_479]) ).
tcf(c_32945,plain,
aElementOf0(xp,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_32944,c_478]) ).
tcf(c_32991,plain,
aElementOf0(xp,iPr_def_11),
inference(superposition,[status(thm)],[c_32945,c_26432]) ).
tcf(c_32995,plain,
sdtlseqdt0(xx,xp),
inference(superposition,[status(thm)],[c_32991,c_32384]) ).
tcf(c_41390,plain,
( ( xp = xx )
| ~ sdtlseqdt0(xx,xp)
| ~ sdtlseqdt0(xp,xx)
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(xp,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_41391,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_41390,c_32995,c_31930,c_31915,c_3436,c_485]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM621+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/5.46 % Computer : n020.cluster.edu
% 0.18/5.46 % Model : x86_64 x86_64
% 0.18/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.46 % Memory : 8046.5625MB
% 0.18/5.46 % OS : Linux 6.8.0-71-generic
% 0.18/5.46 % CPULimit : 300
% 0.18/5.46 % WCLimit : 300
% 0.18/5.46 % DateTime : Thu Sep 24 04:58:40 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.46 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.23/5.52 Running first-order theorem proving
% 0.23/5.53 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
% 0.23/5.54
% 0.23/5.54 % ======== iProver multi-core TPTP/SMT =========
% 0.23/5.54
% 0.23/5.54 % Detected problem language: tptp
% 0.23/5.56 % Proving...
% 27.25/9.58 % SZS status Started for theBenchmark.p
% 27.25/9.58 % SZS status Theorem for theBenchmark.p
% 27.25/9.58
% 27.25/9.58 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 27.25/9.58
% 27.25/9.58 % ------ iProver source info
% 27.25/9.58
% 27.25/9.58 % git: date: 2026-07-19 20:42:38 +0200
% 27.25/9.58 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 27.25/9.58 % git: non_committed_changes: false
% 27.25/9.58
% 27.25/9.58 % ------ Parsing...
% 27.25/9.58 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 27.25/9.58
% 27.25/9.58 % ------ Preprocessing... sup_sim: 16 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 27.25/9.58
% 27.25/9.58 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 27.25/9.58
% 27.25/9.58 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 27.25/9.58 % ------ Proving...
% 27.25/9.58 % ------ Problem Properties
% 27.25/9.58
% 27.25/9.58 %
% 27.25/9.58 % clauses 405
% 27.25/9.58 % conjectures 3
% 27.25/9.58 % EPR 84
% 27.25/9.58 % Horn 330
% 27.25/9.58 % unary 81
% 27.25/9.58 % binary 105
% 27.25/9.58 % lits 1209
% 27.25/9.58 % lits eq 180
% 27.25/9.58 % fd_pure 0
% 27.25/9.58 % fd_pseudo 0
% 27.25/9.58 % fd_cond 11
% 27.25/9.58 % fd_pseudo_cond 39
% 27.25/9.58 % AC symbols 0
% 27.25/9.58
% 27.25/9.58 % ------ Schedule dynamic 5 is on
% 27.25/9.58
% 27.25/9.58 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 27.25/9.58
% 27.25/9.58
% 27.25/9.58 % ------
% 27.25/9.58 % Current options:
% 27.25/9.58 % ------
% 27.25/9.58
% 27.25/9.58
% 27.25/9.58 %
% 27.25/9.58
% 27.25/9.58 % ------ Proving...
% 27.25/9.58 %
% 27.25/9.58
% 27.25/9.58 % SZS status Theorem for theBenchmark.p
% 27.25/9.58
% 27.25/9.58 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.25/9.58
% 27.25/9.58
%------------------------------------------------------------------------------