%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM602+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 : n015.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 02:26:11 PM UTC 2026
% Result : Theorem 6.49s 7.40s
% Output : CNFRefutation 6.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 9 unt; 0 def)
% Number of atoms : 75 ( 29 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 72 ( 25 ~; 19 |; 26 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 17 !; 9 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
fof(f97,axiom,
! [X0] :
( ( aElementOf0(X0,xO)
| ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
=> ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
& aElementOf0(X1,szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4982) ).
fof(f98,axiom,
( aElementOf0(xx,xO)
& ? [X0] :
( sdtlpdtrp0(xe,X0) = xx
& aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5009) ).
fof(f99,conjecture,
? [X0] :
( sdtlpdtrp0(xe,X0) = xx
& aElementOf0(X0,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f100,negated_conjecture,
~ ? [X0] :
( sdtlpdtrp0(xe,X0) = xx
& aElementOf0(X0,szNzAzT0) ),
inference(negated_conjecture,[status(cth)],[f99]) ).
fof(f119,plain,
! [X0] :
( ( aElementOf0(X0,xO)
| ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
=> ? [X2] :
( sdtlpdtrp0(xe,X2) = X0
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
& aElementOf0(X2,szNzAzT0) ) ),
inference(rectify,[],[f97]) ).
fof(f246,plain,
! [X0] :
( ( ~ aElementOf0(X0,xO)
& ! [X1] :
( sdtlpdtrp0(xe,X1) != X0
| ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ? [X2] :
( sdtlpdtrp0(xe,X2) = X0
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
& aElementOf0(X2,szNzAzT0) ) ),
inference(ennf_transformation,[],[f119]) ).
fof(f247,plain,
! [X0] :
( sdtlpdtrp0(xe,X0) != xx
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f100]) ).
fof(f426,plain,
! [X0] :
( ( ~ aElementOf0(X0,xO)
& ! [X2] :
( sdtlpdtrp0(xe,X2) != X0
| ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
& aElementOf0(X1,szNzAzT0) ) ),
inference(rectify,[],[f246]) ).
fof(f427,plain,
! [X0] :
( ( ~ aElementOf0(X0,xO)
& ! [X2] :
( sdtlpdtrp0(xe,X2) != X0
| ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ( sdtlpdtrp0(xe,sK70(X0)) = X0
& aElementOf0(sK70(X0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) = sdtlpdtrp0(xd,sK70(X0))
& aElementOf0(sK70(X0),szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(X1,sK70(X0))],[f426]) ).
fof(f428,plain,
( aElementOf0(xx,xO)
& xx = sdtlpdtrp0(xe,sK71)
& aElementOf0(sK71,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(X0,sK71)],[f98]) ).
fof(f811,plain,
! [X0] :
( ~ aElementOf0(X0,xO)
| sdtlpdtrp0(xe,sK70(X0)) = X0 ),
inference(cnf_transformation,[],[f427]) ).
fof(f818,plain,
! [X2,X0] :
( sdtlpdtrp0(xe,X2) != X0
| ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(sK70(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f427]) ).
fof(f819,plain,
aElementOf0(xx,xO),
inference(cnf_transformation,[],[f428]) ).
fof(f820,plain,
xx = sdtlpdtrp0(xe,sK71),
inference(cnf_transformation,[],[f428]) ).
fof(f821,plain,
aElementOf0(sK71,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(cnf_transformation,[],[f428]) ).
fof(f822,plain,
! [X0] :
( sdtlpdtrp0(xe,X0) != xx
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f877,plain,
! [X2] :
( ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(sK70(sdtlpdtrp0(xe,X2)),szNzAzT0) ),
inference(equality_resolution,[],[f818]) ).
tcf(c_431,plain,
! [X0: $i] :
( aElementOf0(sK70(sdtlpdtrp0(xe,X0)),szNzAzT0)
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(cnf_transformation,[],[f877]) ).
tcf(c_438,plain,
! [X0: $i] :
( ( sdtlpdtrp0(xe,sK70(X0)) = X0 )
| ~ aElementOf0(X0,xO) ),
inference(cnf_transformation,[],[f811]) ).
tcf(c_439,plain,
aElementOf0(sK71,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(cnf_transformation,[],[f821]) ).
tcf(c_440,plain,
sdtlpdtrp0(xe,sK71) = xx,
inference(cnf_transformation,[],[f820]) ).
tcf(c_441,plain,
aElementOf0(xx,xO),
inference(cnf_transformation,[],[f819]) ).
tcf(c_442,negated_conjecture,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ( sdtlpdtrp0(xe,X0) != xx ) ),
inference(cnf_transformation,[],[f822]) ).
tcf(c_14061,plain,
( ~ aElementOf0(sK70(xx),szNzAzT0)
| ( sdtlpdtrp0(xe,sK70(xx)) != xx ) ),
inference(instantiation,[status(thm)],[c_442]) ).
tcf(c_15427,plain,
( ( sdtlpdtrp0(xe,sK70(xx)) = xx )
| ~ aElementOf0(xx,xO) ),
inference(instantiation,[status(thm)],[c_438]) ).
tcf(c_18821,plain,
aElementOf0(sK70(sdtlpdtrp0(xe,sK71)),szNzAzT0),
inference(superposition,[status(thm)],[c_439,c_431]) ).
tcf(c_18822,plain,
aElementOf0(sK70(xx),szNzAzT0),
inference(demodulation,[status(thm)],[c_18821,c_440]) ).
tcf(c_18849,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_18822,c_15427,c_14061,c_441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM602+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.39 % Computer : n015.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Thu Sep 24 04:55:02 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.45 Running first-order theorem proving
% 0.16/5.45 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
% 0.16/5.47
% 0.16/5.47 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.47
% 0.16/5.47 % Detected problem language: tptp
% 0.16/5.49 % Proving...
% 6.49/7.40 % SZS status Started for theBenchmark.p
% 6.49/7.40 % SZS status Theorem for theBenchmark.p
% 6.49/7.40
% 6.49/7.40 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.49/7.40
% 6.49/7.40 % ------ iProver source info
% 6.49/7.40
% 6.49/7.40 % git: date: 2026-07-19 20:42:38 +0200
% 6.49/7.40 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.49/7.40 % git: non_committed_changes: false
% 6.49/7.40
% 6.49/7.40 % ------ Parsing...
% 6.49/7.40 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.49/7.40
% 6.49/7.40 % ------ Preprocessing... sup_sim: 0 pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 6.49/7.40
% 6.49/7.40 % ------ Preprocessing... gs_s sp: 4 0s gs_e scvd_s sp: 10 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 6.49/7.40
% 6.49/7.40 % ------ Preprocessing...
% 6.49/7.40 % ------ Proving...
% 6.49/7.40 % ------ Problem Properties
% 6.49/7.40
% 6.49/7.40 %
% 6.49/7.40 % clauses 438
% 6.49/7.40 % conjectures 1
% 6.49/7.40 % EPR 80
% 6.49/7.40 % Horn 349
% 6.49/7.40 % unary 41
% 6.49/7.40 % binary 167
% 6.49/7.40 % lits 1337
% 6.49/7.40 % lits eq 169
% 6.49/7.40 % fd_pure 0
% 6.49/7.40 % fd_pseudo 0
% 6.49/7.40 % fd_cond 10
% 6.49/7.40 % fd_pseudo_cond 46
% 6.49/7.40 % AC symbols 0
% 6.49/7.40
% 6.49/7.40 % ------ Input Options Time Limit: Unbounded
% 6.49/7.40
% 6.49/7.40
% 6.49/7.40 % ------
% 6.49/7.40 % Current options:
% 6.49/7.40 % ------
% 6.49/7.40
% 6.49/7.40
% 6.49/7.40 %
% 6.49/7.40
% 6.49/7.40 % ------ Proving...
% 6.49/7.40 %
% 6.49/7.40
% 6.49/7.40 % SZS status Theorem for theBenchmark.p
% 6.49/7.40
% 6.49/7.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.49/7.40
% 6.49/7.40
%------------------------------------------------------------------------------