%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM627+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 : n001.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 02:26:18 PM UTC 2026
% Result : Theorem 29.41s 4.82s
% Output : CNFRefutation 29.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 102 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 117 ( 51 ~; 39 |; 20 &)
% ( 0 <=>; 7 =>; 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 29 !; 2 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( szszuzczcdt0(X0) != sz00
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
fof(f37,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessTotal) ).
fof(f83,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
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/sandbox/benchmark/theBenchmark.p',m__5309) ).
fof(f115,axiom,
( xx = sdtlpdtrp0(xe,xm)
& aElementOf0(xm,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5389) ).
fof(f117,axiom,
~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
=> aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5442) ).
fof(f118,axiom,
~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> aElementOf0(X0,sdtlpdtrp0(xN,xm)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5461) ).
fof(f173,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != sz00
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f189,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f190,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f189]) ).
fof(f251,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f252,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ),
inference(flattening,[],[f251]) ).
fof(f282,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ? [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
& ~ aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(ennf_transformation,[],[f117]) ).
fof(f283,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
& ? [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
& ~ aElementOf0(X0,sdtlpdtrp0(xN,xm)) ) ),
inference(ennf_transformation,[],[f118]) ).
fof(f469,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& aElementOf0(sK74,sdtlpdtrp0(xN,xm))
& ~ aElementOf0(sK74,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(X0,sK74)],[f282]) ).
fof(f470,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
& aElementOf0(sK75,sdtlpdtrp0(xN,xn))
& ~ aElementOf0(sK75,sdtlpdtrp0(xN,xm)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(X0,sK75)],[f283]) ).
fof(f520,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f173]) ).
fof(f533,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
fof(f693,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) ),
inference(cnf_transformation,[],[f252]) ).
fof(f898,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f911,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f115]) ).
fof(f913,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f469]) ).
fof(f916,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f470]) ).
tcf(c_97,plain,
! [X0: $i] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f520]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f533]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f693]) ).
tcf(c_478,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f898]) ).
tcf(c_488,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f911]) ).
tcf(c_493,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f913]) ).
tcf(c_496,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f916]) ).
tcf(c_1284,plain,
( aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_28006,plain,
( ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(superposition,[status(thm)],[c_272,c_493]) ).
tcf(c_28007,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(superposition,[status(thm)],[c_272,c_496]) ).
tcf(c_28193,plain,
~ sdtlseqdt0(szszuzczcdt0(xn),xm),
inference(global_subsumption_just,[status(thm)],[c_28006,c_488,c_478,c_1284,c_28006]) ).
tcf(c_28195,plain,
( sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(superposition,[status(thm)],[c_111,c_28193]) ).
tcf(c_28196,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_28195,c_28007,c_478,c_488]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM627+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n001.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 05:05:06 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.38 Running first-order theorem proving
% 0.07/0.38 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
% 0.14/0.39
% 0.14/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.39
% 0.14/0.39 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 29.41/4.82 % SZS status Started for theBenchmark.p
% 29.41/4.82 % SZS status Theorem for theBenchmark.p
% 29.41/4.82
% 29.41/4.82 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 29.41/4.82
% 29.41/4.82 % ------ iProver source info
% 29.41/4.82
% 29.41/4.82 % git: date: 2026-07-19 20:42:38 +0200
% 29.41/4.82 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 29.41/4.82 % git: non_committed_changes: false
% 29.41/4.82
% 29.41/4.82 % ------ Parsing...
% 29.41/4.82 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 29.41/4.82
% 29.41/4.82 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e %
% 29.41/4.82
% 29.41/4.82 % ------ Preprocessing...%
% 29.41/4.82
% 29.41/4.82 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 29.41/4.82 % ------ Proving...
% 29.41/4.82 % ------ Problem Properties
% 29.41/4.82
% 29.41/4.82 %
% 29.41/4.82 % clauses 432
% 29.41/4.82 % conjectures 35
% 29.41/4.82 % EPR 86
% 29.41/4.82 % Horn 352
% 29.41/4.82 % unary 80
% 29.41/4.82 % binary 122
% 29.41/4.82 % lits 1288
% 29.41/4.82 % lits eq 173
% 29.41/4.82 % fd_pure 0
% 29.41/4.82 % fd_pseudo 0
% 29.41/4.82 % fd_cond 11
% 29.41/4.82 % fd_pseudo_cond 46
% 29.41/4.82 % AC symbols 0
% 29.41/4.82
% 29.41/4.82 % ------ Input Options Time Limit: Unbounded
% 29.41/4.82
% 29.41/4.82
% 29.41/4.82 % ------
% 29.41/4.82 % Current options:
% 29.41/4.82 % ------
% 29.41/4.82
% 29.41/4.82
% 29.41/4.82 %
% 29.41/4.82
% 29.41/4.82 % ------ Proving...
% 29.41/4.82 %
% 29.41/4.82
% 29.41/4.82 % SZS status Theorem for theBenchmark.p
% 29.41/4.82
% 29.41/4.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 29.41/4.82
% 29.41/4.82
%------------------------------------------------------------------------------