%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM600+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 : n010.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 02:26:10 PM UTC 2026
% Result : Theorem 0.41s 1.61s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 8 unt; 0 def)
% Number of atoms : 189 ( 66 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 230 ( 72 ~; 57 |; 91 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 38 !; 19 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f92,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( ( aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
| ( sbrdtbr0(X1) = xk
& ( aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) )
& aSet0(X1) )
=> sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4730) ).
fof(f95,axiom,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( aElementOf0(X0,xO)
<=> ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( sdtlpdtrp0(xd,X0) = szDzizrdt0(xd)
& aElementOf0(X0,szDzozmdt0(xd)) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).
fof(f97,conjecture,
! [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__) ).
fof(f98,negated_conjecture,
~ ! [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) ) ),
inference(negated_conjecture,[status(cth)],[f97]) ).
fof(f116,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X1] :
( aElementOf0(X1,xO)
<=> ? [X2] :
( sdtlpdtrp0(xe,X2) = X1
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( sdtlpdtrp0(xd,X0) = szDzizrdt0(xd)
& aElementOf0(X0,szDzozmdt0(xd)) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
inference(rectify,[],[f95]) ).
fof(f117,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,[],[f98]) ).
fof(f241,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) )
| ~ aSet0(X1)
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(ennf_transformation,[],[f92]) ).
fof(f242,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) )
| ~ aSet0(X1)
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(flattening,[],[f241]) ).
fof(f244,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,[],[f117]) ).
fof(f245,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(flattening,[],[f244]) ).
fof(f414,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(sK67(X0,X1),X1)
& ~ aElementOf0(sK67(X0,X1),sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) )
| ~ aSet0(X1)
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(X2,sK67(X0,X1))],[f242]) ).
fof(f420,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X1] :
( ( ~ aElementOf0(X1,xO)
| ? [X2] :
( sdtlpdtrp0(xe,X2) = X1
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ( ! [X2] :
( sdtlpdtrp0(xe,X2) != X1
| ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| aElementOf0(X1,xO) ) )
& ! [X0] :
( ( ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xd,X0) = szDzizrdt0(xd)
& aElementOf0(X0,szDzozmdt0(xd)) ) )
& ( sdtlpdtrp0(xd,X0) != szDzizrdt0(xd)
| ~ aElementOf0(X0,szDzozmdt0(xd))
| aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
inference(nnf_transformation,[],[f116]) ).
fof(f421,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X1] :
( ( ~ aElementOf0(X1,xO)
| ? [X2] :
( sdtlpdtrp0(xe,X2) = X1
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ( ! [X2] :
( sdtlpdtrp0(xe,X2) != X1
| ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| aElementOf0(X1,xO) ) )
& ! [X0] :
( ( ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xd,X0) = szDzizrdt0(xd)
& aElementOf0(X0,szDzozmdt0(xd)) ) )
& ( sdtlpdtrp0(xd,X0) != szDzizrdt0(xd)
| ~ aElementOf0(X0,szDzozmdt0(xd))
| aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
inference(flattening,[],[f420]) ).
fof(f422,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X1] :
( ( ~ aElementOf0(X1,xO)
| ? [X3] :
( sdtlpdtrp0(xe,X3) = X1
& aElementOf0(X3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ( ! [X2] :
( sdtlpdtrp0(xe,X2) != X1
| ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| aElementOf0(X1,xO) ) )
& ! [X0] :
( ( ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xd,X0) = szDzizrdt0(xd)
& aElementOf0(X0,szDzozmdt0(xd)) ) )
& ( sdtlpdtrp0(xd,X0) != szDzizrdt0(xd)
| ~ aElementOf0(X0,szDzozmdt0(xd))
| aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
inference(rectify,[],[f421]) ).
fof(f423,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X1] :
( ( ~ aElementOf0(X1,xO)
| ( sdtlpdtrp0(xe,sK69(X1)) = X1
& aElementOf0(sK69(X1),sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ( ! [X2] :
( sdtlpdtrp0(xe,X2) != X1
| ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| aElementOf0(X1,xO) ) )
& ! [X0] :
( ( ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xd,X0) = szDzizrdt0(xd)
& aElementOf0(X0,szDzozmdt0(xd)) ) )
& ( sdtlpdtrp0(xd,X0) != szDzizrdt0(xd)
| ~ aElementOf0(X0,szDzozmdt0(xd))
| aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(X3,sK69(X1))],[f422]) ).
fof(f424,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,[],[f245]) ).
fof(f425,plain,
( aElementOf0(sK70,xO)
& sK70 = sdtlpdtrp0(xe,sK71)
& aElementOf0(sK71,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X1] :
( sdtlpdtrp0(xe,X1) != sK70
| ( ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,X1) != szDzizrdt0(xd) )
| ~ aElementOf0(X1,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70,sK71]),skolemize(X0,sK70),skolemize(X2,sK71)],[f424]) ).
fof(f784,plain,
szNzAzT0 = szDzozmdt0(xd),
inference(cnf_transformation,[],[f414]) ).
fof(f802,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(X0,szDzozmdt0(xd)) ),
inference(cnf_transformation,[],[f423]) ).
fof(f809,plain,
sK70 = sdtlpdtrp0(xe,sK71),
inference(cnf_transformation,[],[f425]) ).
fof(f810,plain,
aElementOf0(sK71,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(cnf_transformation,[],[f425]) ).
fof(f811,plain,
! [X1] :
( sdtlpdtrp0(xe,X1) != sK70
| ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f425]) ).
tcf(c_404,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(cnf_transformation,[],[f784]) ).
tcf(c_423,plain,
! [X0: $i] :
( aElementOf0(X0,szDzozmdt0(xd))
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(cnf_transformation,[],[f802]) ).
tcf(c_432,negated_conjecture,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,X0) != sK70 ) ),
inference(cnf_transformation,[],[f811]) ).
tcf(c_433,negated_conjecture,
aElementOf0(sK71,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(cnf_transformation,[],[f810]) ).
tcf(c_434,negated_conjecture,
sdtlpdtrp0(xe,sK71) = sK70,
inference(cnf_transformation,[],[f809]) ).
tcf(c_505,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(light_normalisation,[status(thm)],[c_423,c_404]) ).
tcf(c_577,plain,
! [X0: $i] :
( ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,X0) != sK70 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_432,c_505]) ).
tcf(c_584,plain,
~ aElementOf0(sK71,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(superposition,[status(thm)],[c_434,c_577]) ).
tcf(c_585,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_433,c_584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM600+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.78 % Computer : n010.cluster.edu
% 0.10/0.78 % Model : x86_64 x86_64
% 0.10/0.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.78 % Memory : 8046.5625MB
% 0.10/0.78 % OS : Linux 6.8.0-71-generic
% 0.10/0.78 % CPULimit : 300
% 0.10/0.78 % WCLimit : 300
% 0.10/0.78 % DateTime : Thu Sep 24 04:51:31 UTC 2026
% 0.10/0.79 % CPUTime :
% 0.10/0.79 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.82 Running first-order theorem proving
% 0.14/0.82 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
% 0.14/0.83
% 0.14/0.83 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.83
% 0.14/0.83 % Detected problem language: tptp
% 0.14/0.84 % Proving...
% 0.41/1.61 % SZS status Started for theBenchmark.p
% 0.41/1.61 % SZS status Theorem for theBenchmark.p
% 0.41/1.61
% 0.41/1.61 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.41/1.61
% 0.41/1.61 % ------ iProver source info
% 0.41/1.61
% 0.41/1.61 % git: date: 2026-07-19 20:42:38 +0200
% 0.41/1.61 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.41/1.61 % git: non_committed_changes: false
% 0.41/1.61
% 0.41/1.61 % ------ Parsing...
% 0.41/1.61 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.41/1.61 % ------ Proving...
% 0.41/1.61 % ------ Problem Properties
% 0.41/1.61
% 0.41/1.61 %
% 0.41/1.61 % clauses 387
% 0.41/1.61 % conjectures 5
% 0.41/1.61 % EPR 63
% 0.41/1.61 % Horn 303
% 0.41/1.61 % unary 42
% 0.41/1.61 % binary 107
% 0.41/1.61 % lits 1258
% 0.41/1.61 % lits eq 165
% 0.41/1.61 % fd_pure 0
% 0.41/1.61 % fd_pseudo 0
% 0.41/1.61 % fd_cond 10
% 0.41/1.61 % fd_pseudo_cond 47
% 0.41/1.61 % AC symbols 0
% 0.41/1.61
% 0.41/1.61 % ------ Input Options Time Limit: Unbounded
% 0.41/1.61
% 0.41/1.61
% 0.41/1.61 % ------
% 0.41/1.61 % Current options:
% 0.41/1.61 % ------
% 0.41/1.61
% 0.41/1.61
% 0.41/1.61 %
% 0.41/1.61
% 0.41/1.61 % ------ Proving...
% 0.41/1.61 %
% 0.41/1.61
% 0.41/1.61 % SZS status Theorem for theBenchmark.p
% 0.41/1.61
% 0.41/1.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.41/1.62
% 0.41/1.62
%------------------------------------------------------------------------------