%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM594+1 : 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 : 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 02:26:09 PM UTC 2026
% Result : Theorem 18.15s 3.32s
% Output : CNFRefutation 18.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 14 unt; 0 def)
% Number of atoms : 180 ( 50 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 227 ( 92 ~; 88 |; 38 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 78 ( 0 sgn 65 !; 13 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f68,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aSubsetOf0(X1,szDzozmdt0(X0))
=> ! [X2] :
( X2 = sdtlcdtrc0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& aSet0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSImg) ).
fof(f92,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
& 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(f94,axiom,
aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4781) ).
fof(f95,conjecture,
? [X0] :
( sdtlpdtrp0(xd,X0) = xx
& aElementOf0(X0,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f96,negated_conjecture,
~ ? [X0] :
( sdtlpdtrp0(xd,X0) = xx
& aElementOf0(X0,szNzAzT0) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f125,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
| ~ aSet0(X1)
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(ennf_transformation,[],[f92]) ).
fof(f126,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
| ~ aSet0(X1)
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(flattening,[],[f125]) ).
fof(f127,plain,
! [X0] :
( sdtlpdtrp0(xd,X0) != xx
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f96]) ).
fof(f146,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f157,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( X2 = sdtlcdtrc0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& aSet0(X2) ) ) ) ),
inference(ennf_transformation,[],[f68]) ).
fof(f233,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( ( sdtlcdtrc0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& ( ~ aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X2)
| X2 = sdtlcdtrc0(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f157]) ).
fof(f234,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( ( sdtlcdtrc0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& ( ~ aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X2)
| X2 = sdtlcdtrc0(X0,X1) ) ) ) ),
inference(flattening,[],[f233]) ).
fof(f235,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( ( sdtlcdtrc0(X0,X1) != X2
| ( ! [X6] :
( ( ~ aElementOf0(X6,X2)
| ? [X8] :
( sdtlpdtrp0(X0,X8) = X6
& aElementOf0(X8,X1) ) )
& ( ! [X7] :
( sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1) )
| aElementOf0(X6,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ? [X5] :
( sdtlpdtrp0(X0,X5) = X3
& aElementOf0(X5,X1) ) )
& ( ~ aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X2)
| X2 = sdtlcdtrc0(X0,X1) ) ) ) ),
inference(rectify,[],[f234]) ).
fof(f236,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( ( sdtlcdtrc0(X0,X1) != X2
| ( ! [X6] :
( ( ~ aElementOf0(X6,X2)
| ( sdtlpdtrp0(X0,sK15(X0,X1,X6)) = X6
& aElementOf0(sK15(X0,X1,X6),X1) ) )
& ( ! [X7] :
( sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1) )
| aElementOf0(X6,X2) ) )
& aSet0(X2) ) )
& ( ( ( aElementOf0(sK13(X0,X1,X2),X2)
| ( sK13(X0,X1,X2) = sdtlpdtrp0(X0,sK14(X0,X1,X2))
& aElementOf0(sK14(X0,X1,X2),X1) ) )
& ( ~ aElementOf0(sK13(X0,X1,X2),X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != sK13(X0,X1,X2)
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X2)
| X2 = sdtlcdtrc0(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X3,sK13(X0,X1,X2)),skolemize(X5,sK14(X0,X1,X2)),skolemize(X8,sK15(X0,X1,X6))],[f235]) ).
fof(f317,plain,
szNzAzT0 = szDzozmdt0(xd),
inference(cnf_transformation,[],[f126]) ).
fof(f318,plain,
aFunction0(xd),
inference(cnf_transformation,[],[f126]) ).
fof(f320,plain,
aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd))),
inference(cnf_transformation,[],[f94]) ).
fof(f321,plain,
! [X0] :
( sdtlpdtrp0(xd,X0) != xx
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f330,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f335,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f349,plain,
! [X2,X0,X1,X6] :
( ~ aFunction0(X0)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| sdtlcdtrc0(X0,X1) != X2
| ~ aElementOf0(X6,X2)
| sdtlpdtrp0(X0,sK15(X0,X1,X6)) = X6 ),
inference(cnf_transformation,[],[f236]) ).
fof(f350,plain,
! [X2,X0,X1,X6] :
( ~ aFunction0(X0)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| sdtlcdtrc0(X0,X1) != X2
| ~ aElementOf0(X6,X2)
| aElementOf0(sK15(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f450,plain,
! [X0,X1,X6] :
( ~ aFunction0(X0)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aElementOf0(X6,sdtlcdtrc0(X0,X1))
| aElementOf0(sK15(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f350]) ).
fof(f451,plain,
! [X0,X1,X6] :
( ~ aFunction0(X0)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aElementOf0(X6,sdtlcdtrc0(X0,X1))
| sdtlpdtrp0(X0,sK15(X0,X1,X6)) = X6 ),
inference(equality_resolution,[],[f349]) ).
tcf(c_91,plain,
aFunction0(xd),
inference(cnf_transformation,[],[f318]) ).
tcf(c_92,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(cnf_transformation,[],[f317]) ).
tcf(c_95,plain,
aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd))),
inference(cnf_transformation,[],[f320]) ).
tcf(c_96,negated_conjecture,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ( sdtlpdtrp0(xd,X0) != xx ) ),
inference(cnf_transformation,[],[f321]) ).
tcf(c_104,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f330]) ).
tcf(c_110,plain,
! [X0: $i] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f335]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sK15(X1,X2,X0),X2)
| ~ aFunction0(X1)
| ~ aSubsetOf0(X2,szDzozmdt0(X1))
| ~ aElementOf0(X0,sdtlcdtrc0(X1,X2)) ),
inference(cnf_transformation,[],[f450]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtlpdtrp0(X1,sK15(X1,X2,X0)) = X0 )
| ~ aFunction0(X1)
| ~ aSubsetOf0(X2,szDzozmdt0(X1))
| ~ aElementOf0(X0,sdtlcdtrc0(X1,X2)) ),
inference(cnf_transformation,[],[f451]) ).
tcf(c_224,plain,
( aSubsetOf0(szNzAzT0,szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_1491,plain,
aElementOf0(xx,sdtlcdtrc0(xd,szNzAzT0)),
inference(light_normalisation,[status(thm)],[c_95,c_92]) ).
tcf(c_27504,plain,
( ( sdtlpdtrp0(xd,sK15(xd,szNzAzT0,xx)) = xx )
| ~ aFunction0(xd)
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd)) ),
inference(superposition,[status(thm)],[c_1491,c_130]) ).
tcf(c_27516,plain,
( ( sdtlpdtrp0(xd,sK15(xd,szNzAzT0,xx)) = xx )
| ~ aFunction0(xd)
| ~ aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(light_normalisation,[status(thm)],[c_27504,c_92]) ).
tcf(c_27517,plain,
( ( sdtlpdtrp0(xd,sK15(xd,szNzAzT0,xx)) = xx )
| ~ aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27516,c_91]) ).
tcf(c_46457,plain,
sdtlpdtrp0(xd,sK15(xd,szNzAzT0,xx)) = xx,
inference(global_subsumption_just,[status(thm)],[c_27517,c_104,c_224,c_27517]) ).
tcf(c_46461,plain,
~ aElementOf0(sK15(xd,szNzAzT0,xx),szNzAzT0),
inference(superposition,[status(thm)],[c_46457,c_96]) ).
tcf(c_46479,plain,
( ~ aFunction0(xd)
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ~ aElementOf0(xx,sdtlcdtrc0(xd,szNzAzT0)) ),
inference(superposition,[status(thm)],[c_129,c_46461]) ).
tcf(c_46482,plain,
( ~ aFunction0(xd)
| ~ aSubsetOf0(szNzAzT0,szNzAzT0)
| ~ aElementOf0(xx,sdtlcdtrc0(xd,szNzAzT0)) ),
inference(light_normalisation,[status(thm)],[c_46479,c_92]) ).
tcf(c_46483,plain,
~ aSubsetOf0(szNzAzT0,szNzAzT0),
inference(forward_subsumption_resolution,[status(thm)],[c_46482,c_91,c_1491]) ).
tcf(c_46487,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_46483,c_224,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM594+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.36 % Computer : n002.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 04:51:33 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 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
% 0.15/0.45
% 0.15/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.45
% 0.15/0.45 % Detected problem language: tptp
% 0.15/0.46 % Proving...
% 18.15/3.32 % SZS status Started for theBenchmark.p
% 18.15/3.32 % SZS status Theorem for theBenchmark.p
% 18.15/3.32
% 18.15/3.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.15/3.32
% 18.15/3.32 % ------ iProver source info
% 18.15/3.32
% 18.15/3.32 % git: date: 2026-07-19 20:42:38 +0200
% 18.15/3.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.15/3.32 % git: non_committed_changes: false
% 18.15/3.32
% 18.15/3.32 % ------ Parsing...
% 18.15/3.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.15/3.32
% 18.15/3.32 % ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 18.15/3.32
% 18.15/3.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.15/3.32
% 18.15/3.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 18.15/3.32 % ------ Proving...
% 18.15/3.32 % ------ Problem Properties
% 18.15/3.32
% 18.15/3.32 %
% 18.15/3.32 % clauses 168
% 18.15/3.32 % conjectures 1
% 18.15/3.32 % EPR 41
% 18.15/3.32 % Horn 136
% 18.15/3.32 % unary 31
% 18.15/3.32 % binary 30
% 18.15/3.32 % lits 554
% 18.15/3.32 % lits eq 85
% 18.15/3.32 % fd_pure 0
% 18.15/3.32 % fd_pseudo 0
% 18.15/3.32 % fd_cond 8
% 18.15/3.32 % fd_pseudo_cond 20
% 18.15/3.32 % AC symbols 0
% 18.15/3.32
% 18.15/3.32 % ------ Schedule dynamic 5 is on
% 18.15/3.32
% 18.15/3.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 18.15/3.32
% 18.15/3.32
% 18.15/3.32 % ------
% 18.15/3.32 % Current options:
% 18.15/3.32 % ------
% 18.15/3.32
% 18.15/3.32
% 18.15/3.32 %
% 18.15/3.32
% 18.15/3.32 % ------ Proving...
% 18.15/3.32 %
% 18.15/3.32
% 18.15/3.32 % SZS status Theorem for theBenchmark.p
% 18.15/3.32
% 18.15/3.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.15/3.32
% 18.15/3.32
%------------------------------------------------------------------------------