%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM606+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 02:20:30 PM UTC 2026
% Result : Theorem 16.53s 2.53s
% Output : Proof 16.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 86 ( 38 unt; 3 def)
% Number of atoms : 237 ( 62 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 276 ( 125 ~; 83 |; 54 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 75 ( 1 sgn 50 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f9_nnf,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [W0,W1,W2] :
( ( ( ( ~ aElementOf0(sk1(W0,W1),W0)
& aElementOf0(sk1(W0,W1),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f9_nnf]) ).
cnf(c11,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi4,axiom,
ifeq(aSet0(X0),true,ifeq(aSubsetOf0(X1,X0),true,aSet0(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
fof(f22,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(f22_nnf,plain,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c52,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi35,axiom,
aSet0(szNzAzT0) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
fof(f74,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(f74_nnf,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c168,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
cnf(hi135,axiom,
aSubsetOf0(xS,szNzAzT0) = true,
inference(equality_encoding,[status(esa)],[c168]) ).
cnf(h416,plain,
aSet0(xS) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi35,hi135]) ).
fof(f13,axiom,
! [W0,W1,W2] :
( ( aSet0(W2)
& aSet0(W1)
& aSet0(W0) )
=> ( ( aSubsetOf0(W1,W2)
& aSubsetOf0(W0,W1) )
=> aSubsetOf0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
fof(f13_nnf,plain,
! [W0,W1,W2] :
( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [W0,W1,W2] :
( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c18,plain,
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi11,axiom,
ifeq(aSet0(X0),true,ifeq(aSet0(X1),true,ifeq(aSet0(X2),true,ifeq(aSubsetOf0(X0,X1),true,ifeq(aSubsetOf0(X1,X2),true,aSubsetOf0(X0,X2),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
fof(f95,hypothesis,
( isCountable0(xO)
& aSet0(xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4908) ).
fof(f95_nnf,plain,
( isCountable0(xO)
& aSet0(xO) ),
inference(nnf_transformation,[status(thm)],[f95]) ).
fof(f95_sk,plain,
( isCountable0(xO)
& aSet0(xO) ),
inference(skolemisation,[status(esa)],[f95_nnf]) ).
cnf(c215,plain,
aSet0(xO),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(hi180,axiom,
aSet0(xO) = true,
inference(equality_encoding,[status(esa)],[c215]) ).
fof(f97,hypothesis,
aSubsetOf0(xO,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4998) ).
fof(f97_nnf,plain,
aSubsetOf0(xO,xS),
inference(nnf_transformation,[status(thm)],[f97]) ).
cnf(c220,plain,
aSubsetOf0(xO,xS),
inference(cnf_transformation,[status(esa)],[f97_nnf]) ).
cnf(hi185,axiom,
aSubsetOf0(xO,xS) = true,
inference(equality_encoding,[status(esa)],[c220]) ).
cnf(h832,plain,
aSubsetOf0(xO,szNzAzT0) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi180,h416,hi35,hi185,hi135]) ).
fof(f99,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
fof(f99_nnf,plain,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
inference(nnf_transformation,[status(thm)],[f99]) ).
fof(f99_sk,plain,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
inference(skolemisation,[status(esa)],[f99_nnf]) ).
cnf(c222,plain,
aSubsetOf0(xQ,xO),
inference(cnf_transformation,[status(esa)],[f99_sk]) ).
cnf(hi187,axiom,
aSubsetOf0(xQ,xO) = true,
inference(equality_encoding,[status(esa)],[c222]) ).
cnf(h833,plain,
aSet0(xQ) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi180,hi187]) ).
cnf(h5506,plain,
aSubsetOf0(xQ,szNzAzT0) = true,
inference(hyper_resolution,[status(thm)],[hi11,h833,hi180,hi35,hi187,h832]) ).
fof(f100,conjecture,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f100_neg,negated_conjecture,
~ aSubsetOf0(xQ,szNzAzT0),
inference(negated_conjecture,[status(cth)],[f100]) ).
fof(f100_nnf,plain,
~ aSubsetOf0(xQ,szNzAzT0),
inference(nnf_transformation,[status(thm)],[f100_neg]) ).
fof(f100_sk,plain,
~ aSubsetOf0(xQ,szNzAzT0),
inference(skolemisation,[status(esa)],[f100_nnf]) ).
cnf(c224,plain,
~ aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f100_sk]) ).
cnf(hi198,negated_conjecture,
ifeq(aSubsetOf0(xQ,szNzAzT0),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c224]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi198,h5506]) ).
cnf(t2282,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f4,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f4_nnf,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [W0,W1] :
( ( aElementOf0(sk0(W0),W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f4_nnf]) ).
cnf(c5,plain,
( ~ aElementOf0(X1,X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f7,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
fof(f7_nnf,plain,
! [W0] :
( ~ isFinite0(W0)
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [W0] :
( ~ isFinite0(W0)
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c9,plain,
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f8,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> W0 != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(f8_nnf,plain,
! [W0] :
( W0 != slcrc0
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [W0] :
( W0 != slcrc0
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c10,plain,
( X0 != slcrc0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f15,definition,
! [W0,W1] :
( ( aElement0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f15_nnf,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3)
& ~ aElementOf0(W3,W2) )
| ( ( W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtmndt0(W0,W1) )
& ( ( ! [W3] :
( ( W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ( ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtmndt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [W0,W1,W2,W3] :
( ( ( ( sk3(W0,W1,W2) != W1
& aElementOf0(sk3(W0,W1,W2),W0)
& aElement0(sk3(W0,W1,W2))
& ~ aElementOf0(sk3(W0,W1,W2),W2) )
| ( ( sk3(W0,W1,W2) = W1
| ~ aElementOf0(sk3(W0,W1,W2),W0)
| ~ aElement0(sk3(W0,W1,W2)) )
& aElementOf0(sk3(W0,W1,W2),W2) )
| ~ aSet0(W2)
| W2 = sdtmndt0(W0,W1) )
& ( ( ( W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ( ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtmndt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f15_nnf]) ).
cnf(c36,plain,
( X3 != X1
| ~ aElementOf0(X3,X2)
| X2 != sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f24,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
fof(f24_nnf,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c56,plain,
( szszuzczcdt0(X0) != sz00
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f27,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> W0 != szszuzczcdt0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatNSucc) ).
fof(f27_nnf,plain,
! [W0] :
( W0 != szszuzczcdt0(W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [W0] :
( W0 != szszuzczcdt0(W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c60,plain,
( X0 != szszuzczcdt0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f30,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNoScLessZr) ).
fof(f30_nnf,plain,
! [W0] :
( ~ sdtlseqdt0(szszuzczcdt0(W0),sz00)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [W0] :
( ~ sdtlseqdt0(szszuzczcdt0(W0),sz00)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c63,plain,
( ~ sdtlseqdt0(szszuzczcdt0(X0),sz00)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f77,hypothesis,
xK != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
fof(f77_nnf,plain,
xK != sz00,
inference(nnf_transformation,[status(thm)],[f77]) ).
fof(f77_sk,plain,
xK != sz00,
inference(skolemisation,[status(esa)],[f77_nnf]) ).
cnf(c177,plain,
xK != sz00,
inference(cnf_transformation,[status(esa)],[f77_sk]) ).
fof(f78,hypothesis,
xK != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3520) ).
fof(f78_nnf,plain,
xK != sz00,
inference(nnf_transformation,[status(thm)],[f78]) ).
fof(f78_sk,plain,
xK != sz00,
inference(skolemisation,[status(esa)],[f78_nnf]) ).
cnf(c178,plain,
xK != sz00,
inference(cnf_transformation,[status(esa)],[f78_sk]) ).
cnf(c223,plain,
xQ != slcrc0,
inference(cnf_transformation,[status(esa)],[f99_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5,c9,c10,c36,c56,c60,c63,c177,c178,c223,c224]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2282]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM606+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 04:52:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.53/2.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.53/2.53 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------