%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM545+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 02:20:19 PM UTC 2026
% Result : Theorem 22.77s 3.35s
% Output : Proof 22.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 20 unt; 2 def)
% Number of atoms : 254 ( 53 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 309 ( 120 ~; 87 |; 82 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-4 aty)
% Number of variables : 82 ( 5 sgn 51 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f56,conjecture,
? [W0] :
( ( ( ! [W1] :
( aElementOf0(W1,slbdtrb0(W0))
<=> ( sdtlseqdt0(szszuzczcdt0(W1),W0)
& aElementOf0(W1,szNzAzT0) ) )
& aSet0(slbdtrb0(W0)) )
=> ( aSubsetOf0(xS,slbdtrb0(W0))
| ! [W1] :
( aElementOf0(W1,xS)
=> aElementOf0(W1,slbdtrb0(W0)) ) ) )
& aElementOf0(W0,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f56_neg,negated_conjecture,
~ ? [W0] :
( ( ( ! [W1] :
( aElementOf0(W1,slbdtrb0(W0))
<=> ( sdtlseqdt0(szszuzczcdt0(W1),W0)
& aElementOf0(W1,szNzAzT0) ) )
& aSet0(slbdtrb0(W0)) )
=> ( aSubsetOf0(xS,slbdtrb0(W0))
| ! [W1] :
( aElementOf0(W1,xS)
=> aElementOf0(W1,slbdtrb0(W0)) ) ) )
& aElementOf0(W0,szNzAzT0) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f56_nnf,plain,
! [W0] :
( ( ~ aSubsetOf0(xS,slbdtrb0(W0))
& ? [W1] :
( ~ aElementOf0(W1,slbdtrb0(W0))
& aElementOf0(W1,xS) )
& ! [W1] :
( ( ~ sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| aElementOf0(W1,slbdtrb0(W0)) )
& ( ( sdtlseqdt0(szszuzczcdt0(W1),W0)
& aElementOf0(W1,szNzAzT0) )
| ~ aElementOf0(W1,slbdtrb0(W0)) ) )
& aSet0(slbdtrb0(W0)) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f56_neg]) ).
fof(f56_sk,plain,
! [W0,W1] :
( ( ~ aSubsetOf0(xS,slbdtrb0(W0))
& ~ aElementOf0(sk9(W0),slbdtrb0(W0))
& aElementOf0(sk9(W0),xS)
& ( ~ sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| aElementOf0(W1,slbdtrb0(W0)) )
& ( ( sdtlseqdt0(szszuzczcdt0(W1),W0)
& aElementOf0(W1,szNzAzT0) )
| ~ aElementOf0(W1,slbdtrb0(W0)) )
& aSet0(slbdtrb0(W0)) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f56_nnf]) ).
cnf(c133,plain,
( aElementOf0(sk9(X0),xS)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(hi108,negated_conjecture,
ifeq(aElementOf0(X0,szNzAzT0),true,aElementOf0(sk9(X0),xS),true) = true,
inference(equality_encoding,[status(esa)],[c133]) ).
fof(f23,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(f23_nnf,plain,
aElementOf0(sz00,szNzAzT0),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c54,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi37,axiom,
aElementOf0(sz00,szNzAzT0) = true,
inference(equality_encoding,[status(esa)],[c54]) ).
cnf(h12,plain,
aElementOf0(sk9(sz00),xS) = true,
inference(hyper_resolution,[status(thm)],[hi108,hi37]) ).
fof(f55,hypothesis,
( ~ ( xS = slcrc0
& ~ ? [W0] : aElementOf0(W0,xS) )
=> ( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
& ! [W0] :
( aElementOf0(W0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(szmzazxdt0(xS)))
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [W0] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(W0,szmzazxdt0(xS)) )
& aElementOf0(szmzazxdt0(xS),xS) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2035) ).
fof(f55_nnf,plain,
( ( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [W0] :
( aElementOf0(W0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(W0,xS) )
& ! [W0] :
( ( ~ sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(szmzazxdt0(xS)))
| ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(W0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
& ( ( sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(szmzazxdt0(xS)))
& aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(W0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ) )
& aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [W0] :
( sdtlseqdt0(W0,szmzazxdt0(xS))
| ~ aElementOf0(W0,xS) )
& aElementOf0(szmzazxdt0(xS),xS) )
| ( xS = slcrc0
& ! [W0] : ~ aElementOf0(W0,xS) ) ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [W0] :
( ( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(W0,xS) )
& ( ~ sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(szmzazxdt0(xS)))
| ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(W0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
& ( ( sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(szmzazxdt0(xS)))
& aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(W0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
& aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ( sdtlseqdt0(W0,szmzazxdt0(xS))
| ~ aElementOf0(W0,xS) )
& aElementOf0(szmzazxdt0(xS),xS) )
| ( xS = slcrc0
& ~ aElementOf0(W0,xS) ) ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c120,plain,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(hi95,axiom,
ifeq(aElementOf0(X0,xS),true,aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))),true) = true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(h444,plain,
aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) = true,
inference(hyper_resolution,[status(thm)],[hi95,h12]) ).
cnf(c113,plain,
( aElementOf0(szmzazxdt0(xS),xS)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(hi88,axiom,
ifeq(aElementOf0(X0,xS),true,aElementOf0(szmzazxdt0(xS),xS),true) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h448,plain,
aElementOf0(szmzazxdt0(xS),xS) = true,
inference(hyper_resolution,[status(thm)],[hi88,h12]) ).
fof(f54,hypothesis,
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1986) ).
fof(f54_nnf,plain,
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,xS) )
& aSet0(xS) ),
inference(nnf_transformation,[status(thm)],[f54]) ).
fof(f54_sk,plain,
! [W0] :
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ( aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,xS) )
& aSet0(xS) ),
inference(skolemisation,[status(esa)],[f54_nnf]) ).
cnf(c110,plain,
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
cnf(hi85,axiom,
ifeq(aElementOf0(X0,xS),true,aElementOf0(X0,szNzAzT0),true) = true,
inference(equality_encoding,[status(esa)],[c110]) ).
cnf(h1083,plain,
aElementOf0(szmzazxdt0(xS),szNzAzT0) = true,
inference(hyper_resolution,[status(thm)],[hi85,h448]) ).
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(c55,plain,
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi38,axiom,
ifeq(aElementOf0(X0,szNzAzT0),true,aElementOf0(szszuzczcdt0(X0),szNzAzT0),true) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(h1544,plain,
aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0) = true,
inference(hyper_resolution,[status(thm)],[hi38,h1083]) ).
cnf(c135,plain,
( ~ aSubsetOf0(xS,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(hi117,negated_conjecture,
ifeq(aElementOf0(X0,szNzAzT0),true,ifeq(aSubsetOf0(xS,slbdtrb0(X0)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c135]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi117,h1544,h444]) ).
cnf(t687,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]) ).
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]) ).
cnf(c134,plain,
( ~ aElementOf0(sk9(X0),slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5,c9,c10,c36,c56,c60,c63,c134,c135]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t687]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM545+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 04:33:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 22.77/3.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.77/3.35 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------