%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM555+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 : n020.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 02:20:21 PM UTC 2026
% Result : Theorem 75.61s 10.07s
% Output : Proof 75.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 82 ( 41 unt; 2 def)
% Number of atoms : 201 ( 70 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 224 ( 105 ~; 60 |; 50 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-4 aty)
% Number of variables : 70 ( 3 sgn 32 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(c35,plain,
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| X2 != sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t219,plain,
ifeq(aSet0(X1),true,ifeq(aElement0(X2),true,ifeq(X3,sdtmndt0(X1,X2),ifeq(aElementOf0(X4,X3),true,aElementOf0(X4,X1),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c35]) ).
cnf(t339,plain,
ifeq(aSet0(X1),true,ifeq(aElement0(X2),true,ifeq(X3,sdtmndt0(X1,X2),ifeq(aElementOf0(X4,X3),true,aElementOf0(X4,X1),true),true),true),true) = true,
inference(orient,[status(thm)],[t219]) ).
cnf(t69,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t69]) ).
cnf(t340,plain,
true = ifeq(aSet0(X1),true,ifeq(aElement0(X2),true,ifeq(aElementOf0(X3,sdtmndt0(X1,X2)),true,aElementOf0(X3,X1),true),true),true),
inference(cp,[status(thm)],[t339,t256]) ).
cnf(t28858,plain,
ifeq(aSet0(X1),true,ifeq(aElement0(X2),true,ifeq(aElementOf0(X3,sdtmndt0(X1,X2)),true,aElementOf0(X3,X1),true),true),true) = true,
inference(orient,[status(thm)],[t340]) ).
fof(f70,conjecture,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f70_neg,negated_conjecture,
~ ~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(negated_conjecture,[status(cth)],[f70]) ).
fof(f70_nnf,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(nnf_transformation,[status(thm)],[f70_neg]) ).
cnf(c141,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(cnf_transformation,[status(esa)],[f70_nnf]) ).
cnf(t63,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)) = true,
inference(equality_encoding,[status(esa)],[c141]) ).
cnf(t703,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)) = true,
inference(orient,[status(thm)],[t63]) ).
cnf(t28999,plain,
true = ifeq(aSet0(xQ),true,ifeq(aElement0(xy),true,ifeq(true,true,aElementOf0(xx,xQ),true),true),true),
inference(cp,[status(thm)],[t28858,t703]) ).
fof(f65,hypothesis,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
fof(f65_nnf,plain,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c133,plain,
aSet0(xQ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(t5,plain,
aSet0(xQ) = true,
inference(equality_encoding,[status(esa)],[c133]) ).
cnf(t1638,plain,
aSet0(xQ) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t31713,plain,
true = ifeq(true,true,ifeq(aElement0(xy),true,ifeq(true,true,aElementOf0(xx,xQ),true),true),true),
inference(step,[status(thm)],[t28999,t1638]) ).
cnf(t31714,plain,
true = ifeq(aElement0(xy),true,ifeq(true,true,aElementOf0(xx,xQ),true),true),
inference(step,[status(thm)],[t31713,t256]) ).
fof(f66,hypothesis,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2304) ).
fof(f66_nnf,plain,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c136,plain,
aElement0(xy),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(t3,plain,
aElement0(xy) = true,
inference(equality_encoding,[status(esa)],[c136]) ).
cnf(t2107,plain,
aElement0(xy) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t31715,plain,
true = ifeq(true,true,ifeq(true,true,aElementOf0(xx,xQ),true),true),
inference(step,[status(thm)],[t31714,t2107]) ).
cnf(t31716,plain,
true = ifeq(true,true,aElementOf0(xx,xQ),true),
inference(step,[status(thm)],[t31715,t256]) ).
cnf(t31717,plain,
true = aElementOf0(xx,xQ),
inference(step,[status(thm)],[t31716,t256]) ).
fof(f67,hypothesis,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2323) ).
fof(f67_nnf,plain,
~ aElementOf0(xx,xQ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
~ aElementOf0(xx,xQ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c138,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(t18,plain,
aElementOf0(xx,xQ) = false,
inference(equality_encoding,[status(esa)],[c138]) ).
cnf(t2755,plain,
aElementOf0(xx,xQ) = false,
inference(orient,[status(thm)],[t18]) ).
cnf(t31718,plain,
true = false,
inference(step,[status(thm)],[t31717,t2755]) ).
cnf(t29117,plain,
false = true,
inference(orient,[status(thm)],[t31718]) ).
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]) ).
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(f61,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f61_nnf,plain,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(nnf_transformation,[status(thm)],[f61]) ).
fof(f61_sk,plain,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(skolemisation,[status(esa)],[f61_nnf]) ).
cnf(c128,plain,
xk != sz00,
inference(cnf_transformation,[status(esa)],[f61_sk]) ).
fof(f62,hypothesis,
( slbdtsldtrb0(xS,xk) != slcrc0
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
fof(f62_nnf,plain,
( slbdtsldtrb0(xS,xk) != slcrc0
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
inference(nnf_transformation,[status(thm)],[f62]) ).
fof(f62_sk,plain,
( slbdtsldtrb0(xS,xk) != slcrc0
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
inference(skolemisation,[status(esa)],[f62_nnf]) ).
cnf(c130,plain,
slbdtsldtrb0(xS,xk) != slcrc0,
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
fof(f68,hypothesis,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2338) ).
fof(f68_nnf,plain,
~ aElementOf0(xx,xQ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
~ aElementOf0(xx,xQ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c139,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5,c9,c10,c36,c56,c60,c63,c128,c130,c138,c139]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t29117]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM555+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.43 % Computer : n020.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Thu Sep 24 04:37:18 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 75.61/10.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 75.61/10.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------