%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM547+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 129.85s 16.98s
% Output : Proof 129.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 88 ( 49 unt; 3 def)
% Number of atoms : 239 ( 95 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 269 ( 118 ~; 81 |; 58 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-4 aty)
% Number of variables : 97 ( 6 sgn 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t117,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t261,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t117]) ).
fof(f4,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox2/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(c6,plain,
( aElementOf0(sk0(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t179,plain,
ifeq(aSet0(X1),true,or(eq(X1,slcrc0),eq(aElementOf0(sk0(X1),X1),true)),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t364,plain,
ifeq(aSet0(X1),true,or(eq(X1,slcrc0),eq(aElementOf0(sk0(X1),X1),true)),true) = true,
inference(orient,[status(thm)],[t179]) ).
fof(f56,definition,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(f56_nnf,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0)
& ~ aElementOf0(W3,W2) )
| ( ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ( ( ! [W3] :
( ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [W0,W1,W2,W3] :
( ( ( ( sbrdtbr0(sk10(W0,W1,W2)) = W1
& aSubsetOf0(sk10(W0,W1,W2),W0)
& ~ aElementOf0(sk10(W0,W1,W2),W2) )
| ( ( sbrdtbr0(sk10(W0,W1,W2)) != W1
| ~ aSubsetOf0(sk10(W0,W1,W2),W0) )
& aElementOf0(sk10(W0,W1,W2),W2) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ( ( ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f56_nnf]) ).
cnf(c112,plain,
( aSet0(X2)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(t193,plain,
ifeq(aSet0(X1),true,ifeq(aElementOf0(X2,szNzAzT0),true,ifeq(X3,slbdtsldtrb0(X1,X2),aSet0(X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t312,plain,
ifeq(aSet0(X1),true,ifeq(aElementOf0(X2,szNzAzT0),true,ifeq(X3,slbdtsldtrb0(X1,X2),aSet0(X3),true),true),true) = true,
inference(orient,[status(thm)],[t193]) ).
cnf(t61,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t61]) ).
cnf(t313,plain,
true = ifeq(aSet0(X1),true,ifeq(aElementOf0(X2,szNzAzT0),true,aSet0(slbdtsldtrb0(X1,X2)),true),true),
inference(cp,[status(thm)],[t312,t256]) ).
cnf(t14067,plain,
ifeq(aSet0(X1),true,ifeq(aElementOf0(X2,szNzAzT0),true,aSet0(slbdtsldtrb0(X1,X2)),true),true) = true,
inference(orient,[status(thm)],[t313]) ).
fof(f60,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202) ).
fof(f60_nnf,plain,
aElementOf0(xk,szNzAzT0),
inference(nnf_transformation,[status(thm)],[f60]) ).
cnf(c125,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f60_nnf]) ).
cnf(t9,plain,
aElementOf0(xk,szNzAzT0) = true,
inference(equality_encoding,[status(esa)],[c125]) ).
cnf(t494,plain,
aElementOf0(xk,szNzAzT0) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t14125,plain,
true = ifeq(aSet0(X1),true,ifeq(true,true,aSet0(slbdtsldtrb0(X1,xk)),true),true),
inference(cp,[status(thm)],[t14067,t494]) ).
cnf(t40689,plain,
true = ifeq(aSet0(X1),true,aSet0(slbdtsldtrb0(X1,xk)),true),
inference(step,[status(thm)],[t14125,t256]) ).
cnf(t37438,plain,
ifeq(aSet0(X1),true,aSet0(slbdtsldtrb0(X1,xk)),true) = true,
inference(orient,[status(thm)],[t40689]) ).
fof(f61,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox2/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(c126,plain,
aSet0(xS),
inference(cnf_transformation,[status(esa)],[f61_sk]) ).
cnf(t1,plain,
aSet0(xS) = true,
inference(equality_encoding,[status(esa)],[c126]) ).
cnf(t1673,plain,
aSet0(xS) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t37519,plain,
true = ifeq(true,true,aSet0(slbdtsldtrb0(xS,xk)),true),
inference(cp,[status(thm)],[t37438,t1673]) ).
cnf(t40691,plain,
true = aSet0(slbdtsldtrb0(xS,xk)),
inference(step,[status(thm)],[t37519,t256]) ).
cnf(t37652,plain,
aSet0(slbdtsldtrb0(xS,xk)) = true,
inference(orient,[status(thm)],[t40691]) ).
cnf(t37709,plain,
true = ifeq(true,true,or(eq(slbdtsldtrb0(xS,xk),slcrc0),eq(aElementOf0(sk0(slbdtsldtrb0(xS,xk)),slbdtsldtrb0(xS,xk)),true)),true),
inference(cp,[status(thm)],[t364,t37652]) ).
cnf(t40692,plain,
true = or(eq(slbdtsldtrb0(xS,xk),slcrc0),eq(aElementOf0(sk0(slbdtsldtrb0(xS,xk)),slbdtsldtrb0(xS,xk)),true)),
inference(step,[status(thm)],[t37709,t256]) ).
fof(f62,hypothesis,
( slbdtsldtrb0(xS,xk) != slcrc0
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
file('/export/starexec/sandbox2/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]) ).
cnf(t60,plain,
eq(slbdtsldtrb0(xS,xk),slcrc0) = false,
inference(equality_encoding,[status(esa)],[c130]) ).
cnf(t3239,plain,
eq(slbdtsldtrb0(xS,xk),slcrc0) = false,
inference(orient,[status(thm)],[t60]) ).
cnf(t40693,plain,
true = or(false,eq(aElementOf0(sk0(slbdtsldtrb0(xS,xk)),slbdtsldtrb0(xS,xk)),true)),
inference(step,[status(thm)],[t40692,t3239]) ).
cnf(t17,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t268,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t17]) ).
cnf(t40694,plain,
true = eq(aElementOf0(sk0(slbdtsldtrb0(xS,xk)),slbdtsldtrb0(xS,xk)),true),
inference(step,[status(thm)],[t40693,t268]) ).
fof(f64,conjecture,
? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f64_neg,negated_conjecture,
~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)),
inference(negated_conjecture,[status(cth)],[f64]) ).
fof(f64_nnf,plain,
! [W0] : ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)),
inference(nnf_transformation,[status(thm)],[f64_neg]) ).
fof(f64_sk,plain,
! [W0] : ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c132,plain,
~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(t55,plain,
aElementOf0(X1,slbdtsldtrb0(xS,xk)) = false,
inference(equality_encoding,[status(esa)],[c132]) ).
cnf(t2972,plain,
aElementOf0(X1,slbdtsldtrb0(xS,xk)) = false,
inference(orient,[status(thm)],[t55]) ).
cnf(t40695,plain,
true = eq(false,true),
inference(step,[status(thm)],[t40694,t2972]) ).
cnf(t37770,plain,
eq(false,true) = true,
inference(orient,[status(thm)],[t40695]) ).
cnf(t37771,plain,
true = ifeq(true,true,false,true),
inference(cp,[status(thm)],[t261,t37770]) ).
cnf(t40697,plain,
true = false,
inference(step,[status(thm)],[t37771,t256]) ).
cnf(t37779,plain,
false = true,
inference(orient,[status(thm)],[t40697]) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(c128,plain,
xk != sz00,
inference(cnf_transformation,[status(esa)],[f61_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5,c9,c10,c36,c56,c60,c63,c128,c130,c132]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t37779]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM547+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.38 % Computer : n001.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Thu Sep 24 04:39:06 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 129.85/16.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 129.85/16.98 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
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