%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM613+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 : n006.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 02:20:31 PM UTC 2026
% Result : Theorem 186.17s 26.81s
% Output : Proof 186.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 98 ( 57 unt; 2 def)
% Number of atoms : 219 ( 108 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 228 ( 107 ~; 65 |; 45 &)
% ( 3 <=>; 8 =>; 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 : 17 ( 17 usr; 10 con; 0-4 aty)
% Number of variables : 70 ( 3 sgn 38 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f109,conjecture,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f109_neg,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(negated_conjecture,[status(cth)],[f109]) ).
fof(f109_nnf,plain,
sbrdtbr0(xP) != xk,
inference(nnf_transformation,[status(thm)],[f109_neg]) ).
fof(f109_sk,plain,
sbrdtbr0(xP) != xk,
inference(skolemisation,[status(esa)],[f109_nnf]) ).
cnf(c236,plain,
sbrdtbr0(xP) != xk,
inference(cnf_transformation,[status(esa)],[f109_sk]) ).
cnf(t63,plain,
eq(sbrdtbr0(xP),xk) = false,
inference(equality_encoding,[status(esa)],[c236]) ).
cnf(t2806,plain,
eq(sbrdtbr0(xP),xk) = false,
inference(orient,[status(thm)],[t63]) ).
fof(f25,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
=> W0 = W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEquSucc) ).
fof(f25_nnf,plain,
! [W0,W1] :
( W0 = W1
| szszuzczcdt0(W0) != szszuzczcdt0(W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [W0,W1] :
( W0 = W1
| szszuzczcdt0(W0) != szszuzczcdt0(W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c57,plain,
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(t146,plain,
ifeq(aElementOf0(X1,szNzAzT0),true,ifeq(aElementOf0(X2,szNzAzT0),true,ifeq(szszuzczcdt0(X1),szszuzczcdt0(X2),X1,X2),X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c57]) ).
cnf(t257,plain,
ifeq(aElementOf0(X1,szNzAzT0),true,ifeq(aElementOf0(X2,szNzAzT0),true,ifeq(szszuzczcdt0(X1),szszuzczcdt0(X2),X1,X2),X2),X2) = X2,
inference(orient,[status(thm)],[t146]) ).
fof(f108,hypothesis,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& sbrdtbr0(xQ) = szszuzczcdt0(xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5255) ).
fof(f108_nnf,plain,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& sbrdtbr0(xQ) = szszuzczcdt0(xk) ),
inference(nnf_transformation,[status(thm)],[f108]) ).
fof(f108_sk,plain,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& sbrdtbr0(xQ) = szszuzczcdt0(xk) ),
inference(skolemisation,[status(esa)],[f108_nnf]) ).
cnf(c235,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(cnf_transformation,[status(esa)],[f108_sk]) ).
cnf(t57,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0) = true,
inference(equality_encoding,[status(esa)],[c235]) ).
cnf(t456,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0) = true,
inference(orient,[status(thm)],[t57]) ).
cnf(t475,plain,
X1 = ifeq(true,true,ifeq(aElementOf0(X1,szNzAzT0),true,ifeq(szszuzczcdt0(sbrdtbr0(xP)),szszuzczcdt0(X1),sbrdtbr0(xP),X1),X1),X1),
inference(cp,[status(thm)],[t257,t456]) ).
cnf(t70,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t70]) ).
cnf(t81954,plain,
X1 = ifeq(aElementOf0(X1,szNzAzT0),true,ifeq(szszuzczcdt0(sbrdtbr0(xP)),szszuzczcdt0(X1),sbrdtbr0(xP),X1),X1),
inference(step,[status(thm)],[t475,t256]) ).
cnf(c234,plain,
szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ),
inference(cnf_transformation,[status(esa)],[f108_sk]) ).
cnf(t68,plain,
szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ),
inference(equality_encoding,[status(esa)],[c234]) ).
cnf(t2979,plain,
szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ),
inference(orient,[status(thm)],[t68]) ).
cnf(c233,plain,
sbrdtbr0(xQ) = szszuzczcdt0(xk),
inference(cnf_transformation,[status(esa)],[f108_sk]) ).
cnf(t56,plain,
szszuzczcdt0(xk) = sbrdtbr0(xQ),
inference(equality_encoding,[status(esa)],[c233]) ).
cnf(t3006,plain,
sbrdtbr0(xQ) = szszuzczcdt0(xk),
inference(orient,[status(thm)],[t56]) ).
cnf(t77503,plain,
szszuzczcdt0(sbrdtbr0(xP)) = szszuzczcdt0(xk),
inference(step,[status(thm)],[t2979,t3006]) ).
cnf(t3007,plain,
szszuzczcdt0(sbrdtbr0(xP)) = szszuzczcdt0(xk),
inference(orient,[status(thm)],[t77503]) ).
fof(f79,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
fof(f79_nnf,plain,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f79]) ).
fof(f79_sk,plain,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f79_nnf]) ).
cnf(c180,plain,
szszuzczcdt0(xk) = xK,
inference(cnf_transformation,[status(esa)],[f79_sk]) ).
cnf(t27,plain,
szszuzczcdt0(xk) = xK,
inference(equality_encoding,[status(esa)],[c180]) ).
cnf(t3024,plain,
szszuzczcdt0(xk) = xK,
inference(orient,[status(thm)],[t27]) ).
cnf(t77505,plain,
szszuzczcdt0(sbrdtbr0(xP)) = xK,
inference(step,[status(thm)],[t3007,t3024]) ).
cnf(t3025,plain,
szszuzczcdt0(sbrdtbr0(xP)) = xK,
inference(orient,[status(thm)],[t77505]) ).
cnf(t81955,plain,
X1 = ifeq(aElementOf0(X1,szNzAzT0),true,ifeq(xK,szszuzczcdt0(X1),sbrdtbr0(xP),X1),X1),
inference(step,[status(thm)],[t81954,t3025]) ).
cnf(t76910,plain,
ifeq(aElementOf0(X1,szNzAzT0),true,ifeq(xK,szszuzczcdt0(X1),sbrdtbr0(xP),X1),X1) = X1,
inference(orient,[status(thm)],[t81955]) ).
cnf(c179,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f79_sk]) ).
cnf(t30,plain,
aElementOf0(xk,szNzAzT0) = true,
inference(equality_encoding,[status(esa)],[c179]) ).
cnf(t951,plain,
aElementOf0(xk,szNzAzT0) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(t76969,plain,
xk = ifeq(true,true,ifeq(xK,szszuzczcdt0(xk),sbrdtbr0(xP),xk),xk),
inference(cp,[status(thm)],[t76910,t951]) ).
cnf(t81956,plain,
xk = ifeq(xK,szszuzczcdt0(xk),sbrdtbr0(xP),xk),
inference(step,[status(thm)],[t76969,t256]) ).
cnf(t81957,plain,
xk = ifeq(xK,xK,sbrdtbr0(xP),xk),
inference(step,[status(thm)],[t81956,t3024]) ).
cnf(t81958,plain,
xk = sbrdtbr0(xP),
inference(step,[status(thm)],[t81957,t256]) ).
cnf(t77007,plain,
sbrdtbr0(xP) = xk,
inference(orient,[status(thm)],[t81958]) ).
cnf(t81962,plain,
eq(xk,xk) = false,
inference(step,[status(thm)],[t2806,t77007]) ).
cnf(t41,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t1202,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t81963,plain,
true = false,
inference(step,[status(thm)],[t81962,t1202]) ).
cnf(t77027,plain,
true = false,
inference(rw,[status(thm)],[t81963]) ).
cnf(t77037,plain,
false = true,
inference(orient,[status(thm)],[t77027]) ).
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]) ).
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(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,c236]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t77037]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM613+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 04:55:11 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 186.17/26.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 186.17/26.81 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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