%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM464+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 02:20:06 PM UTC 2026
% Result : Theorem 59.60s 8.16s
% Output : Proof 59.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 60 ( 41 unt; 0 def)
% Number of atoms : 98 ( 61 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 68 ( 30 ~; 19 |; 15 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 30 ( 2 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,conjecture,
( xm != sz00
=> ( sdtlseqdt0(sz10,xm)
| ? [W0] :
( sdtpldt0(sz10,W0) = xm
& aNaturalNumber0(W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f27_neg,negated_conjecture,
~ ( xm != sz00
=> ( sdtlseqdt0(sz10,xm)
| ? [W0] :
( sdtpldt0(sz10,W0) = xm
& aNaturalNumber0(W0) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f27_nnf,plain,
( ~ sdtlseqdt0(sz10,xm)
& ! [W0] :
( sdtpldt0(sz10,W0) != xm
| ~ aNaturalNumber0(W0) )
& xm != sz00 ),
inference(nnf_transformation,[status(thm)],[f27_neg]) ).
fof(f27_sk,plain,
! [W0] :
( ~ sdtlseqdt0(sz10,xm)
& ( sdtpldt0(sz10,W0) != xm
| ~ aNaturalNumber0(W0) )
& xm != sz00 ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c50,plain,
~ sdtlseqdt0(sz10,xm),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(t30,plain,
sdtlseqdt0(sz10,xm) = false,
inference(equality_encoding,[status(esa)],[c50]) ).
cnf(t5285,plain,
sdtlseqdt0(sz10,xm) = false,
inference(orient,[status(thm)],[t30]) ).
cnf(t153,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t271,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t153]) ).
fof(f25,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtlseqdt0(sz10,W0)
& sz10 != W0 )
| W0 = sz10
| W0 = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLENTr) ).
fof(f25_nnf,plain,
! [W0] :
( ( sdtlseqdt0(sz10,W0)
& sz10 != W0 )
| W0 = sz10
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [W0] :
( ( sdtlseqdt0(sz10,W0)
& sz10 != W0 )
| W0 = sz10
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c45,plain,
( sdtlseqdt0(sz10,X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(t224,plain,
ifeq(aNaturalNumber0(X1),true,or(eq(X1,sz00),or(eq(X1,sz10),sdtlseqdt0(sz10,X1))),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(t2312,plain,
ifeq(aNaturalNumber0(X1),true,or(eq(X1,sz00),or(eq(X1,sz10),sdtlseqdt0(sz10,X1))),true) = true,
inference(orient,[status(thm)],[t224]) ).
cnf(c48,plain,
xm != sz00,
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(t8,plain,
eq(xm,sz00) = false,
inference(equality_encoding,[status(esa)],[c48]) ).
cnf(t5320,plain,
eq(xm,sz00) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t5323,plain,
true = ifeq(aNaturalNumber0(xm),true,or(false,or(eq(xm,sz10),sdtlseqdt0(sz10,xm))),true),
inference(cp,[status(thm)],[t2312,t5320]) ).
fof(f26,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__987) ).
fof(f26_nnf,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c46,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(t2,plain,
aNaturalNumber0(xm) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t295,plain,
aNaturalNumber0(xm) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t5464,plain,
true = ifeq(true,true,or(false,or(eq(xm,sz10),sdtlseqdt0(sz10,xm))),true),
inference(step,[status(thm)],[t5323,t295]) ).
cnf(t65,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t65]) ).
cnf(t5465,plain,
true = or(false,or(eq(xm,sz10),sdtlseqdt0(sz10,xm))),
inference(step,[status(thm)],[t5464,t256]) ).
cnf(t11,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t273,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t11]) ).
cnf(t5466,plain,
true = or(eq(xm,sz10),sdtlseqdt0(sz10,xm)),
inference(step,[status(thm)],[t5465,t273]) ).
cnf(t5467,plain,
true = or(eq(xm,sz10),false),
inference(step,[status(thm)],[t5466,t5285]) ).
cnf(t9,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t272,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t5468,plain,
true = eq(xm,sz10),
inference(step,[status(thm)],[t5467,t272]) ).
cnf(t5385,plain,
eq(xm,sz10) = true,
inference(orient,[status(thm)],[t5468]) ).
cnf(t5386,plain,
sz10 = ifeq(true,true,xm,sz10),
inference(cp,[status(thm)],[t271,t5385]) ).
cnf(t5469,plain,
sz10 = xm,
inference(step,[status(thm)],[t5386,t256]) ).
cnf(t5396,plain,
sz10 = xm,
inference(orient,[status(thm)],[t5469]) ).
cnf(t5470,plain,
sdtlseqdt0(xm,xm) = false,
inference(step,[status(thm)],[t5285,t5396]) ).
fof(f19,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
fof(f19_nnf,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c31,plain,
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi29,axiom,
ifeq(aNaturalNumber0(X0),true,sdtlseqdt0(X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(hi44,axiom,
aNaturalNumber0(xm) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t31,plain,
sdtlseqdt0(xm,xm) = true,
inference(hyper_resolution,[status(thm)],[hi29,hi44]) ).
cnf(t2578,plain,
sdtlseqdt0(xm,xm) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(t5471,plain,
true = false,
inference(step,[status(thm)],[t5470,t2578]) ).
cnf(t5397,plain,
true = false,
inference(rw,[status(thm)],[t5471]) ).
cnf(t5414,plain,
false = true,
inference(orient,[status(thm)],[t5397]) ).
fof(f2,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f2_nnf,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
sz10 != sz00,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(c49,plain,
( sdtpldt0(sz10,X0) != xm
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c48,c49,c50]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t5414]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM464+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.54 % Computer : n014.cluster.edu
% 0.08/0.54 % Model : x86_64 x86_64
% 0.08/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.54 % Memory : 8046.5625MB
% 0.08/0.54 % OS : Linux 6.8.0-71-generic
% 0.08/0.54 % CPULimit : 300
% 0.08/0.54 % WCLimit : 300
% 0.08/0.54 % DateTime : Thu Sep 24 04:06:35 UTC 2026
% 0.08/0.54 % CPUTime :
% 0.08/0.54 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 59.60/8.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 59.60/8.16 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------