%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM464+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 : n015.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 64.63s 8.79s
% Output : Proof 64.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 41 unt; 0 def)
% Number of atoms : 88 ( 56 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 53 ( 24 ~; 14 |; 11 &)
% ( 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 : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 25 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,conjecture,
( xm != sz00
=> sdtlseqdt0(sz10,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f27_neg,negated_conjecture,
~ ( xm != sz00
=> sdtlseqdt0(sz10,xm) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f27_nnf,plain,
( ~ sdtlseqdt0(sz10,xm)
& xm != sz00 ),
inference(nnf_transformation,[status(thm)],[f27_neg]) ).
fof(f27_sk,plain,
( ~ sdtlseqdt0(sz10,xm)
& xm != sz00 ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c49,plain,
~ sdtlseqdt0(sz10,xm),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(t28,plain,
sdtlseqdt0(sz10,xm) = false,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(t5401,plain,
sdtlseqdt0(sz10,xm) = false,
inference(orient,[status(thm)],[t28]) ).
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(t2350,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(t6,plain,
eq(xm,sz00) = false,
inference(equality_encoding,[status(esa)],[c48]) ).
cnf(t5437,plain,
eq(xm,sz00) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t5440,plain,
true = ifeq(aNaturalNumber0(xm),true,or(false,or(eq(xm,sz10),sdtlseqdt0(sz10,xm))),true),
inference(cp,[status(thm)],[t2350,t5437]) ).
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(t5576,plain,
true = ifeq(true,true,or(false,or(eq(xm,sz10),sdtlseqdt0(sz10,xm))),true),
inference(step,[status(thm)],[t5440,t295]) ).
cnf(t64,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t64]) ).
cnf(t5577,plain,
true = or(false,or(eq(xm,sz10),sdtlseqdt0(sz10,xm))),
inference(step,[status(thm)],[t5576,t256]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t273,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t5578,plain,
true = or(eq(xm,sz10),sdtlseqdt0(sz10,xm)),
inference(step,[status(thm)],[t5577,t273]) ).
cnf(t5579,plain,
true = or(eq(xm,sz10),false),
inference(step,[status(thm)],[t5578,t5401]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t272,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t5580,plain,
true = eq(xm,sz10),
inference(step,[status(thm)],[t5579,t272]) ).
cnf(t5500,plain,
eq(xm,sz10) = true,
inference(orient,[status(thm)],[t5580]) ).
cnf(t5501,plain,
sz10 = ifeq(true,true,xm,sz10),
inference(cp,[status(thm)],[t271,t5500]) ).
cnf(t5581,plain,
sz10 = xm,
inference(step,[status(thm)],[t5501,t256]) ).
cnf(t5511,plain,
sz10 = xm,
inference(orient,[status(thm)],[t5581]) ).
cnf(t5582,plain,
sdtlseqdt0(xm,xm) = false,
inference(step,[status(thm)],[t5401,t5511]) ).
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(t29,plain,
sdtlseqdt0(xm,xm) = true,
inference(hyper_resolution,[status(thm)],[hi29,hi44]) ).
cnf(t2617,plain,
sdtlseqdt0(xm,xm) = true,
inference(orient,[status(thm)],[t29]) ).
cnf(t5583,plain,
true = false,
inference(step,[status(thm)],[t5582,t2617]) ).
cnf(t5512,plain,
true = false,
inference(rw,[status(thm)],[t5583]) ).
cnf(t5527,plain,
false = true,
inference(orient,[status(thm)],[t5512]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c48,c49]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t5527]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM464+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 04:10:10 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 64.63/8.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 64.63/8.79 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------