%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM489+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:09 AM UTC 2025
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 22
% Syntax : Number of formulae : 54 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 484 ( 182 equ)
% Maximal formula atoms : 24 ( 8 avg)
% Number of connectives : 754 ( 361 ~; 217 |; 47 &)
% ( 118 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 37 ( 37 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 126 ( 117 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xr_type,type,
xr: $i ).
tff(xp_type,type,
xp: $i ).
tff(xn_type,type,
xn: $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xm_type,type,
xm: $i ).
tff(1,plain,
( ( xr = sdtmndt0(xn,xp) )
<=> ( xr = sdtmndt0(xn,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
tff(3,plain,
xr = sdtmndt0(xn,xp),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sdtpldt0(xp,xr) = sdtpldt0(xp,sdtmndt0(xn,xp)),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
sdtpldt0(xp,sdtmndt0(xn,xp)) = sdtpldt0(xp,xr),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( sdtlseqdt0(xp,xn)
<=> sdtlseqdt0(xp,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
tff(8,plain,
sdtlseqdt0(xp,xn),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
tff(11,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[11,9]) ).
tff(13,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[10]) ).
tff(15,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[15,13]) ).
tff(17,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(transitivity,[status(thm)],[20,18]) ).
tff(22,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
trans(trans(monotonicity(rewrite(( ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )),
rewrite(( ( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
rewrite(( ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ))),
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
tff(28,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[31,21]) ).
tff(33,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[38,32,16,12,8]) ).
tff(40,plain,
( ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) )
| ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) )
| ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ( ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) )
<=> ( sdtmndt0(xn,xp) = sdtmndt0(xn,xp) ) )
<=> ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) )
| ~ ( ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) )
<=> ( sdtmndt0(xn,xp) = sdtmndt0(xn,xp) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) )
| ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) )
| ~ ( ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) )
<=> ( sdtmndt0(xn,xp) = sdtmndt0(xn,xp) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) )
| ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) )
| ~ ( ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) )
<=> ( sdtmndt0(xn,xp) = sdtmndt0(xn,xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) )
| ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ),
inference(unit_resolution,[status(thm)],[45,39]) ).
tff(47,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn )
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) = xn ) ),
inference(tautology,[status(thm)],[]) ).
tff(48,plain,
sdtpldt0(xp,sdtmndt0(xn,xp)) = xn,
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
xn = sdtpldt0(xp,sdtmndt0(xn,xp)),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
xn = sdtpldt0(xp,xr),
inference(transitivity,[status(thm)],[49,5]) ).
tff(51,plain,
( ( xn != sdtpldt0(xp,xr) )
<=> ( xn != sdtpldt0(xp,xr) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
xn != sdtpldt0(xp,xr),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(53,plain,
xn != sdtpldt0(xp,xr),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
$false,
inference(unit_resolution,[status(thm)],[53,50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM489+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:16:48 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% See solution above
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------