TSTP Solution File: NUM431+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM431+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Sun Sep 18 13:09:39 EDT 2022
% Result : Theorem 0.59s 0.60s
% Output : Proof 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 105
% Syntax : Number of formulae : 258 ( 76 unt; 11 typ; 0 def)
% Number of atoms : 1580 ( 460 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 2306 (1070 ~; 874 |; 190 &)
% ( 142 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 97 ( 97 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 451 ( 407 !; 0 ?; 451 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(xc_type,type,
xc: $i ).
tff(xa_type,type,
xa: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xn_type,type,
xn: $i ).
tff(xq_type,type,
xq: $i ).
tff(xb_type,type,
xb: $i ).
tff(aInteger0_type,type,
aInteger0: $i > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(1,plain,
( aInteger0(xb)
<=> aInteger0(xb) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& ( xq != sz00 )
& aInteger0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).
tff(3,plain,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& ( xq != sz00 ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq) ),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
( aInteger0(xa)
& aInteger0(xb) ),
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
aInteger0(xb),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
aInteger0(xb),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
^ [W0: $i] :
refl(
( ( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
<=> ( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
<=> ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
<=> ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
^ [W0: $i] :
rewrite(
( ( aInteger0(W0)
=> aInteger0(smndt0(W0)) )
<=> ( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [W0: $i] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) )
<=> ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,axiom,
! [W0: $i] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
tff(14,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
( ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xb))
| ~ aInteger0(xb) )
<=> ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xb))
| ~ aInteger0(xb) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xb))
| ~ aInteger0(xb) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xb))
| ~ aInteger0(xb) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
aInteger0(smndt0(xb)),
inference(unit_resolution,[status(thm)],[20,17,7]) ).
tff(22,plain,
( aInteger0(xa)
<=> aInteger0(xa) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
aInteger0(xa),
inference(and_elim,[status(thm)],[5]) ).
tff(24,plain,
aInteger0(xa),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(
( ( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
<=> ~ ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
<=> ~ ~ ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
rewrite(
( ~ ~ ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
<=> ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) )
<=> ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ) )),
rewrite(
( ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) )
<=> ( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) )
<=> ( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
rewrite(
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
<=> ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) ) )),
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) )
<=> ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ) )),
rewrite(
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) )
<=> ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ) )),
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) )
<=> ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
tff(33,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[36,26]) ).
tff(38,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ( sdtpldt0(xa,sdtpldt0(smndt0(xb),xb)) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ( sdtpldt0(xa,sdtpldt0(smndt0(xb),xb)) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ( ( sdtpldt0(xa,sdtpldt0(smndt0(xb),xb)) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa) )
<=> ( ~ aInteger0(xb)
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ( sdtpldt0(xa,sdtpldt0(smndt0(xb),xb)) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(xa,sdtpldt0(smndt0(xb),xb)) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ( sdtpldt0(xa,sdtpldt0(smndt0(xb),xb)) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb) ) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(xa,sdtpldt0(smndt0(xb),xb)) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ( sdtpldt0(xa,sdtpldt0(smndt0(xb),xb)) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb) ) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(xa,sdtpldt0(smndt0(xb),xb)) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ( sdtpldt0(xa,sdtpldt0(smndt0(xb),xb)) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
sdtpldt0(xa,sdtpldt0(smndt0(xb),xb)) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),
inference(unit_resolution,[status(thm)],[43,37,24,7,21]) ).
tff(45,plain,
^ [W0: $i] :
refl(
( ( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
^ [W0: $i] :
rewrite(
( ( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
^ [W0: $i] :
rewrite(
( ( aInteger0(W0)
=> ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
tff(53,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[56,46]) ).
tff(58,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(xb)
| ~ ( ( sdtpldt0(xb,smndt0(xb)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xb),xb) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(xb)
| ~ ( ( sdtpldt0(xb,smndt0(xb)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xb),xb) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(xb)
| ~ ( ( sdtpldt0(xb,smndt0(xb)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xb),xb) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(xb)
| ~ ( ( sdtpldt0(xb,smndt0(xb)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xb),xb) ) ) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
~ ( ( sdtpldt0(xb,smndt0(xb)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xb),xb) ) ),
inference(unit_resolution,[status(thm)],[60,57,7]) ).
tff(62,plain,
( ( sdtpldt0(xb,smndt0(xb)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xb),xb) )
| ( sz00 = sdtpldt0(smndt0(xb),xb) ) ),
inference(tautology,[status(thm)],]) ).
tff(63,plain,
sz00 = sdtpldt0(smndt0(xb),xb),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
sdtpldt0(smndt0(xb),xb) = sz00,
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
sdtpldt0(xa,sdtpldt0(smndt0(xb),xb)) = sdtpldt0(xa,sz00),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
sdtpldt0(xa,sz00) = sdtpldt0(xa,sdtpldt0(smndt0(xb),xb)),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
^ [W0: $i] :
refl(
( ( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
^ [W0: $i] :
rewrite(
( ( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
^ [W0: $i] :
rewrite(
( ( aInteger0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,axiom,
! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
tff(75,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[78,68]) ).
tff(80,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtpldt0(xa,sz00) != xa )
| ( xa != sdtpldt0(sz00,xa) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtpldt0(xa,sz00) != xa )
| ( xa != sdtpldt0(sz00,xa) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtpldt0(xa,sz00) != xa )
| ( xa != sdtpldt0(sz00,xa) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtpldt0(xa,sz00) != xa )
| ( xa != sdtpldt0(sz00,xa) ) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
~ ( ( sdtpldt0(xa,sz00) != xa )
| ( xa != sdtpldt0(sz00,xa) ) ),
inference(unit_resolution,[status(thm)],[82,79,24]) ).
tff(84,plain,
( ( sdtpldt0(xa,sz00) != xa )
| ( xa != sdtpldt0(sz00,xa) )
| ( sdtpldt0(xa,sz00) = xa ) ),
inference(tautology,[status(thm)],]) ).
tff(85,plain,
sdtpldt0(xa,sz00) = xa,
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
xa = sdtpldt0(xa,sz00),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
xa = sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),
inference(transitivity,[status(thm)],[86,66,44]) ).
tff(88,plain,
sdtpldt0(xa,smndt0(xc)) = sdtpldt0(sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),smndt0(xc)),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
sdtpldt0(sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),smndt0(xc)) = sdtpldt0(xa,smndt0(xc)),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
^ [W0: $i,W1: $i] :
refl(
( ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(91,plain,
( ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aInteger0(W0)
& aInteger0(W1) )
<=> ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1) )
<=> ~ ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
rewrite(
( ~ ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1) )
<=> ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
rewrite(
( ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [W0: $i,W1: $i] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,axiom,
! [W0: $i,W1: $i] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
tff(98,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[101,91]) ).
tff(103,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| aInteger0(sdtpldt0(xa,smndt0(xb))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| aInteger0(sdtpldt0(xa,smndt0(xb))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa) )
<=> ( ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| aInteger0(sdtpldt0(xa,smndt0(xb))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| aInteger0(sdtpldt0(xa,smndt0(xb))) ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| aInteger0(sdtpldt0(xa,smndt0(xb))) ) ),
inference(transitivity,[status(thm)],[105,103]) ).
tff(107,plain,
( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
aInteger0(sdtpldt0(xa,smndt0(xb))),
inference(unit_resolution,[status(thm)],[108,102,24,21]) ).
tff(110,plain,
( aInteger0(xc)
<=> aInteger0(xc) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
aInteger0(xc),
inference(and_elim,[status(thm)],[2]) ).
tff(112,plain,
aInteger0(xc),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
( ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xc))
| ~ aInteger0(xc) )
<=> ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xc))
| ~ aInteger0(xc) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xc))
| ~ aInteger0(xc) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xc))
| ~ aInteger0(xc) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
aInteger0(smndt0(xc)),
inference(unit_resolution,[status(thm)],[115,17,112]) ).
tff(117,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ( sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) = sdtpldt0(sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),smndt0(xc)) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ( sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) = sdtpldt0(sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),smndt0(xc)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ( ( sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) = sdtpldt0(sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),smndt0(xc)) )
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb)
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) )
<=> ( ~ aInteger0(xb)
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ( sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) = sdtpldt0(sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),smndt0(xc)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) = sdtpldt0(sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),smndt0(xc)) )
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb)
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ( sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) = sdtpldt0(sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),smndt0(xc)) ) ) ),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) = sdtpldt0(sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),smndt0(xc)) )
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb)
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ( sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) = sdtpldt0(sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),smndt0(xc)) ) ) ),
inference(transitivity,[status(thm)],[119,117]) ).
tff(121,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) = sdtpldt0(sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),smndt0(xc)) )
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb)
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ( sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) = sdtpldt0(sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),smndt0(xc)) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) = sdtpldt0(sdtpldt0(sdtpldt0(xa,smndt0(xb)),xb),smndt0(xc)),
inference(unit_resolution,[status(thm)],[122,37,7,116,109]) ).
tff(124,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xc))
| aInteger0(sdtpldt0(xb,smndt0(xc))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xc))
| aInteger0(sdtpldt0(xb,smndt0(xc))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
( ( aInteger0(sdtpldt0(xb,smndt0(xc)))
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb) )
<=> ( ~ aInteger0(xb)
| ~ aInteger0(smndt0(xc))
| aInteger0(sdtpldt0(xb,smndt0(xc))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xb,smndt0(xc)))
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xc))
| aInteger0(sdtpldt0(xb,smndt0(xc))) ) ),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xb,smndt0(xc)))
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xc))
| aInteger0(sdtpldt0(xb,smndt0(xc))) ) ),
inference(transitivity,[status(thm)],[126,124]) ).
tff(128,plain,
( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xb,smndt0(xc)))
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xc))
| aInteger0(sdtpldt0(xb,smndt0(xc))) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
aInteger0(sdtpldt0(xb,smndt0(xc))),
inference(unit_resolution,[status(thm)],[129,102,7,116]) ).
tff(131,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(132,plain,
( ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aInteger0(W0)
& aInteger0(W1) )
<=> ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1) )
<=> ~ ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
rewrite(
( ~ ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1) )
<=> ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ~ aInteger0(W1)
| ~ aInteger0(W0)
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) )),
rewrite(
( ( ~ aInteger0(W1)
| ~ aInteger0(W0)
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(134,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[133]) ).
tff(135,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aInteger0(W0)
& aInteger0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(137,plain,
( ! [W0: $i,W1: $i] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,axiom,
! [W0: $i,W1: $i] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
tff(139,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[139,135]) ).
tff(141,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[140]) ).
tff(142,plain,
! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[141,134]) ).
tff(143,plain,
! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[142,132]) ).
tff(144,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
| ( sdtpldt0(sdtpldt0(xb,smndt0(xc)),sdtpldt0(xa,smndt0(xb))) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
| ( sdtpldt0(sdtpldt0(xb,smndt0(xc)),sdtpldt0(xa,smndt0(xb))) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(145,plain,
( ( ( sdtpldt0(sdtpldt0(xb,smndt0(xc)),sdtpldt0(xa,smndt0(xb))) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) )
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xb,smndt0(xc))) )
<=> ( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
| ( sdtpldt0(sdtpldt0(xb,smndt0(xc)),sdtpldt0(xa,smndt0(xb))) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(146,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(sdtpldt0(xb,smndt0(xc)),sdtpldt0(xa,smndt0(xb))) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) )
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xb,smndt0(xc))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
| ( sdtpldt0(sdtpldt0(xb,smndt0(xc)),sdtpldt0(xa,smndt0(xb))) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) ) ) ),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(sdtpldt0(xb,smndt0(xc)),sdtpldt0(xa,smndt0(xb))) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) )
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xb,smndt0(xc))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
| ( sdtpldt0(sdtpldt0(xb,smndt0(xc)),sdtpldt0(xa,smndt0(xb))) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) ) ) ),
inference(transitivity,[status(thm)],[146,144]) ).
tff(148,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(sdtpldt0(xb,smndt0(xc)),sdtpldt0(xa,smndt0(xb))) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) )
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xb,smndt0(xc))) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
| ( sdtpldt0(sdtpldt0(xb,smndt0(xc)),sdtpldt0(xa,smndt0(xb))) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))) ) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
sdtpldt0(sdtpldt0(xb,smndt0(xc)),sdtpldt0(xa,smndt0(xb))) = sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))),
inference(unit_resolution,[status(thm)],[149,143,109,130]) ).
tff(151,plain,
( aInteger0(xn)
<=> aInteger0(xn) ),
inference(rewrite,[status(thm)],]) ).
tff(152,axiom,
( aInteger0(xn)
& ( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__876) ).
tff(153,plain,
aInteger0(xn),
inference(and_elim,[status(thm)],[152]) ).
tff(154,plain,
aInteger0(xn),
inference(modus_ponens,[status(thm)],[153,151]) ).
tff(155,plain,
( aInteger0(xq)
<=> aInteger0(xq) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
aInteger0(xq),
inference(and_elim,[status(thm)],[4]) ).
tff(157,plain,
aInteger0(xq),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(159,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[158]) ).
tff(160,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aInteger0(W0)
& aInteger0(W1) )
<=> ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1) )
<=> ~ ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
rewrite(
( ~ ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1) )
<=> ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ~ aInteger0(W1)
| ~ aInteger0(W0)
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
rewrite(
( ( ~ aInteger0(W1)
| ~ aInteger0(W0)
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(161,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[160]) ).
tff(162,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(163,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aInteger0(W0)
& aInteger0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(164,plain,
( ! [W0: $i,W1: $i] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[163]) ).
tff(165,axiom,
! [W0: $i,W1: $i] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
tff(166,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[166,162]) ).
tff(168,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[167]) ).
tff(169,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[168,161]) ).
tff(170,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[169,159]) ).
tff(171,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xn)
| ~ aInteger0(xq)
| ( sdtasdt0(xn,xq) = sdtasdt0(xq,xn) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xn)
| ~ aInteger0(xq)
| ( sdtasdt0(xn,xq) = sdtasdt0(xq,xn) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(172,plain,
( ( ( sdtasdt0(xn,xq) = sdtasdt0(xq,xn) )
| ~ aInteger0(xq)
| ~ aInteger0(xn) )
<=> ( ~ aInteger0(xn)
| ~ aInteger0(xq)
| ( sdtasdt0(xn,xq) = sdtasdt0(xq,xn) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(173,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(xn,xq) = sdtasdt0(xq,xn) )
| ~ aInteger0(xq)
| ~ aInteger0(xn) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xn)
| ~ aInteger0(xq)
| ( sdtasdt0(xn,xq) = sdtasdt0(xq,xn) ) ) ),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(xn,xq) = sdtasdt0(xq,xn) )
| ~ aInteger0(xq)
| ~ aInteger0(xn) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xn)
| ~ aInteger0(xq)
| ( sdtasdt0(xn,xq) = sdtasdt0(xq,xn) ) ) ),
inference(transitivity,[status(thm)],[173,171]) ).
tff(175,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(xn,xq) = sdtasdt0(xq,xn) )
| ~ aInteger0(xq)
| ~ aInteger0(xn) ),
inference(quant_inst,[status(thm)],]) ).
tff(176,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xn)
| ~ aInteger0(xq)
| ( sdtasdt0(xn,xq) = sdtasdt0(xq,xn) ) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
sdtasdt0(xn,xq) = sdtasdt0(xq,xn),
inference(unit_resolution,[status(thm)],[176,170,157,154]) ).
tff(178,plain,
sdtasdt0(xq,xn) = sdtasdt0(xn,xq),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
( ( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) )
<=> ( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(180,plain,
sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)),
inference(and_elim,[status(thm)],[152]) ).
tff(181,plain,
sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,xn),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xn,xq),
inference(transitivity,[status(thm)],[182,178]) ).
tff(184,plain,
( aInteger0(xm)
<=> aInteger0(xm) ),
inference(rewrite,[status(thm)],]) ).
tff(185,axiom,
( aInteger0(xm)
& ( sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__899) ).
tff(186,plain,
aInteger0(xm),
inference(and_elim,[status(thm)],[185]) ).
tff(187,plain,
aInteger0(xm),
inference(modus_ponens,[status(thm)],[186,184]) ).
tff(188,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xm)
| ~ aInteger0(xq)
| ( sdtasdt0(xm,xq) = sdtasdt0(xq,xm) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xm)
| ~ aInteger0(xq)
| ( sdtasdt0(xm,xq) = sdtasdt0(xq,xm) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(189,plain,
( ( ( sdtasdt0(xm,xq) = sdtasdt0(xq,xm) )
| ~ aInteger0(xq)
| ~ aInteger0(xm) )
<=> ( ~ aInteger0(xm)
| ~ aInteger0(xq)
| ( sdtasdt0(xm,xq) = sdtasdt0(xq,xm) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(190,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(xm,xq) = sdtasdt0(xq,xm) )
| ~ aInteger0(xq)
| ~ aInteger0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xm)
| ~ aInteger0(xq)
| ( sdtasdt0(xm,xq) = sdtasdt0(xq,xm) ) ) ),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(xm,xq) = sdtasdt0(xq,xm) )
| ~ aInteger0(xq)
| ~ aInteger0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xm)
| ~ aInteger0(xq)
| ( sdtasdt0(xm,xq) = sdtasdt0(xq,xm) ) ) ),
inference(transitivity,[status(thm)],[190,188]) ).
tff(192,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(xm,xq) = sdtasdt0(xq,xm) )
| ~ aInteger0(xq)
| ~ aInteger0(xm) ),
inference(quant_inst,[status(thm)],]) ).
tff(193,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xm)
| ~ aInteger0(xq)
| ( sdtasdt0(xm,xq) = sdtasdt0(xq,xm) ) ),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
sdtasdt0(xm,xq) = sdtasdt0(xq,xm),
inference(unit_resolution,[status(thm)],[193,170,157,187]) ).
tff(195,plain,
sdtasdt0(xq,xm) = sdtasdt0(xm,xq),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
( ( sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)) )
<=> ( sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(197,plain,
sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)),
inference(and_elim,[status(thm)],[185]) ).
tff(198,plain,
sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
sdtpldt0(xb,smndt0(xc)) = sdtasdt0(xq,xm),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
sdtpldt0(xb,smndt0(xc)) = sdtasdt0(xm,xq),
inference(transitivity,[status(thm)],[199,195]) ).
tff(201,plain,
sdtpldt0(sdtpldt0(xb,smndt0(xc)),sdtpldt0(xa,smndt0(xb))) = sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)),
inference(monotonicity,[status(thm)],[200,183]) ).
tff(202,plain,
sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)) = sdtpldt0(sdtpldt0(xb,smndt0(xc)),sdtpldt0(xa,smndt0(xb))),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(
( ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(204,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) ),
inference(quant_intro,[status(thm)],[203]) ).
tff(205,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
<=> ~ ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
<=> ~ ~ ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
rewrite(
( ~ ~ ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
<=> ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
rewrite(
( ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) )
<=> ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )),
( ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) )),
rewrite(
( ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) )),
( ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(206,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) ),
inference(quant_intro,[status(thm)],[205]) ).
tff(207,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(208,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
rewrite(
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
<=> ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) ) )),
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) )),
rewrite(
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) )),
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(209,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) ),
inference(quant_intro,[status(thm)],[208]) ).
tff(210,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistrib) ).
tff(211,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ),
inference(modus_ponens,[status(thm)],[210,209]) ).
tff(212,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ),
inference(modus_ponens,[status(thm)],[211,207]) ).
tff(213,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ),
inference(skolemize,[status(sab)],[212]) ).
tff(214,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ),
inference(modus_ponens,[status(thm)],[213,206]) ).
tff(215,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ),
inference(modus_ponens,[status(thm)],[214,204]) ).
tff(216,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aInteger0(xn)
| ~ aInteger0(xm)
| ~ aInteger0(xq)
| ~ ( ( sdtasdt0(xm,sdtpldt0(xn,xq)) != sdtpldt0(sdtasdt0(xm,xn),sdtasdt0(xm,xq)) )
| ( sdtasdt0(sdtpldt0(xm,xn),xq) != sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aInteger0(xn)
| ~ aInteger0(xm)
| ~ aInteger0(xq)
| ~ ( ( sdtasdt0(xm,sdtpldt0(xn,xq)) != sdtpldt0(sdtasdt0(xm,xn),sdtasdt0(xm,xq)) )
| ( sdtasdt0(sdtpldt0(xm,xn),xq) != sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(217,plain,
( ( ~ aInteger0(xq)
| ~ aInteger0(xn)
| ~ aInteger0(xm)
| ~ ( ( sdtasdt0(xm,sdtpldt0(xn,xq)) != sdtpldt0(sdtasdt0(xm,xn),sdtasdt0(xm,xq)) )
| ( sdtasdt0(sdtpldt0(xm,xn),xq) != sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)) ) ) )
<=> ( ~ aInteger0(xn)
| ~ aInteger0(xm)
| ~ aInteger0(xq)
| ~ ( ( sdtasdt0(xm,sdtpldt0(xn,xq)) != sdtpldt0(sdtasdt0(xm,xn),sdtasdt0(xm,xq)) )
| ( sdtasdt0(sdtpldt0(xm,xn),xq) != sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(218,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aInteger0(xq)
| ~ aInteger0(xn)
| ~ aInteger0(xm)
| ~ ( ( sdtasdt0(xm,sdtpldt0(xn,xq)) != sdtpldt0(sdtasdt0(xm,xn),sdtasdt0(xm,xq)) )
| ( sdtasdt0(sdtpldt0(xm,xn),xq) != sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aInteger0(xn)
| ~ aInteger0(xm)
| ~ aInteger0(xq)
| ~ ( ( sdtasdt0(xm,sdtpldt0(xn,xq)) != sdtpldt0(sdtasdt0(xm,xn),sdtasdt0(xm,xq)) )
| ( sdtasdt0(sdtpldt0(xm,xn),xq) != sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)) ) ) ) ),
inference(monotonicity,[status(thm)],[217]) ).
tff(219,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aInteger0(xq)
| ~ aInteger0(xn)
| ~ aInteger0(xm)
| ~ ( ( sdtasdt0(xm,sdtpldt0(xn,xq)) != sdtpldt0(sdtasdt0(xm,xn),sdtasdt0(xm,xq)) )
| ( sdtasdt0(sdtpldt0(xm,xn),xq) != sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aInteger0(xn)
| ~ aInteger0(xm)
| ~ aInteger0(xq)
| ~ ( ( sdtasdt0(xm,sdtpldt0(xn,xq)) != sdtpldt0(sdtasdt0(xm,xn),sdtasdt0(xm,xq)) )
| ( sdtasdt0(sdtpldt0(xm,xn),xq) != sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)) ) ) ) ),
inference(transitivity,[status(thm)],[218,216]) ).
tff(220,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aInteger0(xq)
| ~ aInteger0(xn)
| ~ aInteger0(xm)
| ~ ( ( sdtasdt0(xm,sdtpldt0(xn,xq)) != sdtpldt0(sdtasdt0(xm,xn),sdtasdt0(xm,xq)) )
| ( sdtasdt0(sdtpldt0(xm,xn),xq) != sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(221,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aInteger0(xn)
| ~ aInteger0(xm)
| ~ aInteger0(xq)
| ~ ( ( sdtasdt0(xm,sdtpldt0(xn,xq)) != sdtpldt0(sdtasdt0(xm,xn),sdtasdt0(xm,xq)) )
| ( sdtasdt0(sdtpldt0(xm,xn),xq) != sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)) ) ) ),
inference(modus_ponens,[status(thm)],[220,219]) ).
tff(222,plain,
~ ( ( sdtasdt0(xm,sdtpldt0(xn,xq)) != sdtpldt0(sdtasdt0(xm,xn),sdtasdt0(xm,xq)) )
| ( sdtasdt0(sdtpldt0(xm,xn),xq) != sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)) ) ),
inference(unit_resolution,[status(thm)],[221,215,157,154,187]) ).
tff(223,plain,
( ( sdtasdt0(xm,sdtpldt0(xn,xq)) != sdtpldt0(sdtasdt0(xm,xn),sdtasdt0(xm,xq)) )
| ( sdtasdt0(sdtpldt0(xm,xn),xq) != sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)) )
| ( sdtasdt0(sdtpldt0(xm,xn),xq) = sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)) ) ),
inference(tautology,[status(thm)],]) ).
tff(224,plain,
sdtasdt0(sdtpldt0(xm,xn),xq) = sdtpldt0(sdtasdt0(xm,xq),sdtasdt0(xn,xq)),
inference(unit_resolution,[status(thm)],[223,222]) ).
tff(225,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(xm,xn) = sdtpldt0(xn,xm) )
| ~ aInteger0(xn)
| ~ aInteger0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(xm,xn) = sdtpldt0(xn,xm) )
| ~ aInteger0(xn)
| ~ aInteger0(xm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(226,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(xm,xn) = sdtpldt0(xn,xm) )
| ~ aInteger0(xn)
| ~ aInteger0(xm) ),
inference(quant_inst,[status(thm)],]) ).
tff(227,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(xm,xn) = sdtpldt0(xn,xm) )
| ~ aInteger0(xn)
| ~ aInteger0(xm) ),
inference(modus_ponens,[status(thm)],[226,225]) ).
tff(228,plain,
sdtpldt0(xm,xn) = sdtpldt0(xn,xm),
inference(unit_resolution,[status(thm)],[227,143,154,187]) ).
tff(229,plain,
sdtasdt0(sdtpldt0(xm,xn),xq) = sdtasdt0(sdtpldt0(xn,xm),xq),
inference(monotonicity,[status(thm)],[228]) ).
tff(230,plain,
sdtasdt0(sdtpldt0(xn,xm),xq) = sdtasdt0(sdtpldt0(xm,xn),xq),
inference(symmetry,[status(thm)],[229]) ).
tff(231,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xn,xm))
| ~ aInteger0(xm)
| ~ aInteger0(xn) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xn,xm))
| ~ aInteger0(xm)
| ~ aInteger0(xn) ) ),
inference(rewrite,[status(thm)],]) ).
tff(232,plain,
( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xn,xm))
| ~ aInteger0(xm)
| ~ aInteger0(xn) ),
inference(quant_inst,[status(thm)],]) ).
tff(233,plain,
( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xn,xm))
| ~ aInteger0(xm)
| ~ aInteger0(xn) ),
inference(modus_ponens,[status(thm)],[232,231]) ).
tff(234,plain,
aInteger0(sdtpldt0(xn,xm)),
inference(unit_resolution,[status(thm)],[233,102,154,187]) ).
tff(235,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm))
| ( sdtasdt0(sdtpldt0(xn,xm),xq) = sdtasdt0(xq,sdtpldt0(xn,xm)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm))
| ( sdtasdt0(sdtpldt0(xn,xm),xq) = sdtasdt0(xq,sdtpldt0(xn,xm)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(236,plain,
( ( ( sdtasdt0(sdtpldt0(xn,xm),xq) = sdtasdt0(xq,sdtpldt0(xn,xm)) )
| ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm)) )
<=> ( ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm))
| ( sdtasdt0(sdtpldt0(xn,xm),xq) = sdtasdt0(xq,sdtpldt0(xn,xm)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(237,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(sdtpldt0(xn,xm),xq) = sdtasdt0(xq,sdtpldt0(xn,xm)) )
| ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm))
| ( sdtasdt0(sdtpldt0(xn,xm),xq) = sdtasdt0(xq,sdtpldt0(xn,xm)) ) ) ),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(sdtpldt0(xn,xm),xq) = sdtasdt0(xq,sdtpldt0(xn,xm)) )
| ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm))
| ( sdtasdt0(sdtpldt0(xn,xm),xq) = sdtasdt0(xq,sdtpldt0(xn,xm)) ) ) ),
inference(transitivity,[status(thm)],[237,235]) ).
tff(239,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(sdtpldt0(xn,xm),xq) = sdtasdt0(xq,sdtpldt0(xn,xm)) )
| ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm)) ),
inference(quant_inst,[status(thm)],]) ).
tff(240,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm))
| ( sdtasdt0(sdtpldt0(xn,xm),xq) = sdtasdt0(xq,sdtpldt0(xn,xm)) ) ),
inference(modus_ponens,[status(thm)],[239,238]) ).
tff(241,plain,
sdtasdt0(sdtpldt0(xn,xm),xq) = sdtasdt0(xq,sdtpldt0(xn,xm)),
inference(unit_resolution,[status(thm)],[240,170,157,234]) ).
tff(242,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtasdt0(sdtpldt0(xn,xm),xq),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
inference(transitivity,[status(thm)],[242,230,224,202,150,123,89]) ).
tff(244,plain,
( ( sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)) )
<=> ( sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(245,axiom,
sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(246,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)),
inference(modus_ponens,[status(thm)],[245,244]) ).
tff(247,plain,
$false,
inference(unit_resolution,[status(thm)],[246,243]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM431+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 10:20:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.59/0.60 % SZS status Theorem
% 0.59/0.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------