TSTP Solution File: NUM426+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM426+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 13:09:37 EDT 2022
% Result : Theorem 98.90s 63.60s
% Output : Proof 98.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 142
% Syntax : Number of formulae : 347 ( 96 unt; 10 typ; 0 def)
% Number of atoms : 2118 ( 739 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 3223 (1566 ~;1181 |; 253 &)
% ( 181 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 124 ( 124 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 572 ( 513 !; 0 ?; 572 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(xa_type,type,
xa: $i ).
tff(xb_type,type,
xb: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(xq_type,type,
xq: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(aInteger0_type,type,
aInteger0: $i > $o ).
tff(sz10_type,type,
sz10: $i ).
tff(1,plain,
( aInteger0(xa)
<=> aInteger0(xa) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& ( xq != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__704) ).
tff(3,plain,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
( aInteger0(xa)
& aInteger0(xb) ),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aInteger0(xa),
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
aInteger0(xa),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
^ [W0: $i] :
refl(
( ( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
<=> ( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
<=> ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
<=> ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(
( ( aInteger0(W0)
=> aInteger0(smndt0(W0)) )
<=> ( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [W0: $i] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) )
<=> ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [W0: $i] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
tff(13,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xa))
| ~ aInteger0(xa) )
<=> ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xa))
| ~ aInteger0(xa) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xa))
| ~ aInteger0(xa) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xa))
| ~ aInteger0(xa) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
aInteger0(smndt0(xa)),
inference(unit_resolution,[status(thm)],[19,16,6]) ).
tff(21,plain,
( aInteger0(xb)
<=> aInteger0(xb) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
aInteger0(xb),
inference(and_elim,[status(thm)],[4]) ).
tff(23,plain,
aInteger0(xb),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,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(25,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)],[24]) ).
tff(26,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(27,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)],[26]) ).
tff(28,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(29,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(30,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)],[29]) ).
tff(31,axiom,
! [W0: $i,W1: $i] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
tff(32,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[35,25]) ).
tff(37,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xa))
| aInteger0(sdtpldt0(xb,smndt0(xa))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xa))
| aInteger0(sdtpldt0(xb,smndt0(xa))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(xa))
| ~ aInteger0(xb) )
<=> ( ~ aInteger0(xb)
| ~ aInteger0(smndt0(xa))
| aInteger0(sdtpldt0(xb,smndt0(xa))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(xa))
| ~ aInteger0(xb) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xa))
| aInteger0(sdtpldt0(xb,smndt0(xa))) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(xa))
| ~ aInteger0(xb) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xa))
| aInteger0(sdtpldt0(xb,smndt0(xa))) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(xa))
| ~ aInteger0(xb) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xa))
| aInteger0(sdtpldt0(xb,smndt0(xa))) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
aInteger0(sdtpldt0(xb,smndt0(xa))),
inference(unit_resolution,[status(thm)],[42,36,23,20]) ).
tff(44,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(45,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)],[44]) ).
tff(46,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(47,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)],[46]) ).
tff(48,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(49,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(50,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)],[49]) ).
tff(51,axiom,
! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
tff(52,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[55,45]) ).
tff(57,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ ( ( sdtpldt0(sdtpldt0(xb,smndt0(xa)),sz00) != sdtpldt0(xb,smndt0(xa)) )
| ( sdtpldt0(xb,smndt0(xa)) != sdtpldt0(sz00,sdtpldt0(xb,smndt0(xa))) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ ( ( sdtpldt0(sdtpldt0(xb,smndt0(xa)),sz00) != sdtpldt0(xb,smndt0(xa)) )
| ( sdtpldt0(xb,smndt0(xa)) != sdtpldt0(sz00,sdtpldt0(xb,smndt0(xa))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ ( ( sdtpldt0(sdtpldt0(xb,smndt0(xa)),sz00) != sdtpldt0(xb,smndt0(xa)) )
| ( sdtpldt0(xb,smndt0(xa)) != sdtpldt0(sz00,sdtpldt0(xb,smndt0(xa))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ ( ( sdtpldt0(sdtpldt0(xb,smndt0(xa)),sz00) != sdtpldt0(xb,smndt0(xa)) )
| ( sdtpldt0(xb,smndt0(xa)) != sdtpldt0(sz00,sdtpldt0(xb,smndt0(xa))) ) ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
~ ( ( sdtpldt0(sdtpldt0(xb,smndt0(xa)),sz00) != sdtpldt0(xb,smndt0(xa)) )
| ( sdtpldt0(xb,smndt0(xa)) != sdtpldt0(sz00,sdtpldt0(xb,smndt0(xa))) ) ),
inference(unit_resolution,[status(thm)],[59,56,43]) ).
tff(61,plain,
( ( sdtpldt0(sdtpldt0(xb,smndt0(xa)),sz00) != sdtpldt0(xb,smndt0(xa)) )
| ( sdtpldt0(xb,smndt0(xa)) != sdtpldt0(sz00,sdtpldt0(xb,smndt0(xa))) )
| ( sdtpldt0(xb,smndt0(xa)) = sdtpldt0(sz00,sdtpldt0(xb,smndt0(xa))) ) ),
inference(tautology,[status(thm)],]) ).
tff(62,plain,
sdtpldt0(xb,smndt0(xa)) = sdtpldt0(sz00,sdtpldt0(xb,smndt0(xa))),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
sdtpldt0(sz00,sdtpldt0(xb,smndt0(xa))) = sdtpldt0(xb,smndt0(xa)),
inference(symmetry,[status(thm)],[62]) ).
tff(64,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(65,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xb))
| ~ aInteger0(xb) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xb))
| ~ aInteger0(xb) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
aInteger0(smndt0(xb)),
inference(unit_resolution,[status(thm)],[66,16,23]) ).
tff(68,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(69,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)],[68]) ).
tff(70,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(71,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)],[70]) ).
tff(72,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(73,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(74,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)],[73]) ).
tff(75,axiom,
! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
tff(76,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[78,71]) ).
tff(80,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[79,69]) ).
tff(81,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(smndt0(xb))
| ~ ( ( sdtpldt0(smndt0(xb),smndt0(smndt0(xb))) != sz00 )
| ( sz00 != sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(smndt0(xb))
| ~ ( ( sdtpldt0(smndt0(xb),smndt0(smndt0(xb))) != sz00 )
| ( sz00 != sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(smndt0(xb))
| ~ ( ( sdtpldt0(smndt0(xb),smndt0(smndt0(xb))) != sz00 )
| ( sz00 != sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(smndt0(xb))
| ~ ( ( sdtpldt0(smndt0(xb),smndt0(smndt0(xb))) != sz00 )
| ( sz00 != sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)) ) ) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
~ ( ( sdtpldt0(smndt0(xb),smndt0(smndt0(xb))) != sz00 )
| ( sz00 != sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)) ) ),
inference(unit_resolution,[status(thm)],[83,80,67]) ).
tff(85,plain,
( ( sdtpldt0(smndt0(xb),smndt0(smndt0(xb))) != sz00 )
| ( sz00 != sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)) )
| ( sz00 = sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)) ) ),
inference(tautology,[status(thm)],]) ).
tff(86,plain,
sz00 = sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
sdtpldt0(sz00,sdtpldt0(xb,smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),sdtpldt0(xb,smndt0(xa))),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
sdtpldt0(sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),sdtpldt0(xb,smndt0(xa))) = sdtpldt0(sz00,sdtpldt0(xb,smndt0(xa))),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(smndt0(xb)))
| ~ aInteger0(smndt0(xb)) )
<=> ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(smndt0(xb)))
| ~ aInteger0(smndt0(xb)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(smndt0(xb)))
| ~ aInteger0(smndt0(xb)) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(smndt0(xb)))
| ~ aInteger0(smndt0(xb)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
aInteger0(smndt0(smndt0(xb))),
inference(unit_resolution,[status(thm)],[91,16,67]) ).
tff(93,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(94,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)],[93]) ).
tff(95,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(96,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)],[95]) ).
tff(97,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(98,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(99,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)],[98]) ).
tff(100,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(101,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)],[100,99]) ).
tff(102,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)],[101,97]) ).
tff(103,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)],[102]) ).
tff(104,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)],[103,96]) ).
tff(105,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)],[104,94]) ).
tff(106,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(smndt0(xb)))
| ( sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),sdtpldt0(xb,smndt0(xa))) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(smndt0(xb)))
| ( sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),sdtpldt0(xb,smndt0(xa))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ( ( sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),sdtpldt0(xb,smndt0(xa))) )
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(smndt0(xb))) )
<=> ( ~ aInteger0(smndt0(xb))
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(smndt0(xb)))
| ( sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),sdtpldt0(xb,smndt0(xa))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),sdtpldt0(xb,smndt0(xa))) )
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(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(smndt0(xb))
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(smndt0(xb)))
| ( sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),sdtpldt0(xb,smndt0(xa))) ) ) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),sdtpldt0(xb,smndt0(xa))) )
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(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(smndt0(xb))
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(smndt0(xb)))
| ( sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),sdtpldt0(xb,smndt0(xa))) ) ) ),
inference(transitivity,[status(thm)],[108,106]) ).
tff(110,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),sdtpldt0(xb,smndt0(xa))) )
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(smndt0(xb))) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(smndt0(xb)))
| ( sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),sdtpldt0(xb,smndt0(xa))) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
( ~ aInteger0(smndt0(smndt0(xb)))
| ( sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),sdtpldt0(xb,smndt0(xa))) ) ),
inference(unit_resolution,[status(thm)],[111,105,67,43]) ).
tff(113,plain,
sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa)))) = sdtpldt0(sdtpldt0(smndt0(smndt0(xb)),smndt0(xb)),sdtpldt0(xb,smndt0(xa))),
inference(unit_resolution,[status(thm)],[112,92]) ).
tff(114,plain,
^ [W0: $i] :
refl(
( ( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(115,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,plain,
^ [W0: $i] :
rewrite(
( ( ~ aInteger0(W0)
| ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
& ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(117,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
& ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
& ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
& ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
^ [W0: $i] :
rewrite(
( ( aInteger0(W0)
=> ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
& ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) )
<=> ( ~ aInteger0(W0)
| ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
& ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(120,plain,
( ! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
& ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
& ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,axiom,
! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
& ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
tff(122,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
& ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
& ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
& ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) ),
inference(modus_ponens,[status(thm)],[124,117]) ).
tff(126,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) ),
inference(modus_ponens,[status(thm)],[125,115]) ).
tff(127,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtasdt0(smndt0(sz10),xa) != smndt0(xa) )
| ( smndt0(xa) != sdtasdt0(xa,smndt0(sz10)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtasdt0(smndt0(sz10),xa) != smndt0(xa) )
| ( smndt0(xa) != sdtasdt0(xa,smndt0(sz10)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtasdt0(smndt0(sz10),xa) != smndt0(xa) )
| ( smndt0(xa) != sdtasdt0(xa,smndt0(sz10)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtasdt0(smndt0(sz10),xa) != smndt0(xa) )
| ( smndt0(xa) != sdtasdt0(xa,smndt0(sz10)) ) ) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
~ ( ( sdtasdt0(smndt0(sz10),xa) != smndt0(xa) )
| ( smndt0(xa) != sdtasdt0(xa,smndt0(sz10)) ) ),
inference(unit_resolution,[status(thm)],[129,126,6]) ).
tff(131,plain,
( ( sdtasdt0(smndt0(sz10),xa) != smndt0(xa) )
| ( smndt0(xa) != sdtasdt0(xa,smndt0(sz10)) )
| ( smndt0(xa) = sdtasdt0(xa,smndt0(sz10)) ) ),
inference(tautology,[status(thm)],]) ).
tff(132,plain,
smndt0(xa) = sdtasdt0(xa,smndt0(sz10)),
inference(unit_resolution,[status(thm)],[131,130]) ).
tff(133,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(smndt0(xa))
| ~ ( ( smndt0(xa) != sdtpldt0(sz00,smndt0(xa)) )
| ( sdtpldt0(smndt0(xa),sz00) != smndt0(xa) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(smndt0(xa))
| ~ ( ( smndt0(xa) != sdtpldt0(sz00,smndt0(xa)) )
| ( sdtpldt0(smndt0(xa),sz00) != smndt0(xa) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( ~ aInteger0(smndt0(xa))
| ~ ( ( sdtpldt0(smndt0(xa),sz00) != smndt0(xa) )
| ( smndt0(xa) != sdtpldt0(sz00,smndt0(xa)) ) ) )
<=> ( ~ aInteger0(smndt0(xa))
| ~ ( ( smndt0(xa) != sdtpldt0(sz00,smndt0(xa)) )
| ( sdtpldt0(smndt0(xa),sz00) != smndt0(xa) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(smndt0(xa))
| ~ ( ( sdtpldt0(smndt0(xa),sz00) != smndt0(xa) )
| ( smndt0(xa) != sdtpldt0(sz00,smndt0(xa)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(smndt0(xa))
| ~ ( ( smndt0(xa) != sdtpldt0(sz00,smndt0(xa)) )
| ( sdtpldt0(smndt0(xa),sz00) != smndt0(xa) ) ) ) ),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(smndt0(xa))
| ~ ( ( sdtpldt0(smndt0(xa),sz00) != smndt0(xa) )
| ( smndt0(xa) != sdtpldt0(sz00,smndt0(xa)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(smndt0(xa))
| ~ ( ( smndt0(xa) != sdtpldt0(sz00,smndt0(xa)) )
| ( sdtpldt0(smndt0(xa),sz00) != smndt0(xa) ) ) ) ),
inference(transitivity,[status(thm)],[135,133]) ).
tff(137,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(smndt0(xa))
| ~ ( ( sdtpldt0(smndt0(xa),sz00) != smndt0(xa) )
| ( smndt0(xa) != sdtpldt0(sz00,smndt0(xa)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aInteger0(smndt0(xa))
| ~ ( ( smndt0(xa) != sdtpldt0(sz00,smndt0(xa)) )
| ( sdtpldt0(smndt0(xa),sz00) != smndt0(xa) ) ) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
~ ( ( smndt0(xa) != sdtpldt0(sz00,smndt0(xa)) )
| ( sdtpldt0(smndt0(xa),sz00) != smndt0(xa) ) ),
inference(unit_resolution,[status(thm)],[138,56,20]) ).
tff(140,plain,
( ( smndt0(xa) != sdtpldt0(sz00,smndt0(xa)) )
| ( sdtpldt0(smndt0(xa),sz00) != smndt0(xa) )
| ( smndt0(xa) = sdtpldt0(sz00,smndt0(xa)) ) ),
inference(tautology,[status(thm)],]) ).
tff(141,plain,
smndt0(xa) = sdtpldt0(sz00,smndt0(xa)),
inference(unit_resolution,[status(thm)],[140,139]) ).
tff(142,plain,
sdtpldt0(sz00,smndt0(xa)) = smndt0(xa),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
sdtasdt0(xa,smndt0(sz10)) = smndt0(xa),
inference(symmetry,[status(thm)],[132]) ).
tff(144,plain,
^ [W0: $i] :
refl(
( ( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(145,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,plain,
^ [W0: $i] :
rewrite(
( ( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(147,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,plain,
^ [W0: $i] :
rewrite(
( ( aInteger0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(150,plain,
( ! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,axiom,
! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
tff(152,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[152,148]) ).
tff(154,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(skolemize,[status(sab)],[153]) ).
tff(155,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[154,147]) ).
tff(156,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[155,145]) ).
tff(157,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtasdt0(xa,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xa) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtasdt0(xa,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xa) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtasdt0(xa,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xa) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtasdt0(xa,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xa) ) ) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
~ ( ( sdtasdt0(xa,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xa) ) ),
inference(unit_resolution,[status(thm)],[159,156,6]) ).
tff(161,plain,
( ( sdtasdt0(xa,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xa) )
| ( sdtasdt0(xa,sz00) = sz00 ) ),
inference(tautology,[status(thm)],]) ).
tff(162,plain,
sdtasdt0(xa,sz00) = sz00,
inference(unit_resolution,[status(thm)],[161,160]) ).
tff(163,plain,
sdtpldt0(sdtasdt0(xa,sz00),sdtasdt0(xa,smndt0(sz10))) = sdtpldt0(sz00,smndt0(xa)),
inference(monotonicity,[status(thm)],[162,143]) ).
tff(164,plain,
sz00 = sdtasdt0(xa,sz00),
inference(symmetry,[status(thm)],[162]) ).
tff(165,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(166,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(167,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)],[166,165]) ).
tff(168,plain,
~ ( ( sdtpldt0(xb,smndt0(xb)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xb),xb) ) ),
inference(unit_resolution,[status(thm)],[167,80,23]) ).
tff(169,plain,
( ( sdtpldt0(xb,smndt0(xb)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xb),xb) )
| ( sz00 = sdtpldt0(smndt0(xb),xb) ) ),
inference(tautology,[status(thm)],]) ).
tff(170,plain,
sz00 = sdtpldt0(smndt0(xb),xb),
inference(unit_resolution,[status(thm)],[169,168]) ).
tff(171,plain,
sdtpldt0(smndt0(xb),xb) = sz00,
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
sdtpldt0(smndt0(xb),xb) = sdtasdt0(xa,sz00),
inference(transitivity,[status(thm)],[171,164]) ).
tff(173,plain,
sdtpldt0(sdtpldt0(smndt0(xb),xb),smndt0(xa)) = sdtpldt0(sdtasdt0(xa,sz00),sdtasdt0(xa,smndt0(sz10))),
inference(monotonicity,[status(thm)],[172,132]) ).
tff(174,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(xb))
| ~ aInteger0(smndt0(xa))
| ( sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb),xb),smndt0(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(smndt0(xb))
| ~ aInteger0(smndt0(xa))
| ( sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb),xb),smndt0(xa)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(175,plain,
( ( ( sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb),xb),smndt0(xa)) )
| ~ aInteger0(smndt0(xa))
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xb)) )
<=> ( ~ aInteger0(xb)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(xa))
| ( sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb),xb),smndt0(xa)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(176,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb),xb),smndt0(xa)) )
| ~ aInteger0(smndt0(xa))
| ~ aInteger0(xb)
| ~ aInteger0(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(xb))
| ~ aInteger0(smndt0(xa))
| ( sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb),xb),smndt0(xa)) ) ) ),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb),xb),smndt0(xa)) )
| ~ aInteger0(smndt0(xa))
| ~ aInteger0(xb)
| ~ aInteger0(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(xb))
| ~ aInteger0(smndt0(xa))
| ( sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb),xb),smndt0(xa)) ) ) ),
inference(transitivity,[status(thm)],[176,174]) ).
tff(178,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb),xb),smndt0(xa)) )
| ~ aInteger0(smndt0(xa))
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xb)) ),
inference(quant_inst,[status(thm)],]) ).
tff(179,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(xb))
| ~ aInteger0(smndt0(xa))
| ( sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb),xb),smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa))) = sdtpldt0(sdtpldt0(smndt0(xb),xb),smndt0(xa)),
inference(unit_resolution,[status(thm)],[179,105,23,67,20]) ).
tff(181,plain,
sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa))) = sdtasdt0(xa,smndt0(sz10)),
inference(transitivity,[status(thm)],[180,173,163,142,132]) ).
tff(182,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(smndt0(xb))
| ~ ( ( sdtasdt0(smndt0(sz10),smndt0(xb)) != smndt0(smndt0(xb)) )
| ( smndt0(smndt0(xb)) != sdtasdt0(smndt0(xb),smndt0(sz10)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(smndt0(xb))
| ~ ( ( sdtasdt0(smndt0(sz10),smndt0(xb)) != smndt0(smndt0(xb)) )
| ( smndt0(smndt0(xb)) != sdtasdt0(smndt0(xb),smndt0(sz10)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(183,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(smndt0(xb))
| ~ ( ( sdtasdt0(smndt0(sz10),smndt0(xb)) != smndt0(smndt0(xb)) )
| ( smndt0(smndt0(xb)) != sdtasdt0(smndt0(xb),smndt0(sz10)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(184,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(smndt0(xb))
| ~ ( ( sdtasdt0(smndt0(sz10),smndt0(xb)) != smndt0(smndt0(xb)) )
| ( smndt0(smndt0(xb)) != sdtasdt0(smndt0(xb),smndt0(sz10)) ) ) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
~ ( ( sdtasdt0(smndt0(sz10),smndt0(xb)) != smndt0(smndt0(xb)) )
| ( smndt0(smndt0(xb)) != sdtasdt0(smndt0(xb),smndt0(sz10)) ) ),
inference(unit_resolution,[status(thm)],[184,126,67]) ).
tff(186,plain,
( ( sdtasdt0(smndt0(sz10),smndt0(xb)) != smndt0(smndt0(xb)) )
| ( smndt0(smndt0(xb)) != sdtasdt0(smndt0(xb),smndt0(sz10)) )
| ( smndt0(smndt0(xb)) = sdtasdt0(smndt0(xb),smndt0(sz10)) ) ),
inference(tautology,[status(thm)],]) ).
tff(187,plain,
smndt0(smndt0(xb)) = sdtasdt0(smndt0(xb),smndt0(sz10)),
inference(unit_resolution,[status(thm)],[186,185]) ).
tff(188,plain,
sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa)))) = sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))),
inference(monotonicity,[status(thm)],[187,181]) ).
tff(189,plain,
sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) = sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xa)))),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
( aInteger0(sz10)
<=> aInteger0(sz10) ),
inference(rewrite,[status(thm)],]) ).
tff(191,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
tff(192,plain,
aInteger0(sz10),
inference(modus_ponens,[status(thm)],[191,190]) ).
tff(193,plain,
( ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(sz10))
| ~ aInteger0(sz10) )
<=> ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(sz10))
| ~ aInteger0(sz10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(194,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(sz10))
| ~ aInteger0(sz10) ),
inference(quant_inst,[status(thm)],]) ).
tff(195,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(sz10))
| ~ aInteger0(sz10) ),
inference(modus_ponens,[status(thm)],[194,193]) ).
tff(196,plain,
aInteger0(smndt0(sz10)),
inference(unit_resolution,[status(thm)],[195,192,16]) ).
tff(197,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(198,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)],[197]) ).
tff(199,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(200,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)],[199]) ).
tff(201,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(202,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(203,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)],[202]) ).
tff(204,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(205,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)],[204,203]) ).
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)) ) ) ),
inference(modus_ponens,[status(thm)],[205,201]) ).
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)) ) ) ),
inference(skolemize,[status(sab)],[206]) ).
tff(208,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)],[207,200]) ).
tff(209,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)],[208,198]) ).
tff(210,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(xa)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(sz10))
| ~ ( ( sdtasdt0(smndt0(xb),sdtpldt0(xa,smndt0(sz10))) != sdtpldt0(sdtasdt0(smndt0(xb),xa),sdtasdt0(smndt0(xb),smndt0(sz10))) )
| ( sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) != sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) ) ) )
<=> ( ~ ! [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(xa)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(sz10))
| ~ ( ( sdtasdt0(smndt0(xb),sdtpldt0(xa,smndt0(sz10))) != sdtpldt0(sdtasdt0(smndt0(xb),xa),sdtasdt0(smndt0(xb),smndt0(sz10))) )
| ( sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) != sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(211,plain,
( ( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ~ ( ( sdtasdt0(smndt0(xb),sdtpldt0(xa,smndt0(sz10))) != sdtpldt0(sdtasdt0(smndt0(xb),xa),sdtasdt0(smndt0(xb),smndt0(sz10))) )
| ( sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) != sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) ) ) )
<=> ( ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(sz10))
| ~ ( ( sdtasdt0(smndt0(xb),sdtpldt0(xa,smndt0(sz10))) != sdtpldt0(sdtasdt0(smndt0(xb),xa),sdtasdt0(smndt0(xb),smndt0(sz10))) )
| ( sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) != sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(212,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(smndt0(sz10))
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ~ ( ( sdtasdt0(smndt0(xb),sdtpldt0(xa,smndt0(sz10))) != sdtpldt0(sdtasdt0(smndt0(xb),xa),sdtasdt0(smndt0(xb),smndt0(sz10))) )
| ( sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) != sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) ) ) )
<=> ( ~ ! [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(xa)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(sz10))
| ~ ( ( sdtasdt0(smndt0(xb),sdtpldt0(xa,smndt0(sz10))) != sdtpldt0(sdtasdt0(smndt0(xb),xa),sdtasdt0(smndt0(xb),smndt0(sz10))) )
| ( sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) != sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) ) ) ) ),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,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(smndt0(sz10))
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ~ ( ( sdtasdt0(smndt0(xb),sdtpldt0(xa,smndt0(sz10))) != sdtpldt0(sdtasdt0(smndt0(xb),xa),sdtasdt0(smndt0(xb),smndt0(sz10))) )
| ( sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) != sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) ) ) )
<=> ( ~ ! [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(xa)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(sz10))
| ~ ( ( sdtasdt0(smndt0(xb),sdtpldt0(xa,smndt0(sz10))) != sdtpldt0(sdtasdt0(smndt0(xb),xa),sdtasdt0(smndt0(xb),smndt0(sz10))) )
| ( sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) != sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) ) ) ) ),
inference(transitivity,[status(thm)],[212,210]) ).
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)) ) ) )
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ~ ( ( sdtasdt0(smndt0(xb),sdtpldt0(xa,smndt0(sz10))) != sdtpldt0(sdtasdt0(smndt0(xb),xa),sdtasdt0(smndt0(xb),smndt0(sz10))) )
| ( sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) != sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
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)) ) ) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(sz10))
| ~ ( ( sdtasdt0(smndt0(xb),sdtpldt0(xa,smndt0(sz10))) != sdtpldt0(sdtasdt0(smndt0(xb),xa),sdtasdt0(smndt0(xb),smndt0(sz10))) )
| ( sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) != sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) ) ) ),
inference(modus_ponens,[status(thm)],[214,213]) ).
tff(216,plain,
~ ( ( sdtasdt0(smndt0(xb),sdtpldt0(xa,smndt0(sz10))) != sdtpldt0(sdtasdt0(smndt0(xb),xa),sdtasdt0(smndt0(xb),smndt0(sz10))) )
| ( sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) != sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) ) ),
inference(unit_resolution,[status(thm)],[215,209,6,67,196]) ).
tff(217,plain,
( ( sdtasdt0(smndt0(xb),sdtpldt0(xa,smndt0(sz10))) != sdtpldt0(sdtasdt0(smndt0(xb),xa),sdtasdt0(smndt0(xb),smndt0(sz10))) )
| ( sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) != sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) )
| ( sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) ) ),
inference(tautology,[status(thm)],]) ).
tff(218,plain,
sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) = sdtpldt0(sdtasdt0(smndt0(xb),smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))),
inference(unit_resolution,[status(thm)],[217,216]) ).
tff(219,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(220,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)],[219]) ).
tff(221,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(222,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)],[221]) ).
tff(223,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(224,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(225,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)],[224]) ).
tff(226,axiom,
! [W0: $i,W1: $i] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
tff(227,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[226,225]) ).
tff(228,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[227,223]) ).
tff(229,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[228]) ).
tff(230,plain,
! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[229,222]) ).
tff(231,plain,
! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[230,220]) ).
tff(232,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ( sdtpldt0(smndt0(xb),xa) = sdtpldt0(xa,smndt0(xb)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ( sdtpldt0(smndt0(xb),xa) = sdtpldt0(xa,smndt0(xb)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(233,plain,
( ( ( sdtpldt0(smndt0(xb),xa) = sdtpldt0(xa,smndt0(xb)) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb)) )
<=> ( ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ( sdtpldt0(smndt0(xb),xa) = sdtpldt0(xa,smndt0(xb)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(234,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(smndt0(xb),xa) = sdtpldt0(xa,smndt0(xb)) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ( sdtpldt0(smndt0(xb),xa) = sdtpldt0(xa,smndt0(xb)) ) ) ),
inference(monotonicity,[status(thm)],[233]) ).
tff(235,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(smndt0(xb),xa) = sdtpldt0(xa,smndt0(xb)) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ( sdtpldt0(smndt0(xb),xa) = sdtpldt0(xa,smndt0(xb)) ) ) ),
inference(transitivity,[status(thm)],[234,232]) ).
tff(236,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtpldt0(smndt0(xb),xa) = sdtpldt0(xa,smndt0(xb)) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb)) ),
inference(quant_inst,[status(thm)],]) ).
tff(237,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ( sdtpldt0(smndt0(xb),xa) = sdtpldt0(xa,smndt0(xb)) ) ),
inference(modus_ponens,[status(thm)],[236,235]) ).
tff(238,plain,
sdtpldt0(smndt0(xb),xa) = sdtpldt0(xa,smndt0(xb)),
inference(unit_resolution,[status(thm)],[237,231,6,67]) ).
tff(239,plain,
sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)) = sdtasdt0(sdtpldt0(xa,smndt0(xb)),smndt0(sz10)),
inference(monotonicity,[status(thm)],[238]) ).
tff(240,plain,
sdtasdt0(sdtpldt0(xa,smndt0(xb)),smndt0(sz10)) = sdtasdt0(sdtpldt0(smndt0(xb),xa),smndt0(sz10)),
inference(symmetry,[status(thm)],[239]) ).
tff(241,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(242,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(243,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)],[242]) ).
tff(244,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)],[243,241]) ).
tff(245,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(246,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)],[245,244]) ).
tff(247,plain,
aInteger0(sdtpldt0(xa,smndt0(xb))),
inference(unit_resolution,[status(thm)],[246,36,6,67]) ).
tff(248,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ ( ( sdtasdt0(smndt0(sz10),sdtpldt0(xa,smndt0(xb))) != smndt0(sdtpldt0(xa,smndt0(xb))) )
| ( smndt0(sdtpldt0(xa,smndt0(xb))) != sdtasdt0(sdtpldt0(xa,smndt0(xb)),smndt0(sz10)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ ( ( sdtasdt0(smndt0(sz10),sdtpldt0(xa,smndt0(xb))) != smndt0(sdtpldt0(xa,smndt0(xb))) )
| ( smndt0(sdtpldt0(xa,smndt0(xb))) != sdtasdt0(sdtpldt0(xa,smndt0(xb)),smndt0(sz10)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(249,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ ( ( sdtasdt0(smndt0(sz10),sdtpldt0(xa,smndt0(xb))) != smndt0(sdtpldt0(xa,smndt0(xb))) )
| ( smndt0(sdtpldt0(xa,smndt0(xb))) != sdtasdt0(sdtpldt0(xa,smndt0(xb)),smndt0(sz10)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(250,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ ( ( sdtasdt0(smndt0(sz10),sdtpldt0(xa,smndt0(xb))) != smndt0(sdtpldt0(xa,smndt0(xb))) )
| ( smndt0(sdtpldt0(xa,smndt0(xb))) != sdtasdt0(sdtpldt0(xa,smndt0(xb)),smndt0(sz10)) ) ) ),
inference(modus_ponens,[status(thm)],[249,248]) ).
tff(251,plain,
~ ( ( sdtasdt0(smndt0(sz10),sdtpldt0(xa,smndt0(xb))) != smndt0(sdtpldt0(xa,smndt0(xb))) )
| ( smndt0(sdtpldt0(xa,smndt0(xb))) != sdtasdt0(sdtpldt0(xa,smndt0(xb)),smndt0(sz10)) ) ),
inference(unit_resolution,[status(thm)],[250,126,247]) ).
tff(252,plain,
( ( sdtasdt0(smndt0(sz10),sdtpldt0(xa,smndt0(xb))) != smndt0(sdtpldt0(xa,smndt0(xb))) )
| ( smndt0(sdtpldt0(xa,smndt0(xb))) != sdtasdt0(sdtpldt0(xa,smndt0(xb)),smndt0(sz10)) )
| ( smndt0(sdtpldt0(xa,smndt0(xb))) = sdtasdt0(sdtpldt0(xa,smndt0(xb)),smndt0(sz10)) ) ),
inference(tautology,[status(thm)],]) ).
tff(253,plain,
smndt0(sdtpldt0(xa,smndt0(xb))) = sdtasdt0(sdtpldt0(xa,smndt0(xb)),smndt0(sz10)),
inference(unit_resolution,[status(thm)],[252,251]) ).
tff(254,plain,
( ( sdtasdt0(smndt0(sz10),sdtpldt0(xa,smndt0(xb))) != smndt0(sdtpldt0(xa,smndt0(xb))) )
| ( smndt0(sdtpldt0(xa,smndt0(xb))) != sdtasdt0(sdtpldt0(xa,smndt0(xb)),smndt0(sz10)) )
| ( sdtasdt0(smndt0(sz10),sdtpldt0(xa,smndt0(xb))) = smndt0(sdtpldt0(xa,smndt0(xb))) ) ),
inference(tautology,[status(thm)],]) ).
tff(255,plain,
sdtasdt0(smndt0(sz10),sdtpldt0(xa,smndt0(xb))) = smndt0(sdtpldt0(xa,smndt0(xb))),
inference(unit_resolution,[status(thm)],[254,251]) ).
tff(256,plain,
( aInteger0(xn)
<=> aInteger0(xn) ),
inference(rewrite,[status(thm)],]) ).
tff(257,axiom,
( aInteger0(xn)
& ( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__747) ).
tff(258,plain,
aInteger0(xn),
inference(and_elim,[status(thm)],[257]) ).
tff(259,plain,
aInteger0(xn),
inference(modus_ponens,[status(thm)],[258,256]) ).
tff(260,plain,
( aInteger0(xq)
<=> aInteger0(xq) ),
inference(rewrite,[status(thm)],]) ).
tff(261,plain,
aInteger0(xq),
inference(and_elim,[status(thm)],[3]) ).
tff(262,plain,
aInteger0(xq),
inference(modus_ponens,[status(thm)],[261,260]) ).
tff(263,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(264,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)],[263]) ).
tff(265,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(266,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)],[265]) ).
tff(267,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(268,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(269,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)],[268]) ).
tff(270,axiom,
! [W0: $i,W1: $i] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
tff(271,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[270,269]) ).
tff(272,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[271,267]) ).
tff(273,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[272]) ).
tff(274,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[273,266]) ).
tff(275,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[274,264]) ).
tff(276,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(277,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(278,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)],[277]) ).
tff(279,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)],[278,276]) ).
tff(280,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(281,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)],[280,279]) ).
tff(282,plain,
sdtasdt0(xn,xq) = sdtasdt0(xq,xn),
inference(unit_resolution,[status(thm)],[281,275,262,259]) ).
tff(283,plain,
sdtasdt0(xq,xn) = sdtasdt0(xn,xq),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
( ( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) )
<=> ( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(285,plain,
sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)),
inference(and_elim,[status(thm)],[257]) ).
tff(286,plain,
sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)),
inference(modus_ponens,[status(thm)],[285,284]) ).
tff(287,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,xn),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xn,xq),
inference(transitivity,[status(thm)],[287,283]) ).
tff(289,plain,
sdtasdt0(smndt0(sz10),sdtpldt0(xa,smndt0(xb))) = sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)),
inference(monotonicity,[status(thm)],[288]) ).
tff(290,plain,
sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)) = sdtasdt0(smndt0(sz10),sdtpldt0(xa,smndt0(xb))),
inference(symmetry,[status(thm)],[289]) ).
tff(291,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(
( ( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(292,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[291]) ).
tff(293,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) )
| ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) )
<=> ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ) )),
rewrite(
( ( ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) )
<=> ( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) )
<=> ( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(294,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[293]) ).
tff(295,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(296,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,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) )
<=> ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ) )),
rewrite(
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) )
<=> ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ) )),
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) )
<=> ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ) )),
inference(bind,[status(th)],]) ).
tff(297,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ) ),
inference(quant_intro,[status(thm)],[296]) ).
tff(298,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
tff(299,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ),
inference(modus_ponens,[status(thm)],[298,297]) ).
tff(300,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ),
inference(modus_ponens,[status(thm)],[299,295]) ).
tff(301,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
| ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ),
inference(skolemize,[status(sab)],[300]) ).
tff(302,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[301,294]) ).
tff(303,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[302,292]) ).
tff(304,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xn)
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(sz10))
| ( sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)) = sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xn)
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(sz10))
| ( sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)) = sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(305,plain,
( ( ( sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)) = sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq) )
| ~ aInteger0(xq)
| ~ aInteger0(xn)
| ~ aInteger0(smndt0(sz10)) )
<=> ( ~ aInteger0(xn)
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(sz10))
| ( sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)) = sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(306,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)) = sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq) )
| ~ aInteger0(xq)
| ~ aInteger0(xn)
| ~ aInteger0(smndt0(sz10)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xn)
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(sz10))
| ( sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)) = sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq) ) ) ),
inference(monotonicity,[status(thm)],[305]) ).
tff(307,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)) = sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq) )
| ~ aInteger0(xq)
| ~ aInteger0(xn)
| ~ aInteger0(smndt0(sz10)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xn)
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(sz10))
| ( sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)) = sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq) ) ) ),
inference(transitivity,[status(thm)],[306,304]) ).
tff(308,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)) = sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq) )
| ~ aInteger0(xq)
| ~ aInteger0(xn)
| ~ aInteger0(smndt0(sz10)) ),
inference(quant_inst,[status(thm)],]) ).
tff(309,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xn)
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(sz10))
| ( sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)) = sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq) ) ),
inference(modus_ponens,[status(thm)],[308,307]) ).
tff(310,plain,
( ~ aInteger0(smndt0(sz10))
| ( sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)) = sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq) ) ),
inference(unit_resolution,[status(thm)],[309,303,262,259]) ).
tff(311,plain,
sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)) = sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq),
inference(unit_resolution,[status(thm)],[310,196]) ).
tff(312,plain,
sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq) = sdtasdt0(smndt0(sz10),sdtasdt0(xn,xq)),
inference(symmetry,[status(thm)],[311]) ).
tff(313,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(xn)
| ~ ( ( sdtasdt0(smndt0(sz10),xn) != smndt0(xn) )
| ( smndt0(xn) != sdtasdt0(xn,smndt0(sz10)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(xn)
| ~ ( ( sdtasdt0(smndt0(sz10),xn) != smndt0(xn) )
| ( smndt0(xn) != sdtasdt0(xn,smndt0(sz10)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(314,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(xn)
| ~ ( ( sdtasdt0(smndt0(sz10),xn) != smndt0(xn) )
| ( smndt0(xn) != sdtasdt0(xn,smndt0(sz10)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(315,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(smndt0(sz10),W0) != smndt0(W0) )
| ( smndt0(W0) != sdtasdt0(W0,smndt0(sz10)) ) ) )
| ~ aInteger0(xn)
| ~ ( ( sdtasdt0(smndt0(sz10),xn) != smndt0(xn) )
| ( smndt0(xn) != sdtasdt0(xn,smndt0(sz10)) ) ) ),
inference(modus_ponens,[status(thm)],[314,313]) ).
tff(316,plain,
~ ( ( sdtasdt0(smndt0(sz10),xn) != smndt0(xn) )
| ( smndt0(xn) != sdtasdt0(xn,smndt0(sz10)) ) ),
inference(unit_resolution,[status(thm)],[315,126,259]) ).
tff(317,plain,
( ( sdtasdt0(smndt0(sz10),xn) != smndt0(xn) )
| ( smndt0(xn) != sdtasdt0(xn,smndt0(sz10)) )
| ( sdtasdt0(smndt0(sz10),xn) = smndt0(xn) ) ),
inference(tautology,[status(thm)],]) ).
tff(318,plain,
sdtasdt0(smndt0(sz10),xn) = smndt0(xn),
inference(unit_resolution,[status(thm)],[317,316]) ).
tff(319,plain,
sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq) = sdtasdt0(smndt0(xn),xq),
inference(monotonicity,[status(thm)],[318]) ).
tff(320,plain,
sdtasdt0(smndt0(xn),xq) = sdtasdt0(sdtasdt0(smndt0(sz10),xn),xq),
inference(symmetry,[status(thm)],[319]) ).
tff(321,plain,
( ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xn))
| ~ aInteger0(xn) )
<=> ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xn))
| ~ aInteger0(xn) ) ),
inference(rewrite,[status(thm)],]) ).
tff(322,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xn))
| ~ aInteger0(xn) ),
inference(quant_inst,[status(thm)],]) ).
tff(323,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xn))
| ~ aInteger0(xn) ),
inference(modus_ponens,[status(thm)],[322,321]) ).
tff(324,plain,
aInteger0(smndt0(xn)),
inference(unit_resolution,[status(thm)],[323,16,259]) ).
tff(325,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(xn))
| ( sdtasdt0(smndt0(xn),xq) = sdtasdt0(xq,smndt0(xn)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(xn))
| ( sdtasdt0(smndt0(xn),xq) = sdtasdt0(xq,smndt0(xn)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(326,plain,
( ( ( sdtasdt0(smndt0(xn),xq) = sdtasdt0(xq,smndt0(xn)) )
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(xn)) )
<=> ( ~ aInteger0(xq)
| ~ aInteger0(smndt0(xn))
| ( sdtasdt0(smndt0(xn),xq) = sdtasdt0(xq,smndt0(xn)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(327,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(smndt0(xn),xq) = sdtasdt0(xq,smndt0(xn)) )
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(xn)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(xn))
| ( sdtasdt0(smndt0(xn),xq) = sdtasdt0(xq,smndt0(xn)) ) ) ),
inference(monotonicity,[status(thm)],[326]) ).
tff(328,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(smndt0(xn),xq) = sdtasdt0(xq,smndt0(xn)) )
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(xn)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(xn))
| ( sdtasdt0(smndt0(xn),xq) = sdtasdt0(xq,smndt0(xn)) ) ) ),
inference(transitivity,[status(thm)],[327,325]) ).
tff(329,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(smndt0(xn),xq) = sdtasdt0(xq,smndt0(xn)) )
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(xn)) ),
inference(quant_inst,[status(thm)],]) ).
tff(330,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(xn))
| ( sdtasdt0(smndt0(xn),xq) = sdtasdt0(xq,smndt0(xn)) ) ),
inference(modus_ponens,[status(thm)],[329,328]) ).
tff(331,plain,
sdtasdt0(smndt0(xn),xq) = sdtasdt0(xq,smndt0(xn)),
inference(unit_resolution,[status(thm)],[330,275,262,324]) ).
tff(332,plain,
sdtasdt0(xq,smndt0(xn)) = sdtasdt0(smndt0(xn),xq),
inference(symmetry,[status(thm)],[331]) ).
tff(333,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(transitivity,[status(thm)],[332,320,312,290,255,253,240,218,189,113,88,63]) ).
tff(334,plain,
( ( sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)) )
<=> ( sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(335,axiom,
sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(336,plain,
sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)),
inference(modus_ponens,[status(thm)],[335,334]) ).
tff(337,plain,
$false,
inference(unit_resolution,[status(thm)],[336,333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM426+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 10:17:05 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 98.90/63.60 % SZS status Theorem
% 98.90/63.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------