TSTP Solution File: NUM435+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM435+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 13:09:41 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 33
% Syntax : Number of formulae : 73 ( 24 unt; 10 typ; 0 def)
% Number of atoms : 395 ( 98 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 501 ( 205 ~; 173 |; 75 &)
% ( 39 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 36 ( 36 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 117 ( 102 !; 0 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xp_type,type,
xp: $i ).
tff(xq_type,type,
xq: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(xb_type,type,
xb: $i ).
tff(xa_type,type,
xa: $i ).
tff(aInteger0_type,type,
aInteger0: $i > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(1,plain,
( aInteger0(xm)
<=> aInteger0(xm) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
( aInteger0(xm)
& ( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1032) ).
tff(3,plain,
aInteger0(xm),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aInteger0(xm),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( aInteger0(xq)
<=> aInteger0(xq) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& ( xp != sz00 )
& aInteger0(xq)
& ( xq != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__979) ).
tff(7,plain,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& ( xp != sz00 )
& aInteger0(xq) ),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
aInteger0(xq),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
aInteger0(xq),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
( aInteger0(xp)
<=> aInteger0(xp) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& ( xp != sz00 ) ),
inference(and_elim,[status(thm)],[7]) ).
tff(12,plain,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp) ),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
aInteger0(xp),
inference(and_elim,[status(thm)],[12]) ).
tff(14,plain,
aInteger0(xp),
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,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(16,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)],[15]) ).
tff(17,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(18,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)],[17]) ).
tff(19,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(20,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(21,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)],[20]) ).
tff(22,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(23,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)],[22,21]) ).
tff(24,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)],[23,19]) ).
tff(25,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)],[24]) ).
tff(26,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)],[25,18]) ).
tff(27,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)],[26,16]) ).
tff(28,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xp)
| ~ aInteger0(xq)
| ~ aInteger0(xm)
| ( sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(sdtasdt0(xq,xp),xm) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xp)
| ~ aInteger0(xq)
| ~ aInteger0(xm)
| ( sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(sdtasdt0(xq,xp),xm) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( ( sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(sdtasdt0(xq,xp),xm) )
| ~ aInteger0(xm)
| ~ aInteger0(xp)
| ~ aInteger0(xq) )
<=> ( ~ aInteger0(xp)
| ~ aInteger0(xq)
| ~ aInteger0(xm)
| ( sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(sdtasdt0(xq,xp),xm) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(sdtasdt0(xq,xp),xm) )
| ~ aInteger0(xm)
| ~ aInteger0(xp)
| ~ aInteger0(xq) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xp)
| ~ aInteger0(xq)
| ~ aInteger0(xm)
| ( sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(sdtasdt0(xq,xp),xm) ) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(sdtasdt0(xq,xp),xm) )
| ~ aInteger0(xm)
| ~ aInteger0(xp)
| ~ aInteger0(xq) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xp)
| ~ aInteger0(xq)
| ~ aInteger0(xm)
| ( sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(sdtasdt0(xq,xp),xm) ) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(sdtasdt0(xq,xp),xm) )
| ~ aInteger0(xm)
| ~ aInteger0(xp)
| ~ aInteger0(xq) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xp)
| ~ aInteger0(xq)
| ~ aInteger0(xm)
| ( sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(sdtasdt0(xq,xp),xm) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(sdtasdt0(xq,xp),xm),
inference(unit_resolution,[status(thm)],[33,27,14,9,4]) ).
tff(35,plain,
sdtasdt0(sdtasdt0(xq,xp),xm) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(symmetry,[status(thm)],[34]) ).
tff(36,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(37,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)],[36]) ).
tff(38,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(39,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)],[38]) ).
tff(40,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(41,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(42,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)],[41]) ).
tff(43,axiom,
! [W0: $i,W1: $i] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
tff(44,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [W0: $i,W1: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[47,37]) ).
tff(49,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(xq,xp) = sdtasdt0(xp,xq) )
| ~ aInteger0(xp)
| ~ aInteger0(xq) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(xq,xp) = sdtasdt0(xp,xq) )
| ~ aInteger0(xp)
| ~ aInteger0(xq) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(xq,xp) = sdtasdt0(xp,xq) )
| ~ aInteger0(xp)
| ~ aInteger0(xq) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( sdtasdt0(xq,xp) = sdtasdt0(xp,xq) )
| ~ aInteger0(xp)
| ~ aInteger0(xq) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
sdtasdt0(xq,xp) = sdtasdt0(xp,xq),
inference(unit_resolution,[status(thm)],[51,48,14,9]) ).
tff(53,plain,
sdtasdt0(sdtasdt0(xq,xp),xm) = sdtasdt0(sdtasdt0(xp,xq),xm),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtasdt0(sdtasdt0(xq,xp),xm),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
( ( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)) )
<=> ( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)),
inference(and_elim,[status(thm)],[2]) ).
tff(57,plain,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(sdtasdt0(xp,xq),xm),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(transitivity,[status(thm)],[58,54,35]) ).
tff(60,plain,
( ( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)) )
<=> ( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,axiom,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(62,plain,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
$false,
inference(unit_resolution,[status(thm)],[62,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM435+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 10:40:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------