TSTP Solution File: COM017+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM017+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Tue Sep 6 18:05:49 EDT 2022
% Result : Theorem 0.18s 0.41s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 53
% Syntax : Number of formulae : 107 ( 26 unt; 16 typ; 0 def)
% Number of atoms : 1155 ( 0 equ)
% Maximal formula atoms : 76 ( 12 avg)
% Number of connectives : 2014 ( 972 ~; 729 |; 250 &)
% ( 52 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 22 ( 22 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 289 ( 254 !; 27 ?; 289 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtmndtasgtdt0_type,type,
sdtmndtasgtdt0: ( $i * $i * $i ) > $o ).
tff(tptp_fun_W4_1_type,type,
tptp_fun_W4_1: ( $i * $i * $i ) > $i ).
tff(xR_type,type,
xR: $i ).
tff(xu_type,type,
xu: $i ).
tff(xv_type,type,
xv: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(aReductOfIn0_type,type,
aReductOfIn0: ( $i * $i * $i ) > $o ).
tff(isLocallyConfluent0_type,type,
isLocallyConfluent0: $i > $o ).
tff(tptp_fun_W3_5_type,type,
tptp_fun_W3_5: $i > $i ).
tff(tptp_fun_W2_6_type,type,
tptp_fun_W2_6: $i > $i ).
tff(tptp_fun_W1_7_type,type,
tptp_fun_W1_7: $i > $i ).
tff(aRewritingSystem0_type,type,
aRewritingSystem0: $i > $o ).
tff(isTerminating0_type,type,
isTerminating0: $i > $o ).
tff(xa_type,type,
xa: $i ).
tff(xc_type,type,
xc: $i ).
tff(xb_type,type,
xb: $i ).
tff(1,plain,
( aRewritingSystem0(xR)
<=> aRewritingSystem0(xR) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
tff(3,plain,
aRewritingSystem0(xR),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W0: $i] :
refl(
( ( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) )
<=> ( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [W0: $i] :
rewrite(
( ( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) )
<=> ( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[7,5]) ).
tff(9,plain,
^ [W0: $i] :
rewrite(
( ( ~ aRewritingSystem0(W0)
| ( ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ( aElement0(tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) ) ) )
& ( isLocallyConfluent0(W0)
| ( aElement0(tptp_fun_W1_7(W0))
& aElement0(tptp_fun_W2_6(W0))
& aElement0(tptp_fun_W3_5(W0))
& aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
& aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
& ! [W4: $i] :
~ ( aElement0(W4)
& sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
& sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) )
<=> ( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ( ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ( aElement0(tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) ) ) )
& ( isLocallyConfluent0(W0)
| ( aElement0(tptp_fun_W1_7(W0))
& aElement0(tptp_fun_W2_6(W0))
& aElement0(tptp_fun_W3_5(W0))
& aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
& aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
& ! [W4: $i] :
~ ( aElement0(W4)
& sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
& sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [W0: $i] :
rewrite(
( ( ~ aRewritingSystem0(W0)
| ( ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ( aElement0(tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) ) ) )
& ( isLocallyConfluent0(W0)
| ( ~ ~ ( aElement0(tptp_fun_W1_7(W0))
& aElement0(tptp_fun_W2_6(W0))
& aElement0(tptp_fun_W3_5(W0))
& aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
& aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0) )
& ! [W4: $i] :
~ ( aElement0(W4)
& sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
& sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) )
<=> ( ~ aRewritingSystem0(W0)
| ( ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ( aElement0(tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) ) ) )
& ( isLocallyConfluent0(W0)
| ( aElement0(tptp_fun_W1_7(W0))
& aElement0(tptp_fun_W2_6(W0))
& aElement0(tptp_fun_W3_5(W0))
& aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
& aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
& ! [W4: $i] :
~ ( aElement0(W4)
& sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
& sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ( ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ( aElement0(tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) ) ) )
& ( isLocallyConfluent0(W0)
| ( ~ ~ ( aElement0(tptp_fun_W1_7(W0))
& aElement0(tptp_fun_W2_6(W0))
& aElement0(tptp_fun_W3_5(W0))
& aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
& aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0) )
& ! [W4: $i] :
~ ( aElement0(W4)
& sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
& sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ( ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ( aElement0(tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) ) ) )
& ( isLocallyConfluent0(W0)
| ( aElement0(tptp_fun_W1_7(W0))
& aElement0(tptp_fun_W2_6(W0))
& aElement0(tptp_fun_W3_5(W0))
& aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
& aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
& ! [W4: $i] :
~ ( aElement0(W4)
& sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
& sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) )
<=> ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
=> ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) )
<=> ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) )),
( ( aRewritingSystem0(W0)
=> ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
=> ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) )
<=> ( aRewritingSystem0(W0)
=> ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) ) )),
rewrite(
( ( aRewritingSystem0(W0)
=> ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) )
<=> ( ~ aRewritingSystem0(W0)
| ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) ) )),
( ( aRewritingSystem0(W0)
=> ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
=> ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) )
<=> ( ~ aRewritingSystem0(W0)
| ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [W0: $i] :
( aRewritingSystem0(W0)
=> ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
=> ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) )
<=> ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [W0: $i] :
( aRewritingSystem0(W0)
=> ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
=> ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mWCRDef) ).
tff(17,plain,
! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ( isLocallyConfluent0(W0)
<=> ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ? [W4: $i] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ( ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ( aElement0(tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) ) ) )
& ( isLocallyConfluent0(W0)
| ( ~ ~ ( aElement0(tptp_fun_W1_7(W0))
& aElement0(tptp_fun_W2_6(W0))
& aElement0(tptp_fun_W3_5(W0))
& aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
& aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0) )
& ! [W4: $i] :
~ ( aElement0(W4)
& sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
& sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ( ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
| ( aElement0(tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
& sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) ) ) )
& ( isLocallyConfluent0(W0)
| ( aElement0(tptp_fun_W1_7(W0))
& aElement0(tptp_fun_W2_6(W0))
& aElement0(tptp_fun_W3_5(W0))
& aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
& aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
& ! [W4: $i] :
~ ( aElement0(W4)
& sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
& sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,10]) ).
tff(22,plain,
! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,8]) ).
tff(23,plain,
( ( ~ ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) )
| ~ aRewritingSystem0(xR)
| ~ ( ~ ( ~ isLocallyConfluent0(xR)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) ) )
| ~ ( isLocallyConfluent0(xR)
| ~ ( ~ aElement0(tptp_fun_W1_7(xR))
| ~ aElement0(tptp_fun_W2_6(xR))
| ~ aElement0(tptp_fun_W3_5(xR))
| ~ aReductOfIn0(tptp_fun_W2_6(xR),tptp_fun_W1_7(xR),xR)
| ~ aReductOfIn0(tptp_fun_W3_5(xR),tptp_fun_W1_7(xR),xR)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(xR),xR,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(xR),xR,W4) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) )
| ~ aRewritingSystem0(xR)
| ~ ( ~ ( ~ isLocallyConfluent0(xR)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) ) )
| ~ ( isLocallyConfluent0(xR)
| ~ ( ~ aElement0(tptp_fun_W1_7(xR))
| ~ aElement0(tptp_fun_W2_6(xR))
| ~ aElement0(tptp_fun_W3_5(xR))
| ~ aReductOfIn0(tptp_fun_W2_6(xR),tptp_fun_W1_7(xR),xR)
| ~ aReductOfIn0(tptp_fun_W3_5(xR),tptp_fun_W1_7(xR),xR)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(xR),xR,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(xR),xR,W4) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) )
| ~ aRewritingSystem0(xR)
| ~ ( ~ ( ~ isLocallyConfluent0(xR)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) ) )
| ~ ( isLocallyConfluent0(xR)
| ~ ( ~ aElement0(tptp_fun_W1_7(xR))
| ~ aElement0(tptp_fun_W2_6(xR))
| ~ aElement0(tptp_fun_W3_5(xR))
| ~ aReductOfIn0(tptp_fun_W2_6(xR),tptp_fun_W1_7(xR),xR)
| ~ aReductOfIn0(tptp_fun_W3_5(xR),tptp_fun_W1_7(xR),xR)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(xR),xR,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(xR),xR,W4) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ ( ~ ( ~ isLocallyConfluent0(W0)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W2,W0,tptp_fun_W4_1(W3,W2,W0))
| ~ sdtmndtasgtdt0(W3,W0,tptp_fun_W4_1(W3,W2,W0)) )
| ~ aReductOfIn0(W2,W1,W0)
| ~ aReductOfIn0(W3,W1,W0) ) )
| ~ ( isLocallyConfluent0(W0)
| ~ ( ~ aElement0(tptp_fun_W1_7(W0))
| ~ aElement0(tptp_fun_W2_6(W0))
| ~ aElement0(tptp_fun_W3_5(W0))
| ~ aReductOfIn0(tptp_fun_W2_6(W0),tptp_fun_W1_7(W0),W0)
| ~ aReductOfIn0(tptp_fun_W3_5(W0),tptp_fun_W1_7(W0),W0)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(W0),W0,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(W0),W0,W4) ) ) ) ) )
| ~ aRewritingSystem0(xR)
| ~ ( ~ ( ~ isLocallyConfluent0(xR)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) ) )
| ~ ( isLocallyConfluent0(xR)
| ~ ( ~ aElement0(tptp_fun_W1_7(xR))
| ~ aElement0(tptp_fun_W2_6(xR))
| ~ aElement0(tptp_fun_W3_5(xR))
| ~ aReductOfIn0(tptp_fun_W2_6(xR),tptp_fun_W1_7(xR),xR)
| ~ aReductOfIn0(tptp_fun_W3_5(xR),tptp_fun_W1_7(xR),xR)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(xR),xR,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(xR),xR,W4) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ ( ~ ( ~ isLocallyConfluent0(xR)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) ) )
| ~ ( isLocallyConfluent0(xR)
| ~ ( ~ aElement0(tptp_fun_W1_7(xR))
| ~ aElement0(tptp_fun_W2_6(xR))
| ~ aElement0(tptp_fun_W3_5(xR))
| ~ aReductOfIn0(tptp_fun_W2_6(xR),tptp_fun_W1_7(xR),xR)
| ~ aReductOfIn0(tptp_fun_W3_5(xR),tptp_fun_W1_7(xR),xR)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(xR),xR,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(xR),xR,W4) ) ) ) ),
inference(unit_resolution,[status(thm)],[25,22,3]) ).
tff(27,plain,
( ~ ( ~ isLocallyConfluent0(xR)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) ) )
| ~ ( isLocallyConfluent0(xR)
| ~ ( ~ aElement0(tptp_fun_W1_7(xR))
| ~ aElement0(tptp_fun_W2_6(xR))
| ~ aElement0(tptp_fun_W3_5(xR))
| ~ aReductOfIn0(tptp_fun_W2_6(xR),tptp_fun_W1_7(xR),xR)
| ~ aReductOfIn0(tptp_fun_W3_5(xR),tptp_fun_W1_7(xR),xR)
| ~ ! [W4: $i] :
( ~ aElement0(W4)
| ~ sdtmndtasgtdt0(tptp_fun_W2_6(xR),xR,W4)
| ~ sdtmndtasgtdt0(tptp_fun_W3_5(xR),xR,W4) ) ) )
| ~ isLocallyConfluent0(xR)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) ) ),
inference(tautology,[status(thm)],]) ).
tff(28,plain,
( ~ isLocallyConfluent0(xR)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) ) ),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( isLocallyConfluent0(xR)
<=> isLocallyConfluent0(xR) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
( isLocallyConfluent0(xR)
& isTerminating0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656_01) ).
tff(31,plain,
isLocallyConfluent0(xR),
inference(and_elim,[status(thm)],[30]) ).
tff(32,plain,
isLocallyConfluent0(xR),
inference(modus_ponens,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ( ~ isLocallyConfluent0(xR)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) ) )
| ~ isLocallyConfluent0(xR)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) ) ),
inference(tautology,[status(thm)],]) ).
tff(34,plain,
( ~ ( ~ isLocallyConfluent0(xR)
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) ) )
| ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) ) ),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) ),
inference(unit_resolution,[status(thm)],[34,28]) ).
tff(36,plain,
( aReductOfIn0(xv,xa,xR)
<=> aReductOfIn0(xv,xa,xR) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
( aElement0(xv)
& aReductOfIn0(xv,xa,xR)
& sdtmndtasgtdt0(xv,xR,xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__779) ).
tff(38,plain,
( aElement0(xv)
& aReductOfIn0(xv,xa,xR) ),
inference(and_elim,[status(thm)],[37]) ).
tff(39,plain,
aReductOfIn0(xv,xa,xR),
inference(and_elim,[status(thm)],[38]) ).
tff(40,plain,
aReductOfIn0(xv,xa,xR),
inference(modus_ponens,[status(thm)],[39,36]) ).
tff(41,plain,
( aElement0(xv)
<=> aElement0(xv) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
aElement0(xv),
inference(and_elim,[status(thm)],[38]) ).
tff(43,plain,
aElement0(xv),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( aReductOfIn0(xu,xa,xR)
<=> aReductOfIn0(xu,xa,xR) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& sdtmndtasgtdt0(xu,xR,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__755) ).
tff(46,plain,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR) ),
inference(and_elim,[status(thm)],[45]) ).
tff(47,plain,
aReductOfIn0(xu,xa,xR),
inference(and_elim,[status(thm)],[46]) ).
tff(48,plain,
aReductOfIn0(xu,xa,xR),
inference(modus_ponens,[status(thm)],[47,44]) ).
tff(49,plain,
( aElement0(xu)
<=> aElement0(xu) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
aElement0(xu),
inference(and_elim,[status(thm)],[46]) ).
tff(51,plain,
aElement0(xu),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( aElement0(xa)
<=> aElement0(xa) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).
tff(54,plain,
( aElement0(xa)
& aElement0(xb) ),
inference(and_elim,[status(thm)],[53]) ).
tff(55,plain,
aElement0(xa),
inference(and_elim,[status(thm)],[54]) ).
tff(56,plain,
aElement0(xa),
inference(modus_ponens,[status(thm)],[55,52]) ).
tff(57,plain,
( ( ~ ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) )
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR)
| ~ ( ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) ) )
<=> ( ~ ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) )
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR)
| ~ ( ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ( ~ aElement0(xv)
| ~ aElement0(xu)
| ~ aElement0(xa)
| ~ ( ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) )
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR) )
<=> ( ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR)
| ~ ( ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( ~ ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) )
| ~ aElement0(xv)
| ~ aElement0(xu)
| ~ aElement0(xa)
| ~ ( ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) )
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR) )
<=> ( ~ ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) )
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR)
| ~ ( ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) ) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( ~ ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) )
| ~ aElement0(xv)
| ~ aElement0(xu)
| ~ aElement0(xa)
| ~ ( ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) )
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR) )
<=> ( ~ ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) )
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR)
| ~ ( ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) ) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,plain,
( ~ ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) )
| ~ aElement0(xv)
| ~ aElement0(xu)
| ~ aElement0(xa)
| ~ ( ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) )
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [W1: $i,W2: $i,W3: $i] :
( ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ ( ~ aElement0(tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W4_1(W3,W2,xR))
| ~ sdtmndtasgtdt0(W3,xR,tptp_fun_W4_1(W3,W2,xR)) )
| ~ aReductOfIn0(W2,W1,xR)
| ~ aReductOfIn0(W3,W1,xR) )
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR)
| ~ ( ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
~ ( ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) ),
inference(unit_resolution,[status(thm)],[62,56,51,48,43,40,35]) ).
tff(64,plain,
( ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR))
| sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) ),
inference(tautology,[status(thm)],]) ).
tff(65,plain,
sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR))
| sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR)) ),
inference(tautology,[status(thm)],]) ).
tff(67,plain,
sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR)),
inference(unit_resolution,[status(thm)],[66,63]) ).
tff(68,plain,
( ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR))
| aElement0(tptp_fun_W4_1(xv,xu,xR)) ),
inference(tautology,[status(thm)],]) ).
tff(69,plain,
aElement0(tptp_fun_W4_1(xv,xu,xR)),
inference(unit_resolution,[status(thm)],[68,63]) ).
tff(70,plain,
^ [W0: $i] :
refl(
( ( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) )
<=> ( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) )
<=> ~ ( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) ) )),
( ~ ( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) )
<=> ~ ~ ( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) ) )),
rewrite(
( ~ ~ ( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) )
<=> ( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) ) )),
( ~ ( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) )
<=> ( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [W0: $i] :
~ ( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ~ ? [W0: $i] :
( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) )
<=> ~ ? [W0: $i] :
( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ~ ? [W0: $i] :
( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) )
<=> ~ ? [W0: $i] :
( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
~ ? [W0: $i] :
( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(77,plain,
~ ? [W0: $i] :
( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
~ ? [W0: $i] :
( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) ),
inference(modus_ponens,[status(thm)],[77,74]) ).
tff(79,plain,
~ ? [W0: $i] :
( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
~ ? [W0: $i] :
( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) ),
inference(modus_ponens,[status(thm)],[79,74]) ).
tff(81,plain,
~ ? [W0: $i] :
( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) ),
inference(modus_ponens,[status(thm)],[80,74]) ).
tff(82,plain,
~ ? [W0: $i] :
( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) ),
inference(modus_ponens,[status(thm)],[81,74]) ).
tff(83,plain,
~ ? [W0: $i] :
( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) ),
inference(modus_ponens,[status(thm)],[82,74]) ).
tff(84,plain,
^ [W0: $i] :
refl(
$oeq(
~ ( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) ),
~ ( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) ))),
inference(bind,[status(th)],]) ).
tff(85,plain,
! [W0: $i] :
~ ( aElement0(W0)
& sdtmndtasgtdt0(xu,xR,W0)
& sdtmndtasgtdt0(xv,xR,W0) ),
inference(nnf-neg,[status(sab)],[83,84]) ).
tff(86,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) ),
inference(modus_ponens,[status(thm)],[85,73]) ).
tff(87,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) ),
inference(modus_ponens,[status(thm)],[86,71]) ).
tff(88,plain,
( ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) )
| ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) )
<=> ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) )
| ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) )
| ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ sdtmndtasgtdt0(xv,xR,W0) )
| ~ aElement0(tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W4_1(xv,xu,xR))
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W4_1(xv,xu,xR)) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
$false,
inference(unit_resolution,[status(thm)],[90,87,69,67,65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM017+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n020.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 : Tue Aug 30 13:42:15 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.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------