TSTP Solution File: KRS127+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS127+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:44:53 EDT 2022
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 58
% Syntax : Number of formulae : 124 ( 28 unt; 13 typ; 0 def)
% Number of atoms : 1265 ( 123 equ)
% Maximal formula atoms : 32 ( 11 avg)
% Number of connectives : 2172 (1081 ~; 840 |; 160 &)
% ( 85 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 63 ( 63 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 12 >; 2 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 407 ( 364 !; 26 ?; 407 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px1_type,type,
ra_Px1: ( $i * $i ) > $o ).
tff(tptp_fun_Y0_5_type,type,
tptp_fun_Y0_5: $i > $i ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(i2003_11_14_17_22_27794_type,type,
i2003_11_14_17_22_27794: $i ).
tff(cdxcomp_type,type,
cdxcomp: $i > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(cd_type,type,
cd: $i > $o ).
tff(cc_type,type,
cc: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y1_2_type,type,
tptp_fun_Y1_2: $i > $i ).
tff(tptp_fun_Y0_3_type,type,
tptp_fun_Y0_3: $i > $i ).
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) )
<=> ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )),
( ( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
rewrite(
( ( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
( ( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [X: $i] :
( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [X: $i] :
( cdxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) )
<=> ! [X: $i] :
( cdxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
! [X: $i] :
( cdxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(10,plain,
! [X: $i] :
( cdxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i] :
( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
| ~ ( ~ ( ~ cdxcomp(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_1(i2003_11_14_17_22_27794))) )
| ~ ( cdxcomp(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y0) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
~ ( ~ ( ~ cdxcomp(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_1(i2003_11_14_17_22_27794))) )
| ~ ( cdxcomp(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y0) ) ),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ ( ~ cdxcomp(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_1(i2003_11_14_17_22_27794))) )
| ~ ( cdxcomp(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y0) )
| ~ cdxcomp(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_1(i2003_11_14_17_22_27794))) ),
inference(tautology,[status(thm)],]) ).
tff(17,plain,
( ~ cdxcomp(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_1(i2003_11_14_17_22_27794))) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) ),
inference(transitivity,[status(thm)],[23,21]) ).
tff(25,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )),
trans(
monotonicity(
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rr(X,Y)
& cc(Y) )
<=> ~ ( ~ cc(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cc(Y) )
<=> ~ ~ ( ~ cc(Y)
| ~ rr(X,Y) ) )),
rewrite(
( ~ ~ ( ~ cc(Y)
| ~ rr(X,Y) )
<=> ( ~ cc(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cc(Y) )
<=> ( ~ cc(Y)
| ~ rr(X,Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
<=> ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rr(X,Y)
& cd(Y) )
<=> ~ ( ~ cd(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cd(Y) )
<=> ~ ~ ( ~ cd(Y)
| ~ rr(X,Y) ) )),
rewrite(
( ~ ~ ( ~ cd(Y)
| ~ rr(X,Y) )
<=> ( ~ cd(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cd(Y) )
<=> ( ~ cd(Y)
| ~ rr(X,Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
<=> ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) ) )),
rewrite(
( ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
<=> ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )),
rewrite(
( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) )),
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [X: $i] :
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [X: $i] :
rewrite(
( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(33,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) ) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) ) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ),
inference(modus_ponens,[status(thm)],[36,26]) ).
tff(38,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ),
inference(modus_ponens,[status(thm)],[37,24]) ).
tff(39,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[38,19]) ).
tff(40,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794)) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794)) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) ) ) ),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794)) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(43,plain,
( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
( cUnsatisfiable(i2003_11_14_17_22_27794)
<=> cUnsatisfiable(i2003_11_14_17_22_27794) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
cUnsatisfiable(i2003_11_14_17_22_27794),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(46,plain,
cUnsatisfiable(i2003_11_14_17_22_27794),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(48,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) )
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ),
inference(unit_resolution,[status(thm)],[48,43]) ).
tff(50,plain,
( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ),
inference(tautology,[status(thm)],]) ).
tff(51,plain,
! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794)) ),
inference(tautology,[status(thm)],]) ).
tff(53,plain,
rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794)),
inference(unit_resolution,[status(thm)],[52,49]) ).
tff(54,plain,
( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794)) ),
inference(tautology,[status(thm)],]) ).
tff(55,plain,
rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794)),
inference(unit_resolution,[status(thm)],[54,49]) ).
tff(56,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ( tptp_fun_Y_0(i2003_11_14_17_22_27794) = tptp_fun_Y_1(i2003_11_14_17_22_27794) ) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ( tptp_fun_Y_0(i2003_11_14_17_22_27794) = tptp_fun_Y_1(i2003_11_14_17_22_27794) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ( ( tptp_fun_Y_0(i2003_11_14_17_22_27794) = tptp_fun_Y_1(i2003_11_14_17_22_27794) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794)) )
<=> ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ( tptp_fun_Y_0(i2003_11_14_17_22_27794) = tptp_fun_Y_1(i2003_11_14_17_22_27794) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ( tptp_fun_Y_0(i2003_11_14_17_22_27794) = tptp_fun_Y_1(i2003_11_14_17_22_27794) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ( tptp_fun_Y_0(i2003_11_14_17_22_27794) = tptp_fun_Y_1(i2003_11_14_17_22_27794) ) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ( tptp_fun_Y_0(i2003_11_14_17_22_27794) = tptp_fun_Y_1(i2003_11_14_17_22_27794) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ( tptp_fun_Y_0(i2003_11_14_17_22_27794) = tptp_fun_Y_1(i2003_11_14_17_22_27794) ) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ( tptp_fun_Y_0(i2003_11_14_17_22_27794) = tptp_fun_Y_1(i2003_11_14_17_22_27794) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794)) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ( tptp_fun_Y_0(i2003_11_14_17_22_27794) = tptp_fun_Y_1(i2003_11_14_17_22_27794) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
tptp_fun_Y_0(i2003_11_14_17_22_27794) = tptp_fun_Y_1(i2003_11_14_17_22_27794),
inference(unit_resolution,[status(thm)],[61,55,53,51]) ).
tff(63,plain,
tptp_fun_Y_1(i2003_11_14_17_22_27794) = tptp_fun_Y_0(i2003_11_14_17_22_27794),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( cdxcomp(tptp_fun_Y_1(i2003_11_14_17_22_27794))
<=> cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794)) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
<=> cdxcomp(tptp_fun_Y_1(i2003_11_14_17_22_27794)) ),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| cc(tptp_fun_Y_0(i2003_11_14_17_22_27794)) ),
inference(tautology,[status(thm)],]) ).
tff(67,plain,
cc(tptp_fun_Y_0(i2003_11_14_17_22_27794)),
inference(unit_resolution,[status(thm)],[66,49]) ).
tff(68,plain,
^ [X: $i] :
refl(
( ( cdxcomp(X)
| ~ cc(X) )
<=> ( cdxcomp(X)
| ~ cc(X) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
<=> ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
<=> ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
^ [X: $i] :
rewrite(
( ( cc(X)
=> cdxcomp(X) )
<=> ( cdxcomp(X)
| ~ cc(X) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [X: $i] :
( cc(X)
=> cdxcomp(X) )
<=> ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [X: $i] :
( cc(X)
=> cdxcomp(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(74,plain,
! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ~ ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
| cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794)) )
<=> ( ~ ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
| cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ~ ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
| cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794)) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( ~ ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
| cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794)) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794)),
inference(unit_resolution,[status(thm)],[80,77,67]) ).
tff(82,plain,
cdxcomp(tptp_fun_Y_1(i2003_11_14_17_22_27794)),
inference(modus_ponens,[status(thm)],[81,65]) ).
tff(83,plain,
( ~ ( ~ cdxcomp(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_1(i2003_11_14_17_22_27794))) )
| ~ cdxcomp(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_1(i2003_11_14_17_22_27794))) ),
inference(tautology,[status(thm)],]) ).
tff(84,plain,
ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_1(i2003_11_14_17_22_27794))),
inference(unit_resolution,[status(thm)],[83,82,17]) ).
tff(85,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) )
<=> ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) )
<=> ~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) )
<=> ~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
<=> ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )),
( ( ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) )
<=> ( ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) ) )),
rewrite(
( ( ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) )
<=> ~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) ) )),
( ( ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) )
<=> ~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [X: $i] :
( ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [X: $i] :
( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ! [X: $i] :
( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,axiom,
! [X: $i] :
( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(96,plain,
! [X: $i] :
( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [X: $i] :
( ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [X: $i] :
~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
! [X: $i] :
~ ( ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) ) ),
inference(modus_ponens,[status(thm)],[98,91]) ).
tff(100,plain,
! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ),
inference(modus_ponens,[status(thm)],[99,86]) ).
tff(101,plain,
( ~ ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
| ~ ( ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y_4(tptp_fun_Y_1(i2003_11_14_17_22_27794))) )
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
~ ( ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y_4(tptp_fun_Y_1(i2003_11_14_17_22_27794))) )
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) ) ),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
( ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y_4(tptp_fun_Y_1(i2003_11_14_17_22_27794))) )
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) ),
inference(tautology,[status(thm)],]) ).
tff(104,plain,
( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) ),
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| cd(tptp_fun_Y_1(i2003_11_14_17_22_27794)) ),
inference(tautology,[status(thm)],]) ).
tff(106,plain,
cd(tptp_fun_Y_1(i2003_11_14_17_22_27794)),
inference(unit_resolution,[status(thm)],[105,49]) ).
tff(107,plain,
( ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) ),
inference(tautology,[status(thm)],]) ).
tff(108,plain,
( ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) )
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) ),
inference(unit_resolution,[status(thm)],[107,106]) ).
tff(109,plain,
! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y),
inference(unit_resolution,[status(thm)],[108,104]) ).
tff(110,plain,
( ~ ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y)
| ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_1(i2003_11_14_17_22_27794))) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
$false,
inference(unit_resolution,[status(thm)],[110,109,84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS127+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Sep 1 09:32:27 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------