%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS128+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 Jun 21 05:13:27 AM UTC 2025
% Result : Unsatisfiable 0.14s 0.38s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 50
% Syntax : Number of formulae : 121 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 1436 ( 0 equ)
% Maximal formula atoms : 56 ( 11 avg)
% Number of connectives : 2584 (1341 ~; 995 |; 110 &)
% ( 132 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 72 ( 72 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 424 ( 374 !; 32 ?; 424 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px4_type,type,
ra_Px4: ( $i * $i ) > $o ).
tff(tptp_fun_Y0_7_type,type,
tptp_fun_Y0_7: $i > $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_22_31584_type,type,
i2003_11_14_17_22_31584: $i ).
tff(ca_Cx4_type,type,
ca_Cx4: $i > $o ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(cexcomp_type,type,
cexcomp: $i > $o ).
tff(cd_type,type,
cd: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(ca_Cx4xcomp_type,type,
ca_Cx4xcomp: $i > $o ).
tff(tptp_fun_Y_8_type,type,
tptp_fun_Y_8: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) )
<=> ~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) )
<=> ~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) )
<=> ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) )),
( ( ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
& ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) )
<=> ( ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
& ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) ) )),
rewrite(( ( ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
& ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) )
<=> ~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) ) )),
( ( ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
& ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) )
<=> ~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [X: $i] :
( ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
& ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [X: $i] :
( ca_Cx4(X)
<=> ? [Y0: $i] : ra_Px4(X,Y0) )
<=> ! [X: $i] :
( ca_Cx4(X)
<=> ? [Y0: $i] : ra_Px4(X,Y0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
! [X: $i] :
( ca_Cx4(X)
<=> ? [Y0: $i] : ra_Px4(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(10,plain,
! [X: $i] :
( ca_Cx4(X)
<=> ? [Y0: $i] : ra_Px4(X,Y0) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i] :
( ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
& ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Cx4(X)
| ra_Px4(X,tptp_fun_Y0_7(X)) )
| ~ ( ca_Cx4(X)
| ! [Y0: $i] : ~ ra_Px4(X,Y0) ) )
| ~ ( ~ ( ~ ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),tptp_fun_Y0_7(tptp_fun_Y_0(i2003_11_14_17_22_31584))) )
| ~ ( ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ! [Y0: $i] : ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),Y0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
~ ( ~ ( ~ ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),tptp_fun_Y0_7(tptp_fun_Y_0(i2003_11_14_17_22_31584))) )
| ~ ( ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ! [Y0: $i] : ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),Y0) ) ),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ ( ~ ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),tptp_fun_Y0_7(tptp_fun_Y_0(i2003_11_14_17_22_31584))) )
| ~ ( ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ! [Y0: $i] : ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),Y0) )
| ~ ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),tptp_fun_Y0_7(tptp_fun_Y_0(i2003_11_14_17_22_31584))) ),
inference(tautology,[status(thm)],[]) ).
tff(17,plain,
( ~ ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),tptp_fun_Y0_7(tptp_fun_Y_0(i2003_11_14_17_22_31584))) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) ) ),
inference(transitivity,[status(thm)],[23,21]) ).
tff(25,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cexcomp(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) ) )),
trans(monotonicity(quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ( rr(X,Y)
& cexcomp(Y) )
<=> ~ ( ~ rr(X,Y)
| ~ cexcomp(Y) ) )),
( ~ ( rr(X,Y)
& cexcomp(Y) )
<=> ~ ~ ( ~ rr(X,Y)
| ~ cexcomp(Y) ) )),
rewrite(( ~ ~ ( ~ rr(X,Y)
| ~ cexcomp(Y) )
<=> ( ~ rr(X,Y)
| ~ cexcomp(Y) ) )),
( ~ ( rr(X,Y)
& cexcomp(Y) )
<=> ( ~ rr(X,Y)
| ~ cexcomp(Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cexcomp(Y) )
<=> ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cexcomp(Y) )
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) )
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) )
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) ) )
<=> ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cexcomp(Y) )
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) ) )
<=> ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cexcomp(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cexcomp(Y) )
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cexcomp(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cexcomp(Y) )
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cexcomp(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cexcomp(Y) )
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cexcomp(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cexcomp(Y) )
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cexcomp(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cexcomp(Y) )
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cexcomp(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cexcomp(Y) )
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cexcomp(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cexcomp(Y) )
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cexcomp(Y) )
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cexcomp(Y) )
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cexcomp(Y) )
& ! [Y: $i] :
( rr(X,Y)
=> cd(Y) )
& ! [Y: $i] :
( rr(X,Y)
=> ca_Cx4(Y) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cexcomp(Y) )
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cexcomp(Y) )
& ! [Y: $i] :
( rr(X,Y)
=> cd(Y) )
& ! [Y: $i] :
( rr(X,Y)
=> ca_Cx4(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cexcomp(Y) )
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cexcomp(Y) )
& ! [Y: $i] :
( rr(X,Y)
=> cd(Y) )
& ! [Y: $i] :
( rr(X,Y)
=> ca_Cx4(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(33,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cexcomp(Y) )
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cexcomp(Y) )
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cexcomp(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cexcomp(Y) )
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) ) ) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cexcomp(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cexcomp(Y) )
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) ) ) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[36,26]) ).
tff(38,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[37,24]) ).
tff(39,plain,
! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[38,19]) ).
tff(40,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ca_Cx4(tptp_fun_Y_2(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_2(i2003_11_14_17_22_31584)) )
| ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_1(i2003_11_14_17_22_31584)) )
| ! [Y: $i] :
( ~ cexcomp(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ca_Cx4(tptp_fun_Y_2(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_2(i2003_11_14_17_22_31584)) )
| ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_1(i2003_11_14_17_22_31584)) )
| ! [Y: $i] :
( ~ cexcomp(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_1(i2003_11_14_17_22_31584)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_2(i2003_11_14_17_22_31584)) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_22_31584,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ca_Cx4(tptp_fun_Y_2(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_2(i2003_11_14_17_22_31584)) )
| ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_1(i2003_11_14_17_22_31584)) )
| ! [Y: $i] :
( ~ cexcomp(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_1(i2003_11_14_17_22_31584)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_2(i2003_11_14_17_22_31584)) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_22_31584,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ca_Cx4(tptp_fun_Y_2(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_2(i2003_11_14_17_22_31584)) )
| ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_1(i2003_11_14_17_22_31584)) )
| ! [Y: $i] :
( ~ cexcomp(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_1(i2003_11_14_17_22_31584)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_2(i2003_11_14_17_22_31584)) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_22_31584,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ca_Cx4(tptp_fun_Y_2(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_2(i2003_11_14_17_22_31584)) )
| ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_1(i2003_11_14_17_22_31584)) )
| ! [Y: $i] :
( ~ cexcomp(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) ) ) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_1(i2003_11_14_17_22_31584)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_2(i2003_11_14_17_22_31584)) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_22_31584,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_1(X)) )
| ~ ( ca_Cx4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cexcomp(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cexcomp(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
| ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ca_Cx4(tptp_fun_Y_2(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_2(i2003_11_14_17_22_31584)) )
| ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_1(i2003_11_14_17_22_31584)) )
| ! [Y: $i] :
( ~ cexcomp(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) ) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ca_Cx4(tptp_fun_Y_2(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_2(i2003_11_14_17_22_31584)) )
| ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_1(i2003_11_14_17_22_31584)) )
| ! [Y: $i] :
( ~ cexcomp(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) ) ),
inference(unit_resolution,[status(thm)],[45,39]) ).
tff(47,plain,
( ~ ( cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ca_Cx4(tptp_fun_Y_2(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_2(i2003_11_14_17_22_31584)) )
| ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_1(i2003_11_14_17_22_31584)) )
| ! [Y: $i] :
( ~ cexcomp(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(48,plain,
( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) ),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
( cUnsatisfiable(i2003_11_14_17_22_31584)
<=> cUnsatisfiable(i2003_11_14_17_22_31584) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
cUnsatisfiable(i2003_11_14_17_22_31584),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
tff(51,plain,
cUnsatisfiable(i2003_11_14_17_22_31584),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(53,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) )
| ~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) ),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
~ ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ),
inference(unit_resolution,[status(thm)],[53,48]) ).
tff(55,plain,
( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584))
| rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ),
inference(tautology,[status(thm)],[]) ).
tff(56,plain,
rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(58,plain,
! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ),
inference(unit_resolution,[status(thm)],[57,54]) ).
tff(59,plain,
( ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) )
<=> ( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584)),
inference(unit_resolution,[status(thm)],[61,58,56]) ).
tff(63,plain,
( ~ ( ~ ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),tptp_fun_Y0_7(tptp_fun_Y_0(i2003_11_14_17_22_31584))) )
| ~ ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),tptp_fun_Y0_7(tptp_fun_Y_0(i2003_11_14_17_22_31584))) ),
inference(tautology,[status(thm)],[]) ).
tff(64,plain,
( ~ ( ~ ca_Cx4(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),tptp_fun_Y0_7(tptp_fun_Y_0(i2003_11_14_17_22_31584))) )
| ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),tptp_fun_Y0_7(tptp_fun_Y_0(i2003_11_14_17_22_31584))) ),
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),tptp_fun_Y0_7(tptp_fun_Y_0(i2003_11_14_17_22_31584))),
inference(unit_resolution,[status(thm)],[64,17]) ).
tff(66,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) )
<=> ~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ~ ca_Cx4xcomp(X)
| ! [Y: $i] : ~ ra_Px4(X,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [X: $i] :
~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ~ ca_Cx4xcomp(X)
| ! [Y: $i] : ~ ra_Px4(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) )
<=> ~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [X: $i] :
~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) )
<=> ~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [X: $i] :
~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [X: $i] :
~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) )
<=> ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) )),
( ( ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
& ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) )
<=> ( ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
& ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ) )),
rewrite(( ( ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
& ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) )
<=> ~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ) )),
( ( ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
& ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) )
<=> ~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [X: $i] :
( ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
& ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
^ [X: $i] :
rewrite(( ( ( ra_Px4(X,tptp_fun_Y_8(X))
| ca_Cx4xcomp(X) )
& ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) )
<=> ( ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
& ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [X: $i] :
( ( ra_Px4(X,tptp_fun_Y_8(X))
| ca_Cx4xcomp(X) )
& ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) )
<=> ! [X: $i] :
( ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
& ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [X: $i] :
~ ( ? [Y: $i] : ra_Px4(X,Y)
<=> ca_Cx4xcomp(X) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px4(X,Y)
<=> ca_Cx4xcomp(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ~ ? [Y: $i] : ra_Px4(X,Y)
<=> ~ ? [Y: $i] : ra_Px4(X,Y) )),
( ( ca_Cx4xcomp(X)
<=> ~ ? [Y: $i] : ra_Px4(X,Y) )
<=> ( ca_Cx4xcomp(X)
<=> ~ ? [Y: $i] : ra_Px4(X,Y) ) )),
rewrite(( ( ca_Cx4xcomp(X)
<=> ~ ? [Y: $i] : ra_Px4(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px4(X,Y)
<=> ca_Cx4xcomp(X) ) )),
( ( ca_Cx4xcomp(X)
<=> ~ ? [Y: $i] : ra_Px4(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px4(X,Y)
<=> ca_Cx4xcomp(X) ) )),
rewrite(( ~ ( ? [Y: $i] : ra_Px4(X,Y)
<=> ca_Cx4xcomp(X) )
<=> ~ ( ? [Y: $i] : ra_Px4(X,Y)
<=> ca_Cx4xcomp(X) ) )),
( ( ca_Cx4xcomp(X)
<=> ~ ? [Y: $i] : ra_Px4(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px4(X,Y)
<=> ca_Cx4xcomp(X) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [X: $i] :
( ca_Cx4xcomp(X)
<=> ~ ? [Y: $i] : ra_Px4(X,Y) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px4(X,Y)
<=> ca_Cx4xcomp(X) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [X: $i] :
( ca_Cx4xcomp(X)
<=> ~ ? [Y: $i] : ra_Px4(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
tff(81,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px4(X,Y)
<=> ca_Cx4xcomp(X) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px4(X,Y)
<=> ca_Cx4xcomp(X) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [X: $i] :
( ( ra_Px4(X,tptp_fun_Y_8(X))
| ca_Cx4xcomp(X) )
& ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [X: $i] :
( ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
& ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
! [X: $i] :
~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[84,74]) ).
tff(86,plain,
! [X: $i] :
~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[85,72]) ).
tff(87,plain,
! [X: $i] :
~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ~ ca_Cx4xcomp(X)
| ! [Y: $i] : ~ ra_Px4(X,Y) ) ),
inference(modus_ponens,[status(thm)],[86,67]) ).
tff(88,plain,
( ~ ! [X: $i] :
~ ( ~ ( ca_Cx4xcomp(X)
| ra_Px4(X,tptp_fun_Y_8(X)) )
| ~ ( ~ ca_Cx4xcomp(X)
| ! [Y: $i] : ~ ra_Px4(X,Y) ) )
| ~ ( ~ ( ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_22_31584))) )
| ~ ( ~ ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ! [Y: $i] : ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
~ ( ~ ( ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_22_31584))) )
| ~ ( ~ ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ! [Y: $i] : ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),Y) ) ),
inference(unit_resolution,[status(thm)],[88,87]) ).
tff(90,plain,
( ~ ( ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_22_31584))) )
| ~ ( ~ ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ! [Y: $i] : ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),Y) )
| ~ ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ! [Y: $i] : ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),Y) ),
inference(tautology,[status(thm)],[]) ).
tff(91,plain,
( ~ ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ! [Y: $i] : ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),Y) ),
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
^ [X: $i] :
refl(( ~ ( ( ~ cd(X)
| ~ cexcomp(X) )
<=> ca_Cx4xcomp(X) )
<=> ~ ( ( ~ cd(X)
| ~ cexcomp(X) )
<=> ca_Cx4xcomp(X) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [X: $i] :
~ ( ( ~ cd(X)
| ~ cexcomp(X) )
<=> ca_Cx4xcomp(X) )
<=> ! [X: $i] :
~ ( ( ~ cd(X)
| ~ cexcomp(X) )
<=> ca_Cx4xcomp(X) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ( cd(X)
& cexcomp(X) )
<=> ~ ( ~ cd(X)
| ~ cexcomp(X) ) )),
( ( ca_Cx4xcomp(X)
<=> ( cd(X)
& cexcomp(X) ) )
<=> ( ca_Cx4xcomp(X)
<=> ~ ( ~ cd(X)
| ~ cexcomp(X) ) ) )),
rewrite(( ( ca_Cx4xcomp(X)
<=> ~ ( ~ cd(X)
| ~ cexcomp(X) ) )
<=> ~ ( ( ~ cd(X)
| ~ cexcomp(X) )
<=> ca_Cx4xcomp(X) ) )),
( ( ca_Cx4xcomp(X)
<=> ( cd(X)
& cexcomp(X) ) )
<=> ~ ( ( ~ cd(X)
| ~ cexcomp(X) )
<=> ca_Cx4xcomp(X) ) )),
rewrite(( ~ ( ( ~ cd(X)
| ~ cexcomp(X) )
<=> ca_Cx4xcomp(X) )
<=> ~ ( ( ~ cd(X)
| ~ cexcomp(X) )
<=> ca_Cx4xcomp(X) ) )),
( ( ca_Cx4xcomp(X)
<=> ( cd(X)
& cexcomp(X) ) )
<=> ~ ( ( ~ cd(X)
| ~ cexcomp(X) )
<=> ca_Cx4xcomp(X) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [X: $i] :
( ca_Cx4xcomp(X)
<=> ( cd(X)
& cexcomp(X) ) )
<=> ! [X: $i] :
~ ( ( ~ cd(X)
| ~ cexcomp(X) )
<=> ca_Cx4xcomp(X) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [X: $i] :
( ca_Cx4xcomp(X)
<=> ( cd(X)
& cexcomp(X) ) )
<=> ! [X: $i] :
( ca_Cx4xcomp(X)
<=> ( cd(X)
& cexcomp(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
! [X: $i] :
( ca_Cx4xcomp(X)
<=> ( cd(X)
& cexcomp(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
tff(98,plain,
! [X: $i] :
( ca_Cx4xcomp(X)
<=> ( cd(X)
& cexcomp(X) ) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [X: $i] :
( ca_Cx4xcomp(X)
<=> ( cd(X)
& cexcomp(X) ) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [X: $i] :
~ ( ( ~ cd(X)
| ~ cexcomp(X) )
<=> ca_Cx4xcomp(X) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [X: $i] :
~ ( ( ~ cd(X)
| ~ cexcomp(X) )
<=> ca_Cx4xcomp(X) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
( ~ ! [X: $i] :
~ ( ( ~ cd(X)
| ~ cexcomp(X) )
<=> ca_Cx4xcomp(X) )
| ~ ( ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584)) )
<=> ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
~ ( ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584)) )
<=> ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584)) ),
inference(unit_resolution,[status(thm)],[102,101]) ).
tff(104,plain,
( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(105,plain,
! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) ),
inference(unit_resolution,[status(thm)],[104,54]) ).
tff(106,plain,
( ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| cd(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) )
<=> ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| cd(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| cd(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| cd(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584)) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
cd(tptp_fun_Y_0(i2003_11_14_17_22_31584)),
inference(unit_resolution,[status(thm)],[108,105,56]) ).
tff(110,plain,
( ~ ! [Y: $i] :
( ca_Cx4(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_22_31584,Y) )
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ rr(i2003_11_14_17_22_31584,tptp_fun_Y_0(i2003_11_14_17_22_31584))
| cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584)) ),
inference(tautology,[status(thm)],[]) ).
tff(111,plain,
cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584)),
inference(unit_resolution,[status(thm)],[110,54]) ).
tff(112,plain,
( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584)) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584)) ),
inference(tautology,[status(thm)],[]) ).
tff(113,plain,
( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584)) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_22_31584)) ),
inference(unit_resolution,[status(thm)],[112,111]) ).
tff(114,plain,
~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584)) ),
inference(unit_resolution,[status(thm)],[113,109]) ).
tff(115,plain,
( ( ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584)) )
<=> ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584)) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ~ cexcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584)) ),
inference(tautology,[status(thm)],[]) ).
tff(116,plain,
ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584)),
inference(unit_resolution,[status(thm)],[115,114,103]) ).
tff(117,plain,
( ~ ( ~ ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ! [Y: $i] : ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),Y) )
| ~ ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ! [Y: $i] : ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),Y) ),
inference(tautology,[status(thm)],[]) ).
tff(118,plain,
( ~ ( ~ ca_Cx4xcomp(tptp_fun_Y_0(i2003_11_14_17_22_31584))
| ! [Y: $i] : ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),Y) )
| ! [Y: $i] : ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),Y) ),
inference(unit_resolution,[status(thm)],[117,116]) ).
tff(119,plain,
! [Y: $i] : ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),Y),
inference(unit_resolution,[status(thm)],[118,91]) ).
tff(120,plain,
( ~ ! [Y: $i] : ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),Y)
| ~ ra_Px4(tptp_fun_Y_0(i2003_11_14_17_22_31584),tptp_fun_Y0_7(tptp_fun_Y_0(i2003_11_14_17_22_31584))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
$false,
inference(unit_resolution,[status(thm)],[120,119,65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KRS128+1 : TPTP v9.0.0. Released v3.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n004.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 Jun 19 19:11:08 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.38 % SZS status Unsatisfiable
% 0.14/0.38 % SZS output start Proof
% See solution above
% 0.22/0.41 % E exiting
%------------------------------------------------------------------------------