TSTP Solution File: KRS120+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS120+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 17:44:51 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 89
% Syntax : Number of formulae : 197 ( 41 unt; 16 typ; 0 def)
% Number of atoms : 1336 ( 63 equ)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 2302 (1216 ~; 819 |; 128 &)
% ( 127 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 69 ( 69 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 15 >; 3 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 436 ( 389 !; 20 ?; 436 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px1_type,type,
ra_Px1: ( $i * $i ) > $o ).
tff(tptp_fun_Y0_2_type,type,
tptp_fun_Y0_2: $i > $i ).
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $i > $i ).
tff(tptp_fun_Y_3_type,type,
tptp_fun_Y_3: $i > $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_21_48796_type,type,
i2003_11_14_17_21_48796: $i ).
tff(rf_type,type,
rf: ( $i * $i ) > $o ).
tff(cowlThing_type,type,
cowlThing: $i > $o ).
tff(cowlNothing_type,type,
cowlNothing: $i > $o ).
tff(cp1xcomp_type,type,
cp1xcomp: $i > $o ).
tff(ca_Vx3_type,type,
ca_Vx3: $i > $o ).
tff(rinvF_type,type,
rinvF: ( $i * $i ) > $o ).
tff(cp1_type,type,
cp1: $i > $o ).
tff(ca_Ax2_type,type,
ca_Ax2: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ~ ( cowlNothing(X)
| ~ cowlThing(X) )
<=> ~ ( cowlNothing(X)
| ~ cowlThing(X) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
~ ( cowlNothing(X)
| ~ cowlThing(X) )
<=> ! [X: $i] :
~ ( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(
( ( cowlThing(X)
& ~ cowlNothing(X) )
<=> ~ ( cowlNothing(X)
| ~ cowlThing(X) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
<=> ! [X: $i] :
~ ( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
<=> ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
tff(7,plain,
! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) ),
inference(skolemize,[status(sab)],[7]) ).
tff(9,plain,
! [X: $i] :
~ ( cowlNothing(X)
| ~ cowlThing(X) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X: $i] :
~ ( cowlNothing(X)
| ~ cowlThing(X) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i] :
~ ( cowlNothing(X)
| ~ cowlThing(X) )
| ~ ( cowlNothing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
~ ( cowlNothing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( cowlNothing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ),
inference(tautology,[status(thm)],]) ).
tff(14,plain,
cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),
inference(unit_resolution,[status(thm)],[13,12]) ).
tff(15,plain,
^ [X: $i] :
refl(
( ( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) )
<=> ( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) )
<=> ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
^ [X: $i] :
rewrite(
( ( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) )
<=> ( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) )
<=> ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) )
<=> ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[18,16]) ).
tff(20,plain,
^ [X: $i] :
rewrite(
( ( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ~ ( rf(X,Y0)
& rf(X,Y1) )
| ( Y0 = Y1 ) ) )
<=> ( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ~ ( rf(X,Y0)
& rf(X,Y1) )
| ( Y0 = Y1 ) ) )
<=> ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ~ ( rf(X,Y0)
& rf(X,Y1) )
| ( Y0 = Y1 ) ) )
<=> ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ~ ( rf(X,Y0)
& rf(X,Y1) )
| ( Y0 = Y1 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
^ [X: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [Y0: $i,Y1: $i] :
rewrite(
( ( ( rf(X,Y0)
& rf(X,Y1) )
=> ( Y0 = Y1 ) )
<=> ( ~ ( rf(X,Y0)
& rf(X,Y1) )
| ( Y0 = Y1 ) ) ))),
( ! [Y0: $i,Y1: $i] :
( ( rf(X,Y0)
& rf(X,Y1) )
=> ( Y0 = Y1 ) )
<=> ! [Y0: $i,Y1: $i] :
( ~ ( rf(X,Y0)
& rf(X,Y1) )
| ( Y0 = Y1 ) ) )),
( ( cowlThing(X)
=> ! [Y0: $i,Y1: $i] :
( ( rf(X,Y0)
& rf(X,Y1) )
=> ( Y0 = Y1 ) ) )
<=> ( cowlThing(X)
=> ! [Y0: $i,Y1: $i] :
( ~ ( rf(X,Y0)
& rf(X,Y1) )
| ( Y0 = Y1 ) ) ) )),
rewrite(
( ( cowlThing(X)
=> ! [Y0: $i,Y1: $i] :
( ~ ( rf(X,Y0)
& rf(X,Y1) )
| ( Y0 = Y1 ) ) )
<=> ( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ~ ( rf(X,Y0)
& rf(X,Y1) )
| ( Y0 = Y1 ) ) ) )),
( ( cowlThing(X)
=> ! [Y0: $i,Y1: $i] :
( ( rf(X,Y0)
& rf(X,Y1) )
=> ( Y0 = Y1 ) ) )
<=> ( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ~ ( rf(X,Y0)
& rf(X,Y1) )
| ( Y0 = Y1 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [X: $i] :
( cowlThing(X)
=> ! [Y0: $i,Y1: $i] :
( ( rf(X,Y0)
& rf(X,Y1) )
=> ( Y0 = Y1 ) ) )
<=> ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ~ ( rf(X,Y0)
& rf(X,Y1) )
| ( Y0 = Y1 ) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,axiom,
! [X: $i] :
( cowlThing(X)
=> ! [Y0: $i,Y1: $i] :
( ( rf(X,Y0)
& rf(X,Y1) )
=> ( Y0 = Y1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(26,plain,
! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ~ ( rf(X,Y0)
& rf(X,Y1) )
| ( Y0 = Y1 ) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ~ ( rf(X,Y0)
& rf(X,Y1) )
| ( Y0 = Y1 ) ) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ~ ( rf(X,Y0)
& rf(X,Y1) )
| ( Y0 = Y1 ) ) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[29,19]) ).
tff(31,plain,
( ( ~ ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) )
| ~ cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y1)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y0) ) )
<=> ( ~ ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) )
| ~ cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y1)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) )
| ~ cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y1)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [X: $i] :
( ~ cowlThing(X)
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(X,Y1)
| ~ rf(X,Y0) ) )
| ~ cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y1)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y0) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y1)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y0) ),
inference(unit_resolution,[status(thm)],[33,30,14]) ).
tff(35,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) ) ),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ca_Vx3(X)
| ( rf(X,tptp_fun_Y_4(X))
& cp1xcomp(tptp_fun_Y_4(X)) ) )
<=> ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) ) )),
rewrite(
( ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp1xcomp(Y) ) )
<=> ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) )),
( ( ( ~ ca_Vx3(X)
| ( rf(X,tptp_fun_Y_4(X))
& cp1xcomp(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp1xcomp(Y) ) ) )
<=> ( ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) ) )),
rewrite(
( ( ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) ) )),
( ( ( ~ ca_Vx3(X)
| ( rf(X,tptp_fun_Y_4(X))
& cp1xcomp(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp1xcomp(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [X: $i] :
( ( ~ ca_Vx3(X)
| ( rf(X,tptp_fun_Y_4(X))
& cp1xcomp(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp1xcomp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rf(X,Y)
& cp1xcomp(Y) ) )
<=> ! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rf(X,Y)
& cp1xcomp(Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rf(X,Y)
& cp1xcomp(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(44,plain,
! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rf(X,Y)
& cp1xcomp(Y) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [X: $i] :
( ( ~ ca_Vx3(X)
| ( rf(X,tptp_fun_Y_4(X))
& cp1xcomp(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp1xcomp(Y) ) ) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rf(X,tptp_fun_Y_4(X))
| ~ cp1xcomp(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ( ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ( ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y) ) ) ),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
( ~ ( ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ( ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y) ) )
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ( ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) ) ),
inference(tautology,[status(thm)],]) ).
tff(51,plain,
( ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ( ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) ) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ca_Ax2(X)
| ( rinvF(X,tptp_fun_Y_3(X))
& ca_Vx3(tptp_fun_Y_3(X))
& cp1(X) ) )
<=> ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) ) )),
rewrite(
( ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& ca_Vx3(Y) ) )
<=> ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )),
( ( ( ~ ca_Ax2(X)
| ( rinvF(X,tptp_fun_Y_3(X))
& ca_Vx3(tptp_fun_Y_3(X))
& cp1(X) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& ca_Vx3(Y) ) ) )
<=> ( ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )),
rewrite(
( ( ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )),
( ( ( ~ ca_Ax2(X)
| ( rinvF(X,tptp_fun_Y_3(X))
& ca_Vx3(tptp_fun_Y_3(X))
& cp1(X) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& ca_Vx3(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( rinvF(X,tptp_fun_Y_3(X))
& ca_Vx3(tptp_fun_Y_3(X))
& cp1(X) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& ca_Vx3(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
^ [X: $i] :
rewrite(
( ( ( ~ ca_Ax2(X)
| ( rinvF(X,tptp_fun_Y_3(X))
& ca_Vx3(tptp_fun_Y_3(X))
& cp1(X) ) )
& ( ca_Ax2(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ( ( ~ ca_Ax2(X)
| ( rinvF(X,tptp_fun_Y_3(X))
& ca_Vx3(tptp_fun_Y_3(X))
& cp1(X) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& ca_Vx3(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( rinvF(X,tptp_fun_Y_3(X))
& ca_Vx3(tptp_fun_Y_3(X))
& cp1(X) ) )
& ( ca_Ax2(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( rinvF(X,tptp_fun_Y_3(X))
& ca_Vx3(tptp_fun_Y_3(X))
& cp1(X) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& ca_Vx3(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [X: $i] :
( ca_Ax2(X)
<=> ( ? [Y: $i] :
( rinvF(X,Y)
& ca_Vx3(Y) )
& cp1(X) ) )
<=> ! [X: $i] :
( ca_Ax2(X)
<=> ( ? [Y: $i] :
( rinvF(X,Y)
& ca_Vx3(Y) )
& cp1(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
! [X: $i] :
( ca_Ax2(X)
<=> ( ? [Y: $i] :
( rinvF(X,Y)
& ca_Vx3(Y) )
& cp1(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(63,plain,
! [X: $i] :
( ca_Ax2(X)
<=> ( ? [Y: $i] :
( rinvF(X,Y)
& ca_Vx3(Y) )
& cp1(X) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [X: $i] :
( ( ~ ca_Ax2(X)
| ( rinvF(X,tptp_fun_Y_3(X))
& ca_Vx3(tptp_fun_Y_3(X))
& cp1(X) ) )
& ( ca_Ax2(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& ca_Vx3(Y) )
| ~ cp1(X) ) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [X: $i] :
( ( ~ ca_Ax2(X)
| ( rinvF(X,tptp_fun_Y_3(X))
& ca_Vx3(tptp_fun_Y_3(X))
& cp1(X) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& ca_Vx3(Y) ) ) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[66,56]) ).
tff(68,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ rinvF(X,tptp_fun_Y_3(X))
| ~ ca_Vx3(tptp_fun_Y_3(X)) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),Y) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
~ ( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),Y) ) ) ),
inference(unit_resolution,[status(thm)],[68,67]) ).
tff(70,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),Y) ) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ) ),
inference(tautology,[status(thm)],]) ).
tff(71,plain,
( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ) ),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) ) )),
rewrite(
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) ) )),
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(78,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ? [Y: $i] :
( rf(X,Y)
& ca_Ax2(Y) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ? [Y: $i] :
( rf(X,Y)
& ca_Ax2(Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ? [Y: $i] :
( rf(X,Y)
& ca_Ax2(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(81,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ? [Y: $i] :
( rf(X,Y)
& ca_Ax2(Y) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_48796)
| ~ ( ~ rf(i2003_11_14_17_21_48796,tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_48796)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_48796,Y) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_48796)
| ~ ( ~ rf(i2003_11_14_17_21_48796,tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_48796)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_48796,Y) ) ) ),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_48796)
| ~ ( ~ rf(i2003_11_14_17_21_48796,tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_48796)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_48796,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_48796)
| ~ ( ~ rf(i2003_11_14_17_21_48796,tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) ) ),
inference(tautology,[status(thm)],]) ).
tff(88,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_48796)
| ~ ( ~ rf(i2003_11_14_17_21_48796,tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) ) ),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
( cUnsatisfiable(i2003_11_14_17_21_48796)
<=> cUnsatisfiable(i2003_11_14_17_21_48796) ),
inference(rewrite,[status(thm)],]) ).
tff(90,axiom,
cUnsatisfiable(i2003_11_14_17_21_48796),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
tff(91,plain,
cUnsatisfiable(i2003_11_14_17_21_48796),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_48796)
| ~ ( ~ rf(i2003_11_14_17_21_48796,tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_48796)
| ~ ( ~ rf(i2003_11_14_17_21_48796,tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) ) ),
inference(tautology,[status(thm)],]) ).
tff(93,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_48796)
| ~ ( ~ rf(i2003_11_14_17_21_48796,tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) ) )
| ~ ( ~ rf(i2003_11_14_17_21_48796,tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) ) ),
inference(unit_resolution,[status(thm)],[92,91]) ).
tff(94,plain,
~ ( ~ rf(i2003_11_14_17_21_48796,tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) ),
inference(unit_resolution,[status(thm)],[93,88]) ).
tff(95,plain,
( ~ rf(i2003_11_14_17_21_48796,tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) ),
inference(tautology,[status(thm)],]) ).
tff(96,plain,
ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)),
inference(unit_resolution,[status(thm)],[95,94]) ).
tff(97,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ) ),
inference(tautology,[status(thm)],]) ).
tff(98,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ) )
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ) ),
inference(unit_resolution,[status(thm)],[97,96]) ).
tff(99,plain,
~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ),
inference(unit_resolution,[status(thm)],[98,71]) ).
tff(100,plain,
( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ),
inference(tautology,[status(thm)],]) ).
tff(101,plain,
ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),
inference(unit_resolution,[status(thm)],[100,99]) ).
tff(102,plain,
( ~ ( ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ( ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) ) )
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ( ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) ) ),
inference(tautology,[status(thm)],]) ).
tff(103,plain,
( ~ ( ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ( ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) ) )
| ~ ( ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) ) ),
inference(unit_resolution,[status(thm)],[102,101]) ).
tff(104,plain,
~ ( ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) ),
inference(unit_resolution,[status(thm)],[103,51]) ).
tff(105,plain,
( ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) ),
inference(tautology,[status(thm)],]) ).
tff(106,plain,
rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))),
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,plain,
^ [X: $i,Y: $i] :
refl(
( ( rinvF(X,Y)
<=> rf(Y,X) )
<=> ( rinvF(X,Y)
<=> rf(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(108,plain,
( ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,plain,
( ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,axiom,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(111,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
( ~ ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
| ( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
<=> rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
<=> rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796)) ),
inference(unit_resolution,[status(thm)],[114,113]) ).
tff(116,plain,
( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) ),
inference(tautology,[status(thm)],]) ).
tff(117,plain,
rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),
inference(unit_resolution,[status(thm)],[116,99]) ).
tff(118,plain,
( ~ ( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
<=> rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796)) )
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796)) ),
inference(tautology,[status(thm)],]) ).
tff(119,plain,
( ~ ( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
<=> rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796)) )
| rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796)) ),
inference(unit_resolution,[status(thm)],[118,117]) ).
tff(120,plain,
rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796)),
inference(unit_resolution,[status(thm)],[119,115]) ).
tff(121,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y1)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y0) )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ( tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) = tptp_fun_Y_0(i2003_11_14_17_21_48796) ) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y1)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y0) )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ( tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) = tptp_fun_Y_0(i2003_11_14_17_21_48796) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ( ( tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) = tptp_fun_Y_0(i2003_11_14_17_21_48796) )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) )
<=> ( ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ( tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) = tptp_fun_Y_0(i2003_11_14_17_21_48796) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y1)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y0) )
| ( tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) = tptp_fun_Y_0(i2003_11_14_17_21_48796) )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y1)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y0) )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ( tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) = tptp_fun_Y_0(i2003_11_14_17_21_48796) ) ) ),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y1)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y0) )
| ( tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) = tptp_fun_Y_0(i2003_11_14_17_21_48796) )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y1)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y0) )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ( tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) = tptp_fun_Y_0(i2003_11_14_17_21_48796) ) ) ),
inference(transitivity,[status(thm)],[123,121]) ).
tff(125,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y1)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y0) )
| ( tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) = tptp_fun_Y_0(i2003_11_14_17_21_48796) )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y1)
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),Y0) )
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ( tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) = tptp_fun_Y_0(i2003_11_14_17_21_48796) ) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) = tptp_fun_Y_0(i2003_11_14_17_21_48796),
inference(unit_resolution,[status(thm)],[126,120,106,34]) ).
tff(128,plain,
tptp_fun_Y_0(i2003_11_14_17_21_48796) = tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
( ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))
<=> ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) ),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
( ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))
<=> ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) ),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(132,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(134,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[133]) ).
tff(135,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[134,132]) ).
tff(136,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) )
<=> ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )),
( ( ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ( ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
rewrite(
( ( ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
( ( ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(137,plain,
( ! [X: $i] :
( ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,plain,
( ! [X: $i] :
( cp1xcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) )
<=> ! [X: $i] :
( cp1xcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,axiom,
! [X: $i] :
( cp1xcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(140,plain,
! [X: $i] :
( cp1xcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
! [X: $i] :
( ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(skolemize,[status(sab)],[140]) ).
tff(142,plain,
! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[141,137]) ).
tff(143,plain,
! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[142,135]) ).
tff(144,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
| ~ ( ~ ( ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) )
| ~ ( cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),Y0) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,plain,
~ ( ~ ( ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) )
| ~ ( cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),Y0) ) ),
inference(unit_resolution,[status(thm)],[144,143]) ).
tff(146,plain,
( ~ ( ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) )
| ~ ( cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),Y0) )
| ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) ),
inference(tautology,[status(thm)],]) ).
tff(147,plain,
( ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) ),
inference(unit_resolution,[status(thm)],[146,145]) ).
tff(148,plain,
( ~ rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)),tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) ),
inference(tautology,[status(thm)],]) ).
tff(149,plain,
cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))),
inference(unit_resolution,[status(thm)],[148,104]) ).
tff(150,plain,
( ~ ( ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) )
| ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) ),
inference(tautology,[status(thm)],]) ).
tff(151,plain,
( ~ ( ~ cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) )
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) ),
inference(unit_resolution,[status(thm)],[150,149]) ).
tff(152,plain,
ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))),
inference(unit_resolution,[status(thm)],[151,147]) ).
tff(153,plain,
ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))),
inference(modus_ponens,[status(thm)],[152,130]) ).
tff(154,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) )
<=> ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(155,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[154]) ).
tff(156,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) )
<=> ~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(157,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) ) ),
inference(quant_intro,[status(thm)],[156]) ).
tff(158,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) )
<=> ~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(159,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) ) ),
inference(quant_intro,[status(thm)],[158]) ).
tff(160,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) ) ),
inference(transitivity,[status(thm)],[159,157]) ).
tff(161,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
<=> ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )),
( ( ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) )
<=> ( ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) ) )),
rewrite(
( ( ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) )
<=> ~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) ) )),
( ( ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) )
<=> ~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(162,plain,
( ! [X: $i] :
( ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) ) ),
inference(quant_intro,[status(thm)],[161]) ).
tff(163,plain,
( ! [X: $i] :
( cp1(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ! [X: $i] :
( cp1(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(164,axiom,
! [X: $i] :
( cp1(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(165,plain,
! [X: $i] :
( cp1(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
! [X: $i] :
( ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) ),
inference(skolemize,[status(sab)],[165]) ).
tff(167,plain,
! [X: $i] :
~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) ),
inference(modus_ponens,[status(thm)],[166,162]) ).
tff(168,plain,
! [X: $i] :
~ ( ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) ) ),
inference(modus_ponens,[status(thm)],[167,160]) ).
tff(169,plain,
! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ),
inference(modus_ponens,[status(thm)],[168,155]) ).
tff(170,plain,
( ~ ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
| ~ ( ~ ( cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) )
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),Y) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
~ ( ~ ( cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) )
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),Y) ) ),
inference(unit_resolution,[status(thm)],[170,169]) ).
tff(172,plain,
( ~ ( cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) )
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),Y) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),Y) ),
inference(tautology,[status(thm)],]) ).
tff(173,plain,
( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),Y) ),
inference(unit_resolution,[status(thm)],[172,171]) ).
tff(174,plain,
( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| ~ ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))
| cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796)) ),
inference(tautology,[status(thm)],]) ).
tff(175,plain,
cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796)),
inference(unit_resolution,[status(thm)],[174,99]) ).
tff(176,plain,
( ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),Y) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),Y) ),
inference(tautology,[status(thm)],]) ).
tff(177,plain,
( ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),Y) )
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),Y) ),
inference(unit_resolution,[status(thm)],[176,175]) ).
tff(178,plain,
! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),Y),
inference(unit_resolution,[status(thm)],[177,173]) ).
tff(179,plain,
( ~ ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),Y)
| ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(180,plain,
~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_48796),tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))),
inference(unit_resolution,[status(thm)],[179,178]) ).
tff(181,plain,
$false,
inference(unit_resolution,[status(thm)],[180,153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KRS120+1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 09:39:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% See solution above
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