%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS112+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:13:24 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 96
% Syntax : Number of formulae : 240 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 2041 ( 88 equ)
% Maximal formula atoms : 40 ( 8 avg)
% Number of connectives : 3590 (1890 ~;1323 |; 172 &)
% ( 190 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 101 ( 101 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 682 ( 597 !; 35 ?; 682 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px1_type,type,
ra_Px1: ( $i * $i ) > $o ).
tff(tptp_fun_Y0_3_type,type,
tptp_fun_Y0_3: $i > $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_21_19256_type,type,
i2003_11_14_17_21_19256: $i ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(tptp_fun_Y_5_type,type,
tptp_fun_Y_5: $i > $i ).
tff(rf1_type,type,
rf1: ( $i * $i ) > $o ).
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(cowlThing_type,type,
cowlThing: $i > $o ).
tff(ca_Vx3_type,type,
ca_Vx3: $i > $o ).
tff(rinvF1_type,type,
rinvF1: ( $i * $i ) > $o ).
tff(cpxcomp_type,type,
cpxcomp: $i > $o ).
tff(ca_Ax2_type,type,
ca_Ax2: $i > $o ).
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $i > $i ).
tff(cp_type,type,
cp: $i > $o ).
tff(rf_type,type,
rf: ( $i * $i ) > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cowlThing(tptp_fun_Y_5(X)) ) )
<=> ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) ) )),
rewrite(( ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) ) )
<=> ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )),
( ( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cowlThing(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) ) ) )
<=> ( ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) )),
rewrite(( ( ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) )),
( ( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cowlThing(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [X: $i] :
( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cowlThing(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) ) )
<=> ! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(10,plain,
! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i] :
( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cowlThing(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) ) ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_19256,Y)
| ~ cowlThing(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_19256,Y)
| ~ cowlThing(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_19256,Y)
| ~ cowlThing(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[16,14]) ).
tff(18,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_19256,Y)
| ~ cowlThing(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) ) ),
inference(unit_resolution,[status(thm)],[19,13]) ).
tff(21,plain,
( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) )
| ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(22,plain,
( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
<=> ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) )),
( ( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ( ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) )),
rewrite(( ( ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) )),
( ( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
^ [X: $i] :
rewrite(( ( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] :
( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
<=> ! [X: $i] :
( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [X: $i] :
rewrite(( ( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( rinvF1(X,Y)
=> ca_Vx3(Y) ) ) )
<=> ( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [X: $i] :
( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( rinvF1(X,Y)
=> ca_Vx3(Y) ) ) )
<=> ! [X: $i] :
( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [X: $i] :
( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( rinvF1(X,Y)
=> ca_Vx3(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(38,plain,
! [X: $i] :
( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [X: $i] :
( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ),
inference(modus_ponens,[status(thm)],[41,31]) ).
tff(43,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ),
inference(modus_ponens,[status(thm)],[42,29]) ).
tff(44,plain,
! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[43,24]) ).
tff(45,plain,
( ~ ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) )
| ~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_19256)))
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_19256)))
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) ) ),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_19256)))
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(48,plain,
( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) ),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& ca_Ax2(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& ca_Ax2(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& ca_Ax2(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(60,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& ca_Ax2(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[62,55]) ).
tff(64,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[63,53]) ).
tff(65,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_19256,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_19256,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_19256,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_19256,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_19256,Y)
| ~ cp(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_19256,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_19256,Y)
| ~ cp(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_19256,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[67,65]) ).
tff(69,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_19256,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_19256,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_19256,Y) ) ) ),
inference(unit_resolution,[status(thm)],[70,64]) ).
tff(72,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_19256,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(73,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) ),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
( cUnsatisfiable(i2003_11_14_17_21_19256)
<=> cUnsatisfiable(i2003_11_14_17_21_19256) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
cUnsatisfiable(i2003_11_14_17_21_19256),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
tff(76,plain,
cUnsatisfiable(i2003_11_14_17_21_19256),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(78,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) )
| ~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) ),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
~ ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ),
inference(unit_resolution,[status(thm)],[78,73]) ).
tff(80,plain,
( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256)) ),
inference(tautology,[status(thm)],[]) ).
tff(81,plain,
ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(83,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) )
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) ),
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ),
inference(unit_resolution,[status(thm)],[83,48]) ).
tff(85,plain,
( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) )
| ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(86,plain,
! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvF1(X,Y)
<=> rf1(Y,X) )
<=> ( rinvF1(X,Y)
<=> rf1(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
tff(91,plain,
! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
( ~ ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) )
| ( rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256)
<=> rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
( rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256)
<=> rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ),
inference(tautology,[status(thm)],[]) ).
tff(97,plain,
rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[96,79]) ).
tff(98,plain,
( ~ ( rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256)
<=> rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) )
| rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256)
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ),
inference(tautology,[status(thm)],[]) ).
tff(99,plain,
( ~ ( rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256)
<=> rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) )
| rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256) ),
inference(unit_resolution,[status(thm)],[98,97]) ).
tff(100,plain,
rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256),
inference(unit_resolution,[status(thm)],[99,95]) ).
tff(101,plain,
( ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) )
| ca_Vx3(i2003_11_14_17_21_19256)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256) )
<=> ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) )
| ca_Vx3(i2003_11_14_17_21_19256)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) )
| ca_Vx3(i2003_11_14_17_21_19256)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) )
| ca_Vx3(i2003_11_14_17_21_19256)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
ca_Vx3(i2003_11_14_17_21_19256),
inference(unit_resolution,[status(thm)],[103,100,86]) ).
tff(105,plain,
( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(106,plain,
( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,plain,
~ ( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(unit_resolution,[status(thm)],[106,22]) ).
tff(108,plain,
( ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(tautology,[status(thm)],[]) ).
tff(109,plain,
rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[108,107]) ).
tff(110,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rs(X,Y)
| rf1(X,Y) )
<=> ( ~ rs(X,Y)
| rf1(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(111,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rs(X,Y)
=> rf1(X,Y) )
<=> ( ~ rs(X,Y)
| rf1(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [X: $i,Y: $i] :
( rs(X,Y)
=> rf1(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,axiom,
! [X: $i,Y: $i] :
( rs(X,Y)
=> rf1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
tff(116,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[116,112]) ).
tff(118,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[118,111]) ).
tff(120,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[122,119,109]) ).
tff(124,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(( ( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
<=> ( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(125,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rf1(X,Y)
& rf1(X,Z) )
<=> ~ ( ~ rf1(X,Y)
| ~ rf1(X,Z) ) )),
( ~ ( rf1(X,Y)
& rf1(X,Z) )
<=> ~ ~ ( ~ rf1(X,Y)
| ~ rf1(X,Z) ) )),
rewrite(( ~ ~ ( ~ rf1(X,Y)
| ~ rf1(X,Z) )
<=> ( ~ rf1(X,Y)
| ~ rf1(X,Z) ) )),
( ~ ( rf1(X,Y)
& rf1(X,Z) )
<=> ( ~ rf1(X,Y)
| ~ rf1(X,Z) ) )),
( ( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ( ~ rf1(X,Y)
| ~ rf1(X,Z)
| ( Y = Z ) ) )),
rewrite(( ( ~ rf1(X,Y)
| ~ rf1(X,Z)
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) ) )),
( ( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( rf1(X,Y)
& rf1(X,Z) )
=> ( Y = Z ) )
<=> ( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ) )),
inference(bind,[status(th)],[]) ).
tff(130,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rf1(X,Y)
& rf1(X,Z) )
=> ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rf1(X,Y)
& rf1(X,Z) )
=> ( Y = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(132,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[132,128]) ).
tff(134,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[133]) ).
tff(135,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) ),
inference(modus_ponens,[status(thm)],[134,127]) ).
tff(136,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) ),
inference(modus_ponens,[status(thm)],[135,125]) ).
tff(137,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,plain,
( ( ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) )
<=> ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(transitivity,[status(thm)],[139,137]) ).
tff(141,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256),
inference(unit_resolution,[status(thm)],[142,136,97,123]) ).
tff(144,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rs(X,Y)
| rf(X,Y) )
<=> ( ~ rs(X,Y)
| rf(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(145,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rs(X,Y)
=> rf(X,Y) )
<=> ( ~ rs(X,Y)
| rf(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(148,plain,
( ! [X: $i,Y: $i] :
( rs(X,Y)
=> rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,axiom,
! [X: $i,Y: $i] :
( rs(X,Y)
=> rf(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
tff(150,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(skolemize,[status(sab)],[151]) ).
tff(153,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[152,145]) ).
tff(154,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[156,153,109]) ).
tff(158,plain,
( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256)) ),
inference(tautology,[status(thm)],[]) ).
tff(159,plain,
rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[158,79]) ).
tff(160,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(( ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
<=> ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(161,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) ),
inference(quant_intro,[status(thm)],[160]) ).
tff(162,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rf(X,Y)
& rf(X,Z) )
<=> ~ ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ~ ( rf(X,Y)
& rf(X,Z) )
<=> ~ ~ ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
rewrite(( ~ ~ ( ~ rf(X,Y)
| ~ rf(X,Z) )
<=> ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ~ ( rf(X,Y)
& rf(X,Z) )
<=> ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ( ~ rf(X,Y)
| ~ rf(X,Z)
| ( Y = Z ) ) )),
rewrite(( ( ~ rf(X,Y)
| ~ rf(X,Z)
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(163,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(165,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) )
<=> ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) )),
inference(bind,[status(th)],[]) ).
tff(166,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) ),
inference(quant_intro,[status(thm)],[165]) ).
tff(167,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(168,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[168,164]) ).
tff(170,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[169]) ).
tff(171,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ),
inference(modus_ponens,[status(thm)],[170,163]) ).
tff(172,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ),
inference(modus_ponens,[status(thm)],[171,161]) ).
tff(173,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(174,plain,
( ( ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256)) )
<=> ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(175,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(transitivity,[status(thm)],[175,173]) ).
tff(177,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(178,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(modus_ponens,[status(thm)],[177,176]) ).
tff(179,plain,
tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256),
inference(unit_resolution,[status(thm)],[178,172,159,157]) ).
tff(180,plain,
tptp_fun_Y_1(i2003_11_14_17_21_19256) = tptp_fun_Y_5(i2003_11_14_17_21_19256),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
tptp_fun_Y_1(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256),
inference(transitivity,[status(thm)],[180,143]) ).
tff(182,plain,
( ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256)))
<=> ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ),
inference(monotonicity,[status(thm)],[181]) ).
tff(183,plain,
( ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256)))
<=> ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(185,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[184]) ).
tff(186,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(187,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[186]) ).
tff(188,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[187,185]) ).
tff(189,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) )
<=> ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )),
( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
rewrite(( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(190,plain,
( ! [X: $i] :
( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[189]) ).
tff(191,plain,
( ! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) )
<=> ! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(192,axiom,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(193,plain,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
! [X: $i] :
( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(skolemize,[status(sab)],[193]) ).
tff(195,plain,
! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[194,190]) ).
tff(196,plain,
! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[195,188]) ).
tff(197,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
| ~ ( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) )
| ~ ( cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(198,plain,
~ ( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) )
| ~ ( cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y0) ) ),
inference(unit_resolution,[status(thm)],[197,196]) ).
tff(199,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) )
| ~ ( cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y0) )
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ),
inference(tautology,[status(thm)],[]) ).
tff(200,plain,
( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ),
inference(unit_resolution,[status(thm)],[199,198]) ).
tff(201,plain,
( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) )
| cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256)) ),
inference(tautology,[status(thm)],[]) ).
tff(202,plain,
cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[201,84]) ).
tff(203,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) )
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ),
inference(tautology,[status(thm)],[]) ).
tff(204,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) )
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ),
inference(unit_resolution,[status(thm)],[203,202]) ).
tff(205,plain,
ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))),
inference(unit_resolution,[status(thm)],[204,200]) ).
tff(206,plain,
ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))),
inference(modus_ponens,[status(thm)],[205,183]) ).
tff(207,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(208,plain,
( ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[207]) ).
tff(209,plain,
^ [X: $i] :
refl(( ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(210,plain,
( ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(quant_intro,[status(thm)],[209]) ).
tff(211,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(212,plain,
( ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(quant_intro,[status(thm)],[211]) ).
tff(213,plain,
( ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(transitivity,[status(thm)],[212,210]) ).
tff(214,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) )
<=> ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )),
( ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
rewrite(( ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
( ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(215,plain,
( ! [X: $i] :
( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(quant_intro,[status(thm)],[214]) ).
tff(216,plain,
^ [X: $i] :
rewrite(( ( ( ra_Px1(X,tptp_fun_Y_2(X))
| cp(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(217,plain,
( ! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_2(X))
| cp(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(quant_intro,[status(thm)],[216]) ).
tff(218,plain,
( ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(219,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ~ ? [Y: $i] : ra_Px1(X,Y)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )),
( ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ) )),
rewrite(( ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) )),
( ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) )),
rewrite(( ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) )),
( ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) )),
inference(bind,[status(th)],[]) ).
tff(220,plain,
( ! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) ),
inference(quant_intro,[status(thm)],[219]) ).
tff(221,axiom,
! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(222,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ),
inference(modus_ponens,[status(thm)],[221,220]) ).
tff(223,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ),
inference(modus_ponens,[status(thm)],[222,218]) ).
tff(224,plain,
! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_2(X))
| cp(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(skolemize,[status(sab)],[223]) ).
tff(225,plain,
! [X: $i] :
( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(modus_ponens,[status(thm)],[224,217]) ).
tff(226,plain,
! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(modus_ponens,[status(thm)],[225,215]) ).
tff(227,plain,
! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(modus_ponens,[status(thm)],[226,213]) ).
tff(228,plain,
! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ),
inference(modus_ponens,[status(thm)],[227,208]) ).
tff(229,plain,
( ~ ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
| ~ ( ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y_2(tptp_fun_Y_1(i2003_11_14_17_21_19256))) )
| ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(230,plain,
~ ( ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y_2(tptp_fun_Y_1(i2003_11_14_17_21_19256))) )
| ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) ) ),
inference(unit_resolution,[status(thm)],[229,228]) ).
tff(231,plain,
( ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y_2(tptp_fun_Y_1(i2003_11_14_17_21_19256))) )
| ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) ),
inference(tautology,[status(thm)],[]) ).
tff(232,plain,
( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) ),
inference(unit_resolution,[status(thm)],[231,230]) ).
tff(233,plain,
( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| cp(tptp_fun_Y_1(i2003_11_14_17_21_19256)) ),
inference(tautology,[status(thm)],[]) ).
tff(234,plain,
cp(tptp_fun_Y_1(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[233,79]) ).
tff(235,plain,
( ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) ),
inference(tautology,[status(thm)],[]) ).
tff(236,plain,
( ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) )
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) ),
inference(unit_resolution,[status(thm)],[235,234]) ).
tff(237,plain,
! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y),
inference(unit_resolution,[status(thm)],[236,232]) ).
tff(238,plain,
( ~ ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y)
| ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(239,plain,
~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))),
inference(unit_resolution,[status(thm)],[238,237]) ).
tff(240,plain,
$false,
inference(unit_resolution,[status(thm)],[239,206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KRS112+1 : TPTP v9.0.0. Released v3.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n007.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 Jun 19 19:12:35 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------