%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS078+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:13:19 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 31
% Syntax : Number of formulae : 77 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 1697 ( 163 equ)
% Maximal formula atoms : 88 ( 22 avg)
% Number of connectives : 2953 (1374 ~;1314 |; 189 &)
% ( 70 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 41 ( 41 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 521 ( 484 !; 27 ?; 521 :)
% Comments :
%------------------------------------------------------------------------------
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(i2003_11_14_17_19_13721_type,type,
i2003_11_14_17_19_13721: $i ).
tff(tptp_fun_Z_1_type,type,
tptp_fun_Z_1: $i > $i ).
tff(rinvR_type,type,
rinvR: ( $i * $i ) > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(cq_type,type,
cq: $i > $o ).
tff(cp_type,type,
cp: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_W_3_type,type,
tptp_fun_W_3: $i > $i ).
tff(tptp_fun_Z1_4_type,type,
tptp_fun_Z1_4: $i > $i ).
tff(tptp_fun_Z0_5_type,type,
tptp_fun_Z0_5: $i > $i ).
tff(1,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvR(X,Y)
<=> rr(Y,X) )
<=> ( rinvR(X,Y)
<=> rr(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(5,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
| ( rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
<=> rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
( rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
<=> rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) ) ),
inference(transitivity,[status(thm)],[15,13]) ).
tff(17,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(tptp_fun_Y_0(X),Z0)
& rinvR(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rs(X,tptp_fun_Y_2(X))
& ~ cq(tptp_fun_Y_2(X))
& ~ cp(tptp_fun_Y_2(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) ) )),
trans(monotonicity(quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) )
<=> ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )),
( ( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) ) )
<=> ( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) ) )),
rewrite(( ( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
<=> ( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) ) )),
( ( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) ) )
<=> ( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) ) ))),
( ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) ) )
<=> ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) ) )),
quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) )
<=> ~ ( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) )),
( ~ ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) )
<=> ~ ~ ( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) )),
rewrite(( ~ ~ ( cp(Y)
| cq(Y)
| ~ rs(X,Y) )
<=> ( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) )),
( ~ ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) )
<=> ( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ))),
( ! [Y: $i] :
~ ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) )
<=> ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(tptp_fun_Y_0(X),Z0)
& rinvR(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rs(X,tptp_fun_Y_2(X))
& ~ cq(tptp_fun_Y_2(X))
& ~ cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(tptp_fun_Y_0(X),Z0)
& rinvR(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rs(X,tptp_fun_Y_2(X))
& ~ cq(tptp_fun_Y_2(X))
& ~ cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(tptp_fun_Y_0(X),Z0)
& rinvR(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rs(X,tptp_fun_Y_2(X))
& ~ cq(tptp_fun_Y_2(X))
& ~ cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(tptp_fun_Y_0(X),Z0)
& rinvR(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rs(X,tptp_fun_Y_2(X))
& ~ cq(tptp_fun_Y_2(X))
& ~ cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(tptp_fun_Y_0(X),Z0)
& rinvR(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rs(X,tptp_fun_Y_2(X))
& ~ cq(tptp_fun_Y_2(X))
& ~ cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(tptp_fun_Y_0(X),Z0)
& rinvR(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rs(X,tptp_fun_Y_2(X))
& ~ cq(tptp_fun_Y_2(X))
& ~ cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(tptp_fun_Y_0(X),Z0)
& rinvR(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rs(X,tptp_fun_Y_2(X))
& ~ cq(tptp_fun_Y_2(X))
& ~ cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rinvR(Y,Z)
& ! [W: $i] :
( cp(W)
| ~ rs(Z,W) ) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(Y,Z0)
& rinvR(Y,Z1) )
| ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rinvR(Y,Z)
& ! [W: $i] :
( cp(W)
| ~ rs(Z,W) ) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(Y,Z0)
& rinvR(Y,Z1) )
| ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rinvR(Y,Z)
& ! [W: $i] :
( rs(Z,W)
=> cp(W) ) )
& ! [Z0: $i,Z1: $i] :
( ( rinvR(Y,Z0)
& rinvR(Y,Z1) )
=> ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rinvR(Y,Z)
& ! [W: $i] :
( cp(W)
| ~ rs(Z,W) ) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(Y,Z0)
& rinvR(Y,Z1) )
| ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rinvR(Y,Z)
& ! [W: $i] :
( rs(Z,W)
=> cp(W) ) )
& ! [Z0: $i,Z1: $i] :
( ( rinvR(Y,Z0)
& rinvR(Y,Z1) )
=> ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rinvR(Y,Z)
& ! [W: $i] :
( cp(W)
| ~ rs(Z,W) ) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(Y,Z0)
& rinvR(Y,Z1) )
| ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rinvR(Y,Z)
& ! [W: $i] :
( rs(Z,W)
=> cp(W) ) )
& ! [Z0: $i,Z1: $i] :
( ( rinvR(Y,Z0)
& rinvR(Y,Z1) )
=> ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(25,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rinvR(Y,Z)
& ! [W: $i] :
( cp(W)
| ~ rs(Z,W) ) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(Y,Z0)
& rinvR(Y,Z1) )
| ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rinvR(Y,Z)
& ! [W: $i] :
( cp(W)
| ~ rs(Z,W) ) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(Y,Z0)
& rinvR(Y,Z1) )
| ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(tptp_fun_Y_0(X),Z0)
& rinvR(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rs(X,tptp_fun_Y_2(X))
& ~ cq(tptp_fun_Y_2(X))
& ~ cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rinvR(tptp_fun_Y_0(X),Z0)
& rinvR(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rs(X,tptp_fun_Y_2(X))
& ~ cq(tptp_fun_Y_2(X))
& ~ cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ ( rinvR(Y,tptp_fun_Z0_5(Y))
& rinvR(Y,tptp_fun_Z1_4(Y)) )
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) ) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[28,18]) ).
tff(30,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) )
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) )
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[29,16]) ).
tff(31,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[30,11]) ).
tff(32,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_13721)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_13721,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(i2003_11_14_17_19_13721,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_13721)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_13721,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(i2003_11_14_17_19_13721,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_13721)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_13721,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(i2003_11_14_17_19_13721,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_13721)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_13721,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(i2003_11_14_17_19_13721,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_13721)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_13721,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(i2003_11_14_17_19_13721,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_13721)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_13721,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(i2003_11_14_17_19_13721,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_13721)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_13721,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(i2003_11_14_17_19_13721,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_13721)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_13721,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(i2003_11_14_17_19_13721,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_13721)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_13721,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(i2003_11_14_17_19_13721,Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rinvR(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| cq(tptp_fun_Y_2(X))
| cp(tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(X),Z0)
| ~ rinvR(tptp_fun_Y_0(X),Z1) )
| ~ rs(X,tptp_fun_Y_2(X))
| ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_13721)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_13721,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(i2003_11_14_17_19_13721,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_13721)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_13721,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(i2003_11_14_17_19_13721,Y) ) ) ),
inference(unit_resolution,[status(thm)],[37,31]) ).
tff(39,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_13721)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_13721,Y)
| ~ ( ~ rinvR(Y,tptp_fun_Z0_5(Y))
| ( tptp_fun_Z0_5(Y) = tptp_fun_Z1_4(Y) )
| ~ rinvR(Y,tptp_fun_Z1_4(Y)) )
| ! [Z: $i] :
( ~ rinvR(Y,Z)
| ~ ( cp(tptp_fun_W_3(Z))
| ~ rs(Z,tptp_fun_W_3(Z)) ) ) )
| ! [Y: $i] :
( cp(Y)
| cq(Y)
| ~ rs(i2003_11_14_17_19_13721,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(40,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) ),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
( cUnsatisfiable(i2003_11_14_17_19_13721)
<=> cUnsatisfiable(i2003_11_14_17_19_13721) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
cUnsatisfiable(i2003_11_14_17_19_13721),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(43,plain,
cUnsatisfiable(i2003_11_14_17_19_13721),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(45,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) )
| ~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ) ),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
~ ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ),
inference(unit_resolution,[status(thm)],[45,40]) ).
tff(47,plain,
( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721))
| rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ),
inference(tautology,[status(thm)],[]) ).
tff(48,plain,
rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
( ~ ( rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
<=> rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) )
| rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) ),
inference(tautology,[status(thm)],[]) ).
tff(50,plain,
( ~ ( rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
<=> rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721)) )
| rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721) ),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721),
inference(unit_resolution,[status(thm)],[50,9]) ).
tff(52,plain,
( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721))
| rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721)) ),
inference(tautology,[status(thm)],[]) ).
tff(53,plain,
rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721)),
inference(unit_resolution,[status(thm)],[52,46]) ).
tff(54,plain,
( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721))
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) ) ),
inference(tautology,[status(thm)],[]) ).
tff(55,plain,
! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) ),
inference(unit_resolution,[status(thm)],[54,46]) ).
tff(56,plain,
( ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
| ( i2003_11_14_17_19_13721 = tptp_fun_Z_1(i2003_11_14_17_19_13721) ) )
<=> ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
| ( i2003_11_14_17_19_13721 = tptp_fun_Z_1(i2003_11_14_17_19_13721) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ( ( i2003_11_14_17_19_13721 = tptp_fun_Z_1(i2003_11_14_17_19_13721) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721)) )
<=> ( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
| ( i2003_11_14_17_19_13721 = tptp_fun_Z_1(i2003_11_14_17_19_13721) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| ( i2003_11_14_17_19_13721 = tptp_fun_Z_1(i2003_11_14_17_19_13721) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721)) )
<=> ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
| ( i2003_11_14_17_19_13721 = tptp_fun_Z_1(i2003_11_14_17_19_13721) ) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| ( i2003_11_14_17_19_13721 = tptp_fun_Z_1(i2003_11_14_17_19_13721) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721)) )
<=> ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
| ( i2003_11_14_17_19_13721 = tptp_fun_Z_1(i2003_11_14_17_19_13721) ) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| ( i2003_11_14_17_19_13721 = tptp_fun_Z_1(i2003_11_14_17_19_13721) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
| ( i2003_11_14_17_19_13721 = tptp_fun_Z_1(i2003_11_14_17_19_13721) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
i2003_11_14_17_19_13721 = tptp_fun_Z_1(i2003_11_14_17_19_13721),
inference(unit_resolution,[status(thm)],[61,55,53,51]) ).
tff(63,plain,
( rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
<=> rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),tptp_fun_Y_2(i2003_11_14_17_19_13721)) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),tptp_fun_Y_2(i2003_11_14_17_19_13721))
<=> rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721)) ),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),tptp_fun_Y_2(i2003_11_14_17_19_13721))
<=> ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721)) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_19_13721)) ),
inference(tautology,[status(thm)],[]) ).
tff(67,plain,
~ cp(tptp_fun_Y_2(i2003_11_14_17_19_13721)),
inference(unit_resolution,[status(thm)],[66,46]) ).
tff(68,plain,
( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721))
| ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) ) ),
inference(tautology,[status(thm)],[]) ).
tff(69,plain,
! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) ),
inference(unit_resolution,[status(thm)],[68,46]) ).
tff(70,plain,
( ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),tptp_fun_Y_2(i2003_11_14_17_19_13721)) )
<=> ( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),tptp_fun_Y_2(i2003_11_14_17_19_13721)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),tptp_fun_Y_2(i2003_11_14_17_19_13721)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),tptp_fun_Y_2(i2003_11_14_17_19_13721)) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),tptp_fun_Y_2(i2003_11_14_17_19_13721)),
inference(unit_resolution,[status(thm)],[72,69,67]) ).
tff(74,plain,
~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721)),
inference(modus_ponens,[status(thm)],[73,65]) ).
tff(75,plain,
( ~ ! [W: $i] :
( cp(W)
| ~ rs(tptp_fun_Z_1(i2003_11_14_17_19_13721),W) )
| ~ rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),Z1) )
| cp(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| cq(tptp_fun_Y_2(i2003_11_14_17_19_13721))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_19_13721),tptp_fun_Z_1(i2003_11_14_17_19_13721))
| ~ rr(i2003_11_14_17_19_13721,tptp_fun_Y_0(i2003_11_14_17_19_13721))
| rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721)) ),
inference(tautology,[status(thm)],[]) ).
tff(76,plain,
rs(i2003_11_14_17_19_13721,tptp_fun_Y_2(i2003_11_14_17_19_13721)),
inference(unit_resolution,[status(thm)],[75,46]) ).
tff(77,plain,
$false,
inference(unit_resolution,[status(thm)],[76,74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KRS078+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n001.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 19:14:49 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% See solution above
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------