%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS085+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:20 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 34
% Syntax : Number of formulae : 79 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 1094 ( 0 equ)
% Maximal formula atoms : 56 ( 13 avg)
% Number of connectives : 2125 (1139 ~; 811 |; 103 &)
% ( 66 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 29 ( 29 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 333 ( 301 !; 18 ?; 333 :)
% Comments :
%------------------------------------------------------------------------------
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(tptp_fun_Z_1_type,type,
tptp_fun_Z_1: $i > $i ).
tff(i2003_11_14_17_19_39537_type,type,
i2003_11_14_17_19_39537: $i ).
tff(rinvR_type,type,
rinvR: ( $i * $i ) > $o ).
tff(cp1_type,type,
cp1: $i > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_W_2_type,type,
tptp_fun_W_2: $i > $i ).
tff(1,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
& cp1(X) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) )
<=> ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rr(Y,Z)
| ~ cp1(Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) )
| ~ cp1(X) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rr(Y,Z)
| ~ cp1(Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) )
| ~ cp1(X) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z)
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(Z,W) ) ) )
& cp1(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z)
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(Z,W) ) ) )
& cp1(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z)
& ! [W: $i] :
( rinvR(Z,W)
=> ~ cp1(W) ) ) )
& cp1(X) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z)
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(Z,W) ) ) )
& cp1(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z)
& ! [W: $i] :
( rinvR(Z,W)
=> ~ cp1(W) ) ) )
& cp1(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z)
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(Z,W) ) ) )
& cp1(X) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z)
& ! [W: $i] :
( rinvR(Z,W)
=> ~ cp1(W) ) ) )
& cp1(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(16,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z)
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(Z,W) ) ) )
& cp1(X) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z)
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(Z,W) ) ) )
& cp1(X) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ rr(Y,Z)
| ~ cp1(Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) )
| ~ cp1(X) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) )
| ~ rr(X,tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ cp1(i2003_11_14_17_19_39537)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_39537,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ cp1(i2003_11_14_17_19_39537)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_39537,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ cp1(i2003_11_14_17_19_39537)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_39537,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ cp1(i2003_11_14_17_19_39537)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_39537,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ cp1(i2003_11_14_17_19_39537)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_39537,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ cp1(i2003_11_14_17_19_39537)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_39537,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ cp1(i2003_11_14_17_19_39537)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_39537,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ cp1(i2003_11_14_17_19_39537)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_39537,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ cp1(i2003_11_14_17_19_39537)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_39537,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp1(X)
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X))
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(X),W) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ cp1(i2003_11_14_17_19_39537)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_39537,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ cp1(i2003_11_14_17_19_39537)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_39537,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ cp1(i2003_11_14_17_19_39537)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_39537,Y)
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ~ ( ~ cp1(tptp_fun_W_2(Z))
| ~ rinvR(Z,tptp_fun_W_2(Z)) ) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(31,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( cUnsatisfiable(i2003_11_14_17_19_39537)
<=> cUnsatisfiable(i2003_11_14_17_19_39537) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
cUnsatisfiable(i2003_11_14_17_19_39537),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(34,plain,
cUnsatisfiable(i2003_11_14_17_19_39537),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_39537)
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) )
| ~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
~ ( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ),
inference(unit_resolution,[status(thm)],[36,31]) ).
tff(38,plain,
( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) ) ),
inference(tautology,[status(thm)],[]) ).
tff(39,plain,
! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) ),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537))
| cp1(i2003_11_14_17_19_39537) ),
inference(tautology,[status(thm)],[]) ).
tff(41,plain,
cp1(i2003_11_14_17_19_39537),
inference(unit_resolution,[status(thm)],[40,37]) ).
tff(42,plain,
( ( ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ cp1(i2003_11_14_17_19_39537)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),i2003_11_14_17_19_39537) )
<=> ( ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ cp1(i2003_11_14_17_19_39537)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),i2003_11_14_17_19_39537) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ cp1(i2003_11_14_17_19_39537)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),i2003_11_14_17_19_39537) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ cp1(i2003_11_14_17_19_39537)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),i2003_11_14_17_19_39537) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),i2003_11_14_17_19_39537),
inference(unit_resolution,[status(thm)],[44,41,39]) ).
tff(46,plain,
( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537))
| rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ),
inference(tautology,[status(thm)],[]) ).
tff(47,plain,
rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)),
inference(unit_resolution,[status(thm)],[46,37]) ).
tff(48,plain,
( ~ cp1(i2003_11_14_17_19_39537)
| ~ ! [W: $i] :
( ~ cp1(W)
| ~ rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),W) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537))
| rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537)) ),
inference(tautology,[status(thm)],[]) ).
tff(49,plain,
rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537)),
inference(unit_resolution,[status(thm)],[48,37]) ).
tff(50,plain,
( ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rr(X,Y)
& rr(Y,Z) )
<=> ~ ( ~ rr(X,Y)
| ~ rr(Y,Z) ) )),
( ~ ( rr(X,Y)
& rr(Y,Z) )
<=> ~ ~ ( ~ rr(X,Y)
| ~ rr(Y,Z) ) )),
rewrite(( ~ ~ ( ~ rr(X,Y)
| ~ rr(Y,Z) )
<=> ( ~ rr(X,Y)
| ~ rr(Y,Z) ) )),
( ~ ( rr(X,Y)
& rr(Y,Z) )
<=> ( ~ rr(X,Y)
| ~ rr(Y,Z) ) )),
( ( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) )
<=> ( ~ rr(X,Y)
| ~ rr(Y,Z)
| rr(X,Z) ) )),
rewrite(( ( ~ rr(X,Y)
| ~ rr(Y,Z)
| rr(X,Z) )
<=> ( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) ) )),
( ( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) )
<=> ( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( rr(X,Y)
& rr(Y,Z) )
=> rr(X,Z) )
<=> ( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rr(X,Y)
& rr(Y,Z) )
=> rr(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rr(X,Y)
& rr(Y,Z) )
=> rr(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(57,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) ),
inference(modus_ponens,[status(thm)],[60,50]) ).
tff(62,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537))
| rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537))
| rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) )
<=> ( ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537))
| rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537))
| rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537))
| rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537))
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Y_0(i2003_11_14_17_19_39537))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_39537),tptp_fun_Z_1(i2003_11_14_17_19_39537))
| rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537)) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537)),
inference(unit_resolution,[status(thm)],[67,61,49,47]) ).
tff(69,plain,
( ~ ( rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),i2003_11_14_17_19_39537)
<=> rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537)) )
| rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),i2003_11_14_17_19_39537)
| ~ rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537)) ),
inference(tautology,[status(thm)],[]) ).
tff(70,plain,
~ ( rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),i2003_11_14_17_19_39537)
<=> rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537)) ),
inference(unit_resolution,[status(thm)],[69,68,45]) ).
tff(71,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvR(X,Y)
<=> rr(Y,X) )
<=> ( rinvR(X,Y)
<=> rr(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(72,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)],[71]) ).
tff(73,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(74,axiom,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(75,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
( ~ ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
| ( rinvR(tptp_fun_Z_1(i2003_11_14_17_19_39537),i2003_11_14_17_19_39537)
<=> rr(i2003_11_14_17_19_39537,tptp_fun_Z_1(i2003_11_14_17_19_39537)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
$false,
inference(unit_resolution,[status(thm)],[78,77,70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KRS085+1 : TPTP v9.0.0. Released v3.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.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 19:10:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38 % SZS output start Proof
% See solution above
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------