%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS076+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 55
% Syntax : Number of formulae : 136 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 1431 ( 88 equ)
% Maximal formula atoms : 64 ( 10 avg)
% Number of connectives : 2517 (1270 ~; 967 |; 168 &)
% ( 97 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 48 ( 48 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 518 ( 458 !; 27 ?; 518 :)
% Comments :
%------------------------------------------------------------------------------
tff(cp_type,type,
cp: $i > $o ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(i2003_11_14_17_19_06193_type,type,
i2003_11_14_17_19_06193: $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(tptp_fun_W_2_type,type,
tptp_fun_W_2: $i > $i ).
tff(rf_type,type,
rf: ( $i * $i ) > $o ).
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(cowlThing_type,type,
cowlThing: $i > $o ).
tff(rinvF1_type,type,
rinvF1: ( $i * $i ) > $o ).
tff(rf1_type,type,
rf1: ( $i * $i ) > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Z_3_type,type,
tptp_fun_Z_3: $i > $i ).
tff(1,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvF1(X,Y)
<=> rf1(Y,X) )
<=> ( rinvF1(X,Y)
<=> rf1(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(5,plain,
! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) )
| ( rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),i2003_11_14_17_19_06193)
<=> rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
( rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),i2003_11_14_17_19_06193)
<=> rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rf1(X,tptp_fun_Y_1(X))
& ~ cp(tptp_fun_Y_1(X))
& ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ( rs(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) ) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ( rinvF1(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cowlThing(W) ) ) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rf1(X,tptp_fun_Y_1(X))
& ~ cp(tptp_fun_Y_1(X))
& ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ( rs(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ( rinvF1(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cowlThing(W) ) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rf1(X,tptp_fun_Y_1(X))
& ~ cp(tptp_fun_Y_1(X))
& ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ( rs(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ( rinvF1(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cowlThing(W) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rf1(X,tptp_fun_Y_1(X))
& ~ cp(tptp_fun_Y_1(X))
& ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ( rs(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ( rinvF1(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cowlThing(W) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rf1(X,tptp_fun_Y_1(X))
& ~ cp(tptp_fun_Y_1(X))
& ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ( rs(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) )
| ! [Y: $i] :
( ~ rf1(X,Y)
| cp(Y)
| ( rinvF1(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cowlThing(W) ) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rf1(X,tptp_fun_Y_1(X))
& ~ cp(tptp_fun_Y_1(X))
& ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ( rs(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ( rinvF1(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cowlThing(W) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rf1(X,tptp_fun_Y_1(X))
& ~ cp(tptp_fun_Y_1(X))
& ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ( rs(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) )
| ! [Y: $i] :
( ~ rf1(X,Y)
| cp(Y)
| ( rinvF1(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cowlThing(W) ) ) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rf1(X,tptp_fun_Y_1(X))
& ~ cp(tptp_fun_Y_1(X))
& ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ( rs(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ( rinvF1(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cowlThing(W) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& cp(Y) )
& ? [Y: $i] :
( rf1(X,Y)
& ~ cp(Y)
& ! [Z: $i] :
( ~ rinvF1(Y,Z)
| ? [W: $i] :
( rs(Z,W)
& cowlThing(W) ) ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& cp(Y) )
& ? [Y: $i] :
( rf1(X,Y)
& ~ cp(Y)
& ! [Z: $i] :
( ~ rinvF1(Y,Z)
| ? [W: $i] :
( rs(Z,W)
& cowlThing(W) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& cp(Y) )
& ? [Y: $i] :
( rf1(X,Y)
& ~ cp(Y)
& ! [Z: $i] :
( rinvF1(Y,Z)
=> ? [W: $i] :
( rs(Z,W)
& cowlThing(W) ) ) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& cp(Y) )
& ? [Y: $i] :
( rf1(X,Y)
& ~ cp(Y)
& ! [Z: $i] :
( ~ rinvF1(Y,Z)
| ? [W: $i] :
( rs(Z,W)
& cowlThing(W) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& cp(Y) )
& ? [Y: $i] :
( rf1(X,Y)
& ~ cp(Y)
& ! [Z: $i] :
( rinvF1(Y,Z)
=> ? [W: $i] :
( rs(Z,W)
& cowlThing(W) ) ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& cp(Y) )
& ? [Y: $i] :
( rf1(X,Y)
& ~ cp(Y)
& ! [Z: $i] :
( ~ rinvF1(Y,Z)
| ? [W: $i] :
( rs(Z,W)
& cowlThing(W) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& cp(Y) )
& ? [Y: $i] :
( rf1(X,Y)
& ~ cp(Y)
& ! [Z: $i] :
( rinvF1(Y,Z)
=> ? [W: $i] :
( rs(Z,W)
& cowlThing(W) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(23,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& cp(Y) )
& ? [Y: $i] :
( rf1(X,Y)
& ~ cp(Y)
& ! [Z: $i] :
( ~ rinvF1(Y,Z)
| ? [W: $i] :
( rs(Z,W)
& cowlThing(W) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& cp(Y) )
& ? [Y: $i] :
( rf1(X,Y)
& ~ cp(Y)
& ! [Z: $i] :
( ~ rinvF1(Y,Z)
| ? [W: $i] :
( rs(Z,W)
& cowlThing(W) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rf1(X,tptp_fun_Y_1(X))
& ~ cp(tptp_fun_Y_1(X))
& ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ( rs(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) )
| ! [Y: $i] :
( ~ rf1(X,Y)
| cp(Y)
| ( rinvF1(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cowlThing(W) ) ) ) ) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rf1(X,tptp_fun_Y_1(X))
& ~ cp(tptp_fun_Y_1(X))
& ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ( rs(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ( rinvF1(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cowlThing(W) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[26,16]) ).
tff(28,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,14]) ).
tff(29,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_06193)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_19_06193,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(i2003_11_14_17_19_06193,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_06193)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_19_06193,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(i2003_11_14_17_19_06193,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| cp(tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_06193)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_19_06193,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(i2003_11_14_17_19_06193,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_06193)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_19_06193,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(i2003_11_14_17_19_06193,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| cp(tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_06193)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_19_06193,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(i2003_11_14_17_19_06193,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_06193)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_19_06193,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(i2003_11_14_17_19_06193,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| cp(tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_06193)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_19_06193,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(i2003_11_14_17_19_06193,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_06193)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_19_06193,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(i2003_11_14_17_19_06193,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| cp(tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_06193)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_19_06193,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(i2003_11_14_17_19_06193,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_1(X))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(X,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_06193)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_19_06193,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(i2003_11_14_17_19_06193,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_06193)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_19_06193,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(i2003_11_14_17_19_06193,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[34,28]) ).
tff(36,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_06193)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_19_06193,Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rf1(i2003_11_14_17_19_06193,Y)
| ~ ( ~ rinvF1(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ rs(tptp_fun_Z_3(Y),W)
| ~ cowlThing(W) ) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(37,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) ),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
( cUnsatisfiable(i2003_11_14_17_19_06193)
<=> cUnsatisfiable(i2003_11_14_17_19_06193) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
cUnsatisfiable(i2003_11_14_17_19_06193),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
tff(40,plain,
cUnsatisfiable(i2003_11_14_17_19_06193),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(42,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
| ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) )
| ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ) ),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
~ ( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ),
inference(unit_resolution,[status(thm)],[42,37]) ).
tff(44,plain,
( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ),
inference(tautology,[status(thm)],[]) ).
tff(45,plain,
rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
( ~ ( rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),i2003_11_14_17_19_06193)
<=> rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) )
| rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),i2003_11_14_17_19_06193)
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ),
inference(tautology,[status(thm)],[]) ).
tff(47,plain,
( ~ ( rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),i2003_11_14_17_19_06193)
<=> rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) )
| rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),i2003_11_14_17_19_06193) ),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),i2003_11_14_17_19_06193),
inference(unit_resolution,[status(thm)],[47,9]) ).
tff(49,plain,
( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(50,plain,
! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) ),
inference(unit_resolution,[status(thm)],[49,43]) ).
tff(51,plain,
( ( ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),i2003_11_14_17_19_06193)
| ~ ( ~ rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| ~ cowlThing(tptp_fun_W_2(i2003_11_14_17_19_06193)) ) )
<=> ( ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),i2003_11_14_17_19_06193)
| ~ ( ~ rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| ~ cowlThing(tptp_fun_W_2(i2003_11_14_17_19_06193)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),i2003_11_14_17_19_06193)
| ~ ( ~ rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| ~ cowlThing(tptp_fun_W_2(i2003_11_14_17_19_06193)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),i2003_11_14_17_19_06193)
| ~ ( ~ rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| ~ cowlThing(tptp_fun_W_2(i2003_11_14_17_19_06193)) ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
~ ( ~ rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| ~ cowlThing(tptp_fun_W_2(i2003_11_14_17_19_06193)) ),
inference(unit_resolution,[status(thm)],[53,50,48]) ).
tff(55,plain,
( ~ rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| ~ cowlThing(tptp_fun_W_2(i2003_11_14_17_19_06193))
| rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ),
inference(tautology,[status(thm)],[]) ).
tff(56,plain,
rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rs(X,Y)
| rf(X,Y) )
<=> ( ~ rs(X,Y)
| rf(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rs(X,Y)
=> rf(X,Y) )
<=> ( ~ rs(X,Y)
| rf(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [X: $i,Y: $i] :
( rs(X,Y)
=> rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,axiom,
! [X: $i,Y: $i] :
( rs(X,Y)
=> rf(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
tff(63,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)),
inference(unit_resolution,[status(thm)],[69,66,56]) ).
tff(71,plain,
( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193)) ),
inference(tautology,[status(thm)],[]) ).
tff(72,plain,
rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193)),
inference(unit_resolution,[status(thm)],[71,43]) ).
tff(73,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(( ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
<=> ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rf(X,Y)
& rf(X,Z) )
<=> ~ ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ~ ( rf(X,Y)
& rf(X,Z) )
<=> ~ ~ ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
rewrite(( ~ ~ ( ~ rf(X,Y)
| ~ rf(X,Z) )
<=> ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ~ ( rf(X,Y)
& rf(X,Z) )
<=> ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ( ~ rf(X,Y)
| ~ rf(X,Z)
| ( Y = Z ) ) )),
rewrite(( ( ~ rf(X,Y)
| ~ rf(X,Z)
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) )
<=> ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(81,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ),
inference(modus_ponens,[status(thm)],[84,74]) ).
tff(86,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_0(i2003_11_14_17_19_06193) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_0(i2003_11_14_17_19_06193) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ( ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_0(i2003_11_14_17_19_06193) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193)) )
<=> ( ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_0(i2003_11_14_17_19_06193) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_0(i2003_11_14_17_19_06193) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_0(i2003_11_14_17_19_06193) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_0(i2003_11_14_17_19_06193) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_0(i2003_11_14_17_19_06193) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ) ),
inference(transitivity,[status(thm)],[88,86]) ).
tff(90,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_0(i2003_11_14_17_19_06193) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_0(i2003_11_14_17_19_06193) )
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_0(i2003_11_14_17_19_06193),
inference(unit_resolution,[status(thm)],[91,85,72,70]) ).
tff(93,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rs(X,Y)
| rf1(X,Y) )
<=> ( ~ rs(X,Y)
| rf1(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(94,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rs(X,Y)
=> rf1(X,Y) )
<=> ( ~ rs(X,Y)
| rf1(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [X: $i,Y: $i] :
( rs(X,Y)
=> rf1(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,axiom,
! [X: $i,Y: $i] :
( rs(X,Y)
=> rf1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
tff(99,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[101,94]) ).
tff(103,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)),
inference(unit_resolution,[status(thm)],[105,102,56]) ).
tff(107,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(( ( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
<=> ( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(108,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rf1(X,Y)
& rf1(X,Z) )
<=> ~ ( ~ rf1(X,Y)
| ~ rf1(X,Z) ) )),
( ~ ( rf1(X,Y)
& rf1(X,Z) )
<=> ~ ~ ( ~ rf1(X,Y)
| ~ rf1(X,Z) ) )),
rewrite(( ~ ~ ( ~ rf1(X,Y)
| ~ rf1(X,Z) )
<=> ( ~ rf1(X,Y)
| ~ rf1(X,Z) ) )),
( ~ ( rf1(X,Y)
& rf1(X,Z) )
<=> ( ~ rf1(X,Y)
| ~ rf1(X,Z) ) )),
( ( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ( ~ rf1(X,Y)
| ~ rf1(X,Z)
| ( Y = Z ) ) )),
rewrite(( ( ~ rf1(X,Y)
| ~ rf1(X,Z)
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) ) )),
( ( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(110,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( rf1(X,Y)
& rf1(X,Z) )
=> ( Y = Z ) )
<=> ( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ) )),
inference(bind,[status(th)],[]) ).
tff(113,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rf1(X,Y)
& rf1(X,Z) )
=> ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ) ),
inference(quant_intro,[status(thm)],[112]) ).
tff(114,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rf1(X,Y)
& rf1(X,Z) )
=> ( Y = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(115,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[115,111]) ).
tff(117,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[116]) ).
tff(118,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) ),
inference(modus_ponens,[status(thm)],[117,110]) ).
tff(119,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) ),
inference(modus_ponens,[status(thm)],[118,108]) ).
tff(120,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_1(i2003_11_14_17_19_06193) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_1(i2003_11_14_17_19_06193) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
( ( ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_1(i2003_11_14_17_19_06193) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) )
<=> ( ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_1(i2003_11_14_17_19_06193) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_1(i2003_11_14_17_19_06193) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_1(i2003_11_14_17_19_06193) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_1(i2003_11_14_17_19_06193) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_1(i2003_11_14_17_19_06193) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ) ),
inference(transitivity,[status(thm)],[122,120]) ).
tff(124,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_1(i2003_11_14_17_19_06193) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193))
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Y)
| ~ rf1(X,Z) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ( tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_1(i2003_11_14_17_19_06193) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_W_2(i2003_11_14_17_19_06193)) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
tptp_fun_W_2(i2003_11_14_17_19_06193) = tptp_fun_Y_1(i2003_11_14_17_19_06193),
inference(unit_resolution,[status(thm)],[125,119,45,106]) ).
tff(127,plain,
tptp_fun_Y_1(i2003_11_14_17_19_06193) = tptp_fun_W_2(i2003_11_14_17_19_06193),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
tptp_fun_Y_1(i2003_11_14_17_19_06193) = tptp_fun_Y_0(i2003_11_14_17_19_06193),
inference(transitivity,[status(thm)],[127,92]) ).
tff(129,plain,
( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
<=> cp(tptp_fun_Y_0(i2003_11_14_17_19_06193)) ),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
( cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
<=> cp(tptp_fun_Y_1(i2003_11_14_17_19_06193)) ),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| cp(tptp_fun_Y_0(i2003_11_14_17_19_06193)) ),
inference(tautology,[status(thm)],[]) ).
tff(132,plain,
cp(tptp_fun_Y_0(i2003_11_14_17_19_06193)),
inference(unit_resolution,[status(thm)],[131,43]) ).
tff(133,plain,
cp(tptp_fun_Y_1(i2003_11_14_17_19_06193)),
inference(modus_ponens,[status(thm)],[132,130]) ).
tff(134,plain,
( cp(tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ rf(i2003_11_14_17_19_06193,tptp_fun_Y_0(i2003_11_14_17_19_06193))
| ~ ! [Z: $i] :
( ~ rinvF1(tptp_fun_Y_1(i2003_11_14_17_19_06193),Z)
| ~ ( ~ rs(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rf1(i2003_11_14_17_19_06193,tptp_fun_Y_1(i2003_11_14_17_19_06193))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_06193)) ),
inference(tautology,[status(thm)],[]) ).
tff(135,plain,
~ cp(tptp_fun_Y_1(i2003_11_14_17_19_06193)),
inference(unit_resolution,[status(thm)],[134,43]) ).
tff(136,plain,
$false,
inference(unit_resolution,[status(thm)],[135,133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS076+1 : TPTP v9.0.0. Released v3.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:10:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------