%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS074+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:19 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 44 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 838 ( 0 equ)
% Maximal formula atoms : 56 ( 19 avg)
% Number of connectives : 1714 ( 933 ~; 650 |; 97 &)
% ( 31 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 13 ( 13 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 221 ( 198 !; 18 ?; 221 :)
% Comments :
%------------------------------------------------------------------------------
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_18_59896_type,type,
i2003_11_14_17_18_59896: $i ).
tff(cp_type,type,
cp: $i > $o ).
tff(rinvS_type,type,
rinvS: ( $i * $i ) > $o ).
tff(tptp_fun_Z_1_type,type,
tptp_fun_Z_1: $i > $i ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp(tptp_fun_Z_1(X))
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
~ ( rinvS(Y,Z)
& cp(Z) ) ) )
<=> ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp(tptp_fun_Z_1(X))
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
~ ( rinvS(Y,Z)
& cp(Z) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp(tptp_fun_Z_1(X))
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
~ ( rinvS(Y,Z)
& cp(Z) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp(tptp_fun_Z_1(X))
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
~ ( rinvS(Y,Z)
& cp(Z) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp(tptp_fun_Z_1(X))
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y)
| ! [Z: $i] :
~ ( rinvS(Y,Z)
& cp(Z) ) )
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp(tptp_fun_Z_1(X))
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
~ ( rinvS(Y,Z)
& cp(Z) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp(tptp_fun_Z_1(X))
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y)
| ! [Z: $i] :
~ ( rinvS(Y,Z)
& cp(Z) ) )
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp(tptp_fun_Z_1(X))
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
~ ( rinvS(Y,Z)
& cp(Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& cp(Y)
& ? [Z: $i] :
( rinvS(Y,Z)
& cp(Z) ) )
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& cp(Y)
& ? [Z: $i] :
( rinvS(Y,Z)
& cp(Z) ) )
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& cp(Y)
& ? [Z: $i] :
( rinvS(Y,Z)
& cp(Z) ) )
& ! [Y: $i] :
( rs(X,Y)
=> ~ cp(Y) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& cp(Y)
& ? [Z: $i] :
( rinvS(Y,Z)
& cp(Z) ) )
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& cp(Y)
& ? [Z: $i] :
( rinvS(Y,Z)
& cp(Z) ) )
& ! [Y: $i] :
( rs(X,Y)
=> ~ cp(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& cp(Y)
& ? [Z: $i] :
( rinvS(Y,Z)
& cp(Z) ) )
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& cp(Y)
& ? [Z: $i] :
( rinvS(Y,Z)
& cp(Z) ) )
& ! [Y: $i] :
( rs(X,Y)
=> ~ cp(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(14,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& cp(Y)
& ? [Z: $i] :
( rinvS(Y,Z)
& cp(Z) ) )
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& cp(Y)
& ? [Z: $i] :
( rinvS(Y,Z)
& cp(Z) ) )
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp(tptp_fun_Z_1(X))
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y)
| ! [Z: $i] :
~ ( rinvS(Y,Z)
& cp(Z) ) )
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) ) ) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp(tptp_fun_Z_1(X))
& ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
~ ( rinvS(Y,Z)
& cp(Z) ) ) ) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) ),
inference(modus_ponens,[status(thm)],[17,7]) ).
tff(19,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,5]) ).
tff(20,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_2(i2003_11_14_17_18_59896)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_2(i2003_11_14_17_18_59896)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_2(i2003_11_14_17_18_59896)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_2(i2003_11_14_17_18_59896)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_2(i2003_11_14_17_18_59896)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_2(i2003_11_14_17_18_59896)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_2(i2003_11_14_17_18_59896)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_2(i2003_11_14_17_18_59896)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) ) ) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_2(i2003_11_14_17_18_59896)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ rinvS(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp(tptp_fun_Z_1(X))
| ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ cp(tptp_fun_Y_2(X))
| ~ rs(X,tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_2(i2003_11_14_17_18_59896)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ ( ~ ( cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_2(i2003_11_14_17_18_59896)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) ) ),
inference(unit_resolution,[status(thm)],[25,19]) ).
tff(27,plain,
( ~ ( cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_2(i2003_11_14_17_18_59896)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y)
| ! [Z: $i] :
( ~ cp(Z)
| ~ rinvS(Y,Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(28,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) ),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( cUnsatisfiable(i2003_11_14_17_18_59896)
<=> cUnsatisfiable(i2003_11_14_17_18_59896) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
cUnsatisfiable(i2003_11_14_17_18_59896),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
tff(31,plain,
cUnsatisfiable(i2003_11_14_17_18_59896),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(33,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_59896)
| ~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) )
| ~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) ),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
~ ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ),
inference(unit_resolution,[status(thm)],[33,28]) ).
tff(35,plain,
( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896))
| rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896))
| cp(tptp_fun_Y_0(i2003_11_14_17_18_59896)) ),
inference(tautology,[status(thm)],[]) ).
tff(38,plain,
cp(tptp_fun_Y_0(i2003_11_14_17_18_59896)),
inference(unit_resolution,[status(thm)],[37,34]) ).
tff(39,plain,
( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_59896),tptp_fun_Z_1(i2003_11_14_17_18_59896))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(40,plain,
! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) ),
inference(unit_resolution,[status(thm)],[39,34]) ).
tff(41,plain,
( ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) )
<=> ( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_18_59896,Y) )
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_18_59896))
| ~ rs(i2003_11_14_17_18_59896,tptp_fun_Y_0(i2003_11_14_17_18_59896)) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
$false,
inference(unit_resolution,[status(thm)],[43,40,38,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KRS074+1 : TPTP v9.0.0. Released v3.1.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n001.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 19:15:04 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% See solution above
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------