%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS122+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:13:26 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 74
% Syntax : Number of formulae : 186 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 1533 ( 44 equ)
% Maximal formula atoms : 24 ( 8 avg)
% Number of connectives : 2819 (1553 ~; 998 |; 103 &)
% ( 159 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 81 ( 81 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 478 ( 415 !; 31 ?; 478 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px1_type,type,
ra_Px1: ( $i * $i ) > $o ).
tff(tptp_fun_Y0_2_type,type,
tptp_fun_Y0_2: $i > $i ).
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $i > $i ).
tff(i2003_11_14_17_21_55116_type,type,
i2003_11_14_17_21_55116: $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(rf_type,type,
rf: ( $i * $i ) > $o ).
tff(cp1xcomp_type,type,
cp1xcomp: $i > $o ).
tff(ca_Vx3_type,type,
ca_Vx3: $i > $o ).
tff(rinvF_type,type,
rinvF: ( $i * $i ) > $o ).
tff(cp1_type,type,
cp1: $i > $o ).
tff(ca_Ax2_type,type,
ca_Ax2: $i > $o ).
tff(tptp_fun_Y_3_type,type,
tptp_fun_Y_3: $i > $i ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ ca_Vx3(X)
| ( rf(X,tptp_fun_Y_4(X))
& cp1xcomp(tptp_fun_Y_4(X)) ) )
<=> ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) )),
rewrite(( ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp1xcomp(Y) ) )
<=> ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) ) )),
( ( ( ~ ca_Vx3(X)
| ( rf(X,tptp_fun_Y_4(X))
& cp1xcomp(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp1xcomp(Y) ) ) )
<=> ( ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) ) ) )),
rewrite(( ( ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) ) )
<=> ~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) ) )),
( ( ( ~ ca_Vx3(X)
| ( rf(X,tptp_fun_Y_4(X))
& cp1xcomp(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp1xcomp(Y) ) ) )
<=> ~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [X: $i] :
( ( ~ ca_Vx3(X)
| ( rf(X,tptp_fun_Y_4(X))
& cp1xcomp(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp1xcomp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rf(X,Y)
& cp1xcomp(Y) ) )
<=> ! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rf(X,Y)
& cp1xcomp(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rf(X,Y)
& cp1xcomp(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(10,plain,
! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rf(X,Y)
& cp1xcomp(Y) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i] :
( ( ~ ca_Vx3(X)
| ( rf(X,tptp_fun_Y_4(X))
& cp1xcomp(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& cp1xcomp(Y) ) ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) )
| ~ ( ~ ( ca_Vx3(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) )
| ~ ( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) )
| ~ ( ~ ( ca_Vx3(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) )
| ~ ( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ( ~ ( ca_Vx3(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_55116,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ) )
<=> ~ ( ~ ( ca_Vx3(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) )
| ~ ( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) )
| ~ ( ~ ( ca_Vx3(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_55116,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) )
| ~ ( ~ ( ca_Vx3(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) )
| ~ ( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) )
| ~ ( ~ ( ca_Vx3(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_55116,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) )
| ~ ( ~ ( ca_Vx3(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) )
| ~ ( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ) ) ) ),
inference(transitivity,[status(thm)],[16,14]) ).
tff(18,plain,
( ~ ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) )
| ~ ( ~ ( ca_Vx3(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_55116,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [X: $i] :
~ ( ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ cp1xcomp(Y) ) )
| ~ ( ~ ca_Vx3(X)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X)) ) ) )
| ~ ( ~ ( ca_Vx3(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) )
| ~ ( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ ( ~ ( ca_Vx3(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) )
| ~ ( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ) ),
inference(unit_resolution,[status(thm)],[19,13]) ).
tff(21,plain,
( ~ ( ca_Vx3(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ cp1xcomp(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) )
| ~ ( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) )
| ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(22,plain,
( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) )
<=> ~ ( ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
<=> ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )),
( ( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) )
<=> ( ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ) )),
rewrite(( ( ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ) )),
( ( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
^ [X: $i] :
rewrite(( ( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) )
<=> ( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
<=> ! [X: $i] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [X: $i] :
rewrite(( ( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( rinvF(X,Y)
=> ca_Vx3(Y) ) ) )
<=> ( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [X: $i] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( rinvF(X,Y)
=> ca_Vx3(Y) ) ) )
<=> ! [X: $i] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [X: $i] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( rinvF(X,Y)
=> ca_Vx3(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(38,plain,
! [X: $i] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [X: $i] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ),
inference(modus_ponens,[status(thm)],[41,31]) ).
tff(43,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) ) ),
inference(modus_ponens,[status(thm)],[42,29]) ).
tff(44,plain,
! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[43,24]) ).
tff(45,plain,
( ~ ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( ca_Vx3(tptp_fun_Y_3(X))
| ~ rinvF(X,tptp_fun_Y_3(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )
| ~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ( ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_55116)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_55116))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ( ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_55116)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_55116))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ) ) ) ),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ( ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_55116)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_55116))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ) ) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(48,plain,
( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ) ) ),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ? [Y: $i] :
( rf(X,Y)
& ca_Ax2(Y) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ? [Y: $i] :
( rf(X,Y)
& ca_Ax2(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ? [Y: $i] :
( rf(X,Y)
& ca_Ax2(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(58,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ? [Y: $i] :
( rf(X,Y)
& ca_Ax2(Y) ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_55116,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_55116,Y)
| ~ ca_Ax2(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_55116,Y)
| ~ ca_Ax2(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_55116,Y)
| ~ ca_Ax2(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) ) ),
inference(unit_resolution,[status(thm)],[67,61]) ).
tff(69,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_55116)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_55116,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(70,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) ),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
( cUnsatisfiable(i2003_11_14_17_21_55116)
<=> cUnsatisfiable(i2003_11_14_17_21_55116) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
cUnsatisfiable(i2003_11_14_17_21_55116),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
tff(73,plain,
cUnsatisfiable(i2003_11_14_17_21_55116),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(75,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) ),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ),
inference(unit_resolution,[status(thm)],[75,70]) ).
tff(77,plain,
( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116)) ),
inference(tautology,[status(thm)],[]) ).
tff(78,plain,
ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116)),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ) ) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(80,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ) ) )
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ) ) ),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ) ),
inference(unit_resolution,[status(thm)],[80,48]) ).
tff(82,plain,
( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) )
| ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(83,plain,
! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ),
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvF(X,Y)
<=> rf(Y,X) )
<=> ( rinvF(X,Y)
<=> rf(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(88,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
( ~ ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
| ( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116)
<=> rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116)
<=> rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ),
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116))
| rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ),
inference(tautology,[status(thm)],[]) ).
tff(94,plain,
rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)),
inference(unit_resolution,[status(thm)],[93,76]) ).
tff(95,plain,
( ~ ( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116)
<=> rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) )
| rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116)
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ),
inference(tautology,[status(thm)],[]) ).
tff(96,plain,
( ~ ( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116)
<=> rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) )
| rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116) ),
inference(unit_resolution,[status(thm)],[95,94]) ).
tff(97,plain,
rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116),
inference(unit_resolution,[status(thm)],[96,92]) ).
tff(98,plain,
( ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) )
| ca_Vx3(i2003_11_14_17_21_55116)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116) )
<=> ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) )
| ca_Vx3(i2003_11_14_17_21_55116)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) )
| ca_Vx3(i2003_11_14_17_21_55116)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) )
| ca_Vx3(i2003_11_14_17_21_55116)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
ca_Vx3(i2003_11_14_17_21_55116),
inference(unit_resolution,[status(thm)],[100,97,83]) ).
tff(102,plain,
( ~ ( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) )
| ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(103,plain,
( ~ ( ~ ca_Vx3(i2003_11_14_17_21_55116)
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) )
| ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ) ),
inference(unit_resolution,[status(thm)],[102,101]) ).
tff(104,plain,
~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ),
inference(unit_resolution,[status(thm)],[103,22]) ).
tff(105,plain,
( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116))
| rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)) ),
inference(tautology,[status(thm)],[]) ).
tff(106,plain,
rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116)),
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,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(108,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)],[107]) ).
tff(109,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(110,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)],[109]) ).
tff(111,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(112,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(113,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)],[112]) ).
tff(114,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(115,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[115,111]) ).
tff(117,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[116]) ).
tff(118,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ),
inference(modus_ponens,[status(thm)],[117,110]) ).
tff(119,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ),
inference(modus_ponens,[status(thm)],[118,108]) ).
tff(120,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ( tptp_fun_Y_4(i2003_11_14_17_21_55116) = tptp_fun_Y_0(i2003_11_14_17_21_55116) ) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ( tptp_fun_Y_4(i2003_11_14_17_21_55116) = tptp_fun_Y_0(i2003_11_14_17_21_55116) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
( ( ( tptp_fun_Y_4(i2003_11_14_17_21_55116) = tptp_fun_Y_0(i2003_11_14_17_21_55116) )
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) )
<=> ( ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ( tptp_fun_Y_4(i2003_11_14_17_21_55116) = tptp_fun_Y_0(i2003_11_14_17_21_55116) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_Y_4(i2003_11_14_17_21_55116) = tptp_fun_Y_0(i2003_11_14_17_21_55116) )
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ( tptp_fun_Y_4(i2003_11_14_17_21_55116) = tptp_fun_Y_0(i2003_11_14_17_21_55116) ) ) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_Y_4(i2003_11_14_17_21_55116) = tptp_fun_Y_0(i2003_11_14_17_21_55116) )
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ( tptp_fun_Y_4(i2003_11_14_17_21_55116) = tptp_fun_Y_0(i2003_11_14_17_21_55116) ) ) ),
inference(transitivity,[status(thm)],[122,120]) ).
tff(124,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_Y_4(i2003_11_14_17_21_55116) = tptp_fun_Y_0(i2003_11_14_17_21_55116) )
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ( tptp_fun_Y_4(i2003_11_14_17_21_55116) = tptp_fun_Y_0(i2003_11_14_17_21_55116) ) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
tptp_fun_Y_4(i2003_11_14_17_21_55116) = tptp_fun_Y_0(i2003_11_14_17_21_55116),
inference(unit_resolution,[status(thm)],[125,119,94,106]) ).
tff(127,plain,
tptp_fun_Y_0(i2003_11_14_17_21_55116) = tptp_fun_Y_4(i2003_11_14_17_21_55116),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116)))
<=> ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))) ),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116)))
<=> ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))) ),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(131,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(133,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[133,131]) ).
tff(135,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) )
<=> ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )),
( ( ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ( ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
rewrite(( ( ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
( ( ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(136,plain,
( ! [X: $i] :
( ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [X: $i] :
( cp1xcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) )
<=> ! [X: $i] :
( cp1xcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,axiom,
! [X: $i] :
( cp1xcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(139,plain,
! [X: $i] :
( cp1xcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
! [X: $i] :
( ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(skolemize,[status(sab)],[139]) ).
tff(141,plain,
! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[140,136]) ).
tff(142,plain,
! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[141,134]) ).
tff(143,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
| ~ ( ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))) )
| ~ ( cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),Y0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(144,plain,
~ ( ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))) )
| ~ ( cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),Y0) ) ),
inference(unit_resolution,[status(thm)],[143,142]) ).
tff(145,plain,
( ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))) )
| ~ ( cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),Y0) )
| ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))) ),
inference(tautology,[status(thm)],[]) ).
tff(146,plain,
( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))) ),
inference(unit_resolution,[status(thm)],[145,144]) ).
tff(147,plain,
( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ~ rf(i2003_11_14_17_21_55116,tptp_fun_Y_4(i2003_11_14_17_21_55116))
| cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116)) ),
inference(tautology,[status(thm)],[]) ).
tff(148,plain,
cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116)),
inference(unit_resolution,[status(thm)],[147,104]) ).
tff(149,plain,
( ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))) )
| ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))) ),
inference(tautology,[status(thm)],[]) ).
tff(150,plain,
( ~ ( ~ cp1xcomp(tptp_fun_Y_4(i2003_11_14_17_21_55116))
| ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))) )
| ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))) ),
inference(unit_resolution,[status(thm)],[149,148]) ).
tff(151,plain,
ra_Px1(tptp_fun_Y_4(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))),
inference(unit_resolution,[status(thm)],[150,146]) ).
tff(152,plain,
ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))),
inference(modus_ponens,[status(thm)],[151,129]) ).
tff(153,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) )
<=> ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(154,plain,
( ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[153]) ).
tff(155,plain,
^ [X: $i] :
refl(( ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) )
<=> ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(156,plain,
( ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) )
<=> ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(158,plain,
( ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,plain,
( ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ) ),
inference(transitivity,[status(thm)],[158,156]) ).
tff(160,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) )
<=> ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) )),
( ( ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) )
<=> ( ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ) )),
rewrite(( ( ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) )
<=> ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ) )),
( ( ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) )
<=> ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(161,plain,
( ! [X: $i] :
( ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ) ),
inference(quant_intro,[status(thm)],[160]) ).
tff(162,plain,
^ [X: $i] :
rewrite(( ( ( ra_Px1(X,tptp_fun_Y_1(X))
| cp1(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) )
<=> ( ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(163,plain,
( ! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_1(X))
| cp1(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) )
<=> ! [X: $i] :
( ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,plain,
( ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp1(X) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp1(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(165,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ~ ? [Y: $i] : ra_Px1(X,Y)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )),
( ( cp1(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ( cp1(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ) )),
rewrite(( ( cp1(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp1(X) ) )),
( ( cp1(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp1(X) ) )),
rewrite(( ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp1(X) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp1(X) ) )),
( ( cp1(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp1(X) ) )),
inference(bind,[status(th)],[]) ).
tff(166,plain,
( ! [X: $i] :
( cp1(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp1(X) ) ),
inference(quant_intro,[status(thm)],[165]) ).
tff(167,axiom,
! [X: $i] :
( cp1(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(168,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp1(X) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp1(X) ),
inference(modus_ponens,[status(thm)],[168,164]) ).
tff(170,plain,
! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_1(X))
| cp1(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(skolemize,[status(sab)],[169]) ).
tff(171,plain,
! [X: $i] :
( ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(modus_ponens,[status(thm)],[170,163]) ).
tff(172,plain,
! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(modus_ponens,[status(thm)],[171,161]) ).
tff(173,plain,
! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(modus_ponens,[status(thm)],[172,159]) ).
tff(174,plain,
! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ),
inference(modus_ponens,[status(thm)],[173,154]) ).
tff(175,plain,
( ~ ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
| ~ ( ~ ( cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),tptp_fun_Y_1(tptp_fun_Y_0(i2003_11_14_17_21_55116))) )
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
~ ( ~ ( cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),tptp_fun_Y_1(tptp_fun_Y_0(i2003_11_14_17_21_55116))) )
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ) ),
inference(unit_resolution,[status(thm)],[175,174]) ).
tff(177,plain,
( ~ ( cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),tptp_fun_Y_1(tptp_fun_Y_0(i2003_11_14_17_21_55116))) )
| ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ),
inference(tautology,[status(thm)],[]) ).
tff(178,plain,
( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ),
inference(unit_resolution,[status(thm)],[177,176]) ).
tff(179,plain,
( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) )
| cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116)) ),
inference(tautology,[status(thm)],[]) ).
tff(180,plain,
cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116)),
inference(unit_resolution,[status(thm)],[179,81]) ).
tff(181,plain,
( ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ),
inference(tautology,[status(thm)],[]) ).
tff(182,plain,
( ~ ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_21_55116))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) )
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y) ),
inference(unit_resolution,[status(thm)],[181,180]) ).
tff(183,plain,
! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y),
inference(unit_resolution,[status(thm)],[182,178]) ).
tff(184,plain,
( ~ ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),Y)
| ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(185,plain,
~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_55116),tptp_fun_Y0_2(tptp_fun_Y_4(i2003_11_14_17_21_55116))),
inference(unit_resolution,[status(thm)],[184,183]) ).
tff(186,plain,
$false,
inference(unit_resolution,[status(thm)],[185,152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KRS122+1 : TPTP v9.0.0. Released v3.1.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.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 19:11:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% See solution above
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------