%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS121+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 75
% Syntax : Number of formulae : 183 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 1723 ( 0 equ)
% Maximal formula atoms : 32 ( 9 avg)
% Number of connectives : 3158 (1714 ~;1136 |; 137 &)
% ( 165 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 96 ( 96 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 490 ( 428 !; 31 ?; 490 :)
% 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(i2003_11_14_17_21_5199_type,type,
i2003_11_14_17_21_5199: $i ).
tff(cp1xcomp_type,type,
cp1xcomp: $i > $o ).
tff(rinvR_type,type,
rinvR: ( $i * $i ) > $o ).
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $i > $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(ca_Ax2_type,type,
ca_Ax2: $i > $o ).
tff(ca_Vx3_type,type,
ca_Vx3: $i > $o ).
tff(cp1_type,type,
cp1: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y_3_type,type,
tptp_fun_Y_3: $i > $i ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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)],[3]) ).
tff(5,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)],[4,2]) ).
tff(6,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(7,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)],[6]) ).
tff(8,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(9,axiom,
! [X: $i] :
( cp1xcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
tff(10,plain,
! [X: $i] :
( cp1xcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,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)],[10]) ).
tff(12,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)],[11,7]) ).
tff(13,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)],[12,5]) ).
tff(14,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cp1xcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cp1xcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
| ~ ( ~ ( ~ cp1xcomp(i2003_11_14_17_21_5199)
| ra_Px1(i2003_11_14_17_21_5199,tptp_fun_Y0_2(i2003_11_14_17_21_5199)) )
| ~ ( cp1xcomp(i2003_11_14_17_21_5199)
| ! [Y0: $i] : ~ ra_Px1(i2003_11_14_17_21_5199,Y0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
~ ( ~ ( ~ cp1xcomp(i2003_11_14_17_21_5199)
| ra_Px1(i2003_11_14_17_21_5199,tptp_fun_Y0_2(i2003_11_14_17_21_5199)) )
| ~ ( cp1xcomp(i2003_11_14_17_21_5199)
| ! [Y0: $i] : ~ ra_Px1(i2003_11_14_17_21_5199,Y0) ) ),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ ( ~ cp1xcomp(i2003_11_14_17_21_5199)
| ra_Px1(i2003_11_14_17_21_5199,tptp_fun_Y0_2(i2003_11_14_17_21_5199)) )
| ~ ( cp1xcomp(i2003_11_14_17_21_5199)
| ! [Y0: $i] : ~ ra_Px1(i2003_11_14_17_21_5199,Y0) )
| ~ cp1xcomp(i2003_11_14_17_21_5199)
| ra_Px1(i2003_11_14_17_21_5199,tptp_fun_Y0_2(i2003_11_14_17_21_5199)) ),
inference(tautology,[status(thm)],[]) ).
tff(17,plain,
( ~ cp1xcomp(i2003_11_14_17_21_5199)
| ra_Px1(i2003_11_14_17_21_5199,tptp_fun_Y0_2(i2003_11_14_17_21_5199)) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvR(X,Y)
<=> rr(Y,X) )
<=> ( rinvR(X,Y)
<=> rr(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
tff(22,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
| ( rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),i2003_11_14_17_21_5199)
<=> rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),i2003_11_14_17_21_5199)
<=> rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ ca_Vx3(X)
| ( rr(X,tptp_fun_Y_4(X))
& ca_Ax2(tptp_fun_Y_4(X)) ) )
<=> ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) ) )),
rewrite(( ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax2(Y) ) )
<=> ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )),
( ( ( ~ ca_Vx3(X)
| ( rr(X,tptp_fun_Y_4(X))
& ca_Ax2(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax2(Y) ) ) )
<=> ( ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) ) )),
rewrite(( ( ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) ) )),
( ( ( ~ ca_Vx3(X)
| ( rr(X,tptp_fun_Y_4(X))
& ca_Ax2(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax2(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X: $i] :
( ( ~ ca_Vx3(X)
| ( rr(X,tptp_fun_Y_4(X))
& ca_Ax2(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax2(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rr(X,Y)
& ca_Ax2(Y) ) )
<=> ! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rr(X,Y)
& ca_Ax2(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rr(X,Y)
& ca_Ax2(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
tff(36,plain,
! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rr(X,Y)
& ca_Ax2(Y) ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X: $i] :
( ( ~ ca_Vx3(X)
| ( rr(X,tptp_fun_Y_4(X))
& ca_Ax2(tptp_fun_Y_4(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax2(Y) ) ) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )
| ~ ( ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),Y) ) )
| ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )
| ~ ( ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),Y) ) )
| ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),Y) ) ) )
<=> ~ ( ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),Y) ) )
| ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )
| ~ ( ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),Y) ) )
| ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )
| ~ ( ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),Y) ) )
| ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ) ) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rr(X,tptp_fun_Y_4(X))
| ~ ca_Ax2(tptp_fun_Y_4(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ) )
| ~ ( ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),Y) ) )
| ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
~ ( ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),Y) ) )
| ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ) ),
inference(unit_resolution,[status(thm)],[45,39]) ).
tff(47,plain,
( ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),Y) ) )
| ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) )
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(48,plain,
( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Vx3(tptp_fun_Y_0(X))
& cp1(X) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) ) )),
trans(monotonicity(quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ( rr(X,Y)
& ca_Vx3(Y) )
<=> ~ ( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) )),
( ~ ( rr(X,Y)
& ca_Vx3(Y) )
<=> ~ ~ ( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) )),
rewrite(( ~ ~ ( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
<=> ( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) )),
( ~ ( rr(X,Y)
& ca_Vx3(Y) )
<=> ( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx3(Y) )
<=> ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx3(Y) )
| ~ cp1(X) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) )),
rewrite(( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx3(Y) )
| ~ cp1(X) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Vx3(tptp_fun_Y_0(X))
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Vx3(tptp_fun_Y_0(X))
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Vx3(tptp_fun_Y_0(X))
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Vx3(tptp_fun_Y_0(X))
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Vx3(tptp_fun_Y_0(X))
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx3(Y) )
| ~ cp1(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Vx3(tptp_fun_Y_0(X))
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx3(Y) )
| ~ cp1(X) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Vx3(tptp_fun_Y_0(X))
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx3(Y) )
| ~ cp1(X) ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ca_Vx3(Y) )
& cp1(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ca_Vx3(Y) )
& cp1(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ca_Vx3(Y) )
& cp1(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(62,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ca_Vx3(Y) )
& cp1(X) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Vx3(tptp_fun_Y_0(X))
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx3(Y) )
| ~ cp1(X) ) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Vx3(tptp_fun_Y_0(X))
& cp1(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx3(Y) )
| ~ cp1(X) ) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) )
| ~ cp1(X) ) ),
inference(modus_ponens,[status(thm)],[65,55]) ).
tff(67,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) ) ),
inference(modus_ponens,[status(thm)],[66,50]) ).
tff(68,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rr(i2003_11_14_17_21_5199,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rr(i2003_11_14_17_21_5199,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ cp1(i2003_11_14_17_21_5199) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_21_5199,Y)
| ~ ca_Vx3(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rr(i2003_11_14_17_21_5199,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ cp1(i2003_11_14_17_21_5199) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_21_5199,Y)
| ~ ca_Vx3(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rr(i2003_11_14_17_21_5199,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ cp1(i2003_11_14_17_21_5199) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_21_5199,Y)
| ~ ca_Vx3(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rr(i2003_11_14_17_21_5199,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ cp1(i2003_11_14_17_21_5199) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_21_5199,Y)
| ~ ca_Vx3(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx3(tptp_fun_Y_0(X))
| ~ cp1(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp1(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ca_Vx3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rr(i2003_11_14_17_21_5199,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rr(i2003_11_14_17_21_5199,Y) ) ) ),
inference(unit_resolution,[status(thm)],[73,67]) ).
tff(75,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] :
( ~ ca_Vx3(Y)
| ~ rr(i2003_11_14_17_21_5199,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(76,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ) ),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
( cUnsatisfiable(i2003_11_14_17_21_5199)
<=> cUnsatisfiable(i2003_11_14_17_21_5199) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
cUnsatisfiable(i2003_11_14_17_21_5199),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
tff(79,plain,
cUnsatisfiable(i2003_11_14_17_21_5199),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(81,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_5199)
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ) )
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ) ),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
~ ( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ),
inference(unit_resolution,[status(thm)],[81,76]) ).
tff(83,plain,
( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199)) ),
inference(tautology,[status(thm)],[]) ).
tff(84,plain,
ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199)),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) )
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(86,plain,
( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ),
inference(unit_resolution,[status(thm)],[86,48]) ).
tff(88,plain,
( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ),
inference(tautology,[status(thm)],[]) ).
tff(89,plain,
rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))),
inference(unit_resolution,[status(thm)],[88,87]) ).
tff(90,plain,
( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)) ),
inference(tautology,[status(thm)],[]) ).
tff(91,plain,
rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199)),
inference(unit_resolution,[status(thm)],[90,82]) ).
tff(92,plain,
( ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rr(X,Y)
& rr(Y,Z) )
<=> ~ ( ~ rr(X,Y)
| ~ rr(Y,Z) ) )),
( ~ ( rr(X,Y)
& rr(Y,Z) )
<=> ~ ~ ( ~ rr(X,Y)
| ~ rr(Y,Z) ) )),
rewrite(( ~ ~ ( ~ rr(X,Y)
| ~ rr(Y,Z) )
<=> ( ~ rr(X,Y)
| ~ rr(Y,Z) ) )),
( ~ ( rr(X,Y)
& rr(Y,Z) )
<=> ( ~ rr(X,Y)
| ~ rr(Y,Z) ) )),
( ( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) )
<=> ( ~ rr(X,Y)
| ~ rr(Y,Z)
| rr(X,Z) ) )),
rewrite(( ( ~ rr(X,Y)
| ~ rr(Y,Z)
| rr(X,Z) )
<=> ( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) ) )),
( ( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) )
<=> ( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(94,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( rr(X,Y)
& rr(Y,Z) )
=> rr(X,Z) )
<=> ( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rr(X,Y)
& rr(Y,Z) )
=> rr(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rr(X,Y)
& rr(Y,Z) )
=> rr(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
tff(99,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rr(X,Y)
& rr(Y,Z) )
| rr(X,Z) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) ),
inference(modus_ponens,[status(thm)],[101,94]) ).
tff(103,plain,
! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) ),
inference(modus_ponens,[status(thm)],[102,92]) ).
tff(104,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
( ( rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) )
<=> ( ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ) ),
inference(transitivity,[status(thm)],[106,104]) ).
tff(108,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( rr(X,Z)
| ~ rr(X,Y)
| ~ rr(Y,Z) )
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))),
inference(unit_resolution,[status(thm)],[109,103,91,89]) ).
tff(111,plain,
( ~ ( rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),i2003_11_14_17_21_5199)
<=> rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) )
| rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),i2003_11_14_17_21_5199)
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ),
inference(tautology,[status(thm)],[]) ).
tff(112,plain,
( ~ ( rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),i2003_11_14_17_21_5199)
<=> rr(i2003_11_14_17_21_5199,tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) )
| rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),i2003_11_14_17_21_5199) ),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),i2003_11_14_17_21_5199),
inference(unit_resolution,[status(thm)],[112,26]) ).
tff(114,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) )
<=> ~ ( ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(115,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(117,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ) ),
inference(transitivity,[status(thm)],[119,117]) ).
tff(121,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
<=> ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) ) )),
( ( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) )
<=> ( ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ) )),
rewrite(( ( ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ) )),
( ( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(122,plain,
( ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
^ [X: $i] :
rewrite(( ( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) )
<=> ( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(124,plain,
( ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,plain,
( ! [X: $i] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
<=> ! [X: $i] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,plain,
^ [X: $i] :
rewrite(( ( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( rinvR(X,Y)
=> cp1xcomp(Y) ) ) )
<=> ( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [X: $i] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( rinvR(X,Y)
=> cp1xcomp(Y) ) ) )
<=> ! [X: $i] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,axiom,
! [X: $i] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( rinvR(X,Y)
=> cp1xcomp(Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
tff(129,plain,
! [X: $i] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
! [X: $i] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[129,125]) ).
tff(131,plain,
! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ),
inference(skolemize,[status(sab)],[130]) ).
tff(132,plain,
! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp1(X)
& ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ),
inference(modus_ponens,[status(thm)],[131,124]) ).
tff(133,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ),
inference(modus_ponens,[status(thm)],[132,122]) ).
tff(134,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) ) ),
inference(modus_ponens,[status(thm)],[133,120]) ).
tff(135,plain,
! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[134,115]) ).
tff(136,plain,
( ~ ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ cp1(X)
| ~ ( cp1xcomp(tptp_fun_Y_3(X))
| ~ rinvR(X,tptp_fun_Y_3(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cp1(X)
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) ) ) ) )
| ~ ( ~ ( ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ cp1(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ( cp1xcomp(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))))
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ( ~ cp1(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
~ ( ~ ( ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ cp1(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ( cp1xcomp(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))))
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ( ~ cp1(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) ) ) ) ),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,plain,
( ~ ( ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ cp1(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ( cp1xcomp(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))))
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ( ~ cp1(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) ) ) )
| ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ( ~ cp1(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(139,plain,
( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ( ~ cp1(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) ) ) ),
inference(unit_resolution,[status(thm)],[138,137]) ).
tff(140,plain,
( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_5199),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))) ),
inference(tautology,[status(thm)],[]) ).
tff(141,plain,
ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199))),
inference(unit_resolution,[status(thm)],[140,87]) ).
tff(142,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ( ~ cp1(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) ) ) )
| ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ( ~ cp1(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(143,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ( ~ cp1(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) ) ) )
| ~ ( ~ cp1(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) ) ) ),
inference(unit_resolution,[status(thm)],[142,141]) ).
tff(144,plain,
~ ( ~ cp1(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) ) ),
inference(unit_resolution,[status(thm)],[143,139]) ).
tff(145,plain,
( ~ cp1(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)))
| ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) )
| ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(146,plain,
! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) ),
inference(unit_resolution,[status(thm)],[145,144]) ).
tff(147,plain,
( ( ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) )
| cp1xcomp(i2003_11_14_17_21_5199)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),i2003_11_14_17_21_5199) )
<=> ( ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) )
| cp1xcomp(i2003_11_14_17_21_5199)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),i2003_11_14_17_21_5199) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,plain,
( ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) )
| cp1xcomp(i2003_11_14_17_21_5199)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),i2003_11_14_17_21_5199) ),
inference(quant_inst,[status(thm)],[]) ).
tff(149,plain,
( ~ ! [Y: $i] :
( cp1xcomp(Y)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),Y) )
| cp1xcomp(i2003_11_14_17_21_5199)
| ~ rinvR(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_5199)),i2003_11_14_17_21_5199) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
cp1xcomp(i2003_11_14_17_21_5199),
inference(unit_resolution,[status(thm)],[149,146,113]) ).
tff(151,plain,
( ~ ( ~ cp1xcomp(i2003_11_14_17_21_5199)
| ra_Px1(i2003_11_14_17_21_5199,tptp_fun_Y0_2(i2003_11_14_17_21_5199)) )
| ~ cp1xcomp(i2003_11_14_17_21_5199)
| ra_Px1(i2003_11_14_17_21_5199,tptp_fun_Y0_2(i2003_11_14_17_21_5199)) ),
inference(tautology,[status(thm)],[]) ).
tff(152,plain,
( ~ ( ~ cp1xcomp(i2003_11_14_17_21_5199)
| ra_Px1(i2003_11_14_17_21_5199,tptp_fun_Y0_2(i2003_11_14_17_21_5199)) )
| ra_Px1(i2003_11_14_17_21_5199,tptp_fun_Y0_2(i2003_11_14_17_21_5199)) ),
inference(unit_resolution,[status(thm)],[151,150]) ).
tff(153,plain,
ra_Px1(i2003_11_14_17_21_5199,tptp_fun_Y0_2(i2003_11_14_17_21_5199)),
inference(unit_resolution,[status(thm)],[152,17]) ).
tff(154,plain,
^ [X: $i] :
refl(( ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
<=> ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(155,plain,
( ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
<=> ! [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)],[154]) ).
tff(156,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
<=> ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(157,plain,
( ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
<=> ! [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)],[156]) ).
tff(158,plain,
( ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
<=> ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) ),
inference(transitivity,[status(thm)],[157,155]) ).
tff(159,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
<=> ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )),
( ( ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
<=> ( ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
rewrite(( ( ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
<=> ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
( ( ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
<=> ~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(160,plain,
( ! [X: $i] :
( ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
<=> ! [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)],[159]) ).
tff(161,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)) )
& ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(162,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)) )
& ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[161]) ).
tff(163,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(164,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(165,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)],[164]) ).
tff(166,axiom,
! [X: $i] :
( cp1(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
tff(167,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp1(X) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp1(X) ),
inference(modus_ponens,[status(thm)],[167,163]) ).
tff(169,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)],[168]) ).
tff(170,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)],[169,162]) ).
tff(171,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)],[170,160]) ).
tff(172,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)],[171,158]) ).
tff(173,plain,
( ~ ! [X: $i] :
~ ( ~ ( cp1(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp1(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
| ~ ( ~ ( cp1(i2003_11_14_17_21_5199)
| ra_Px1(i2003_11_14_17_21_5199,tptp_fun_Y_1(i2003_11_14_17_21_5199)) )
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_5199,Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
~ ( ~ ( cp1(i2003_11_14_17_21_5199)
| ra_Px1(i2003_11_14_17_21_5199,tptp_fun_Y_1(i2003_11_14_17_21_5199)) )
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_5199,Y) ) ),
inference(unit_resolution,[status(thm)],[173,172]) ).
tff(175,plain,
( ~ ( cp1(i2003_11_14_17_21_5199)
| ra_Px1(i2003_11_14_17_21_5199,tptp_fun_Y_1(i2003_11_14_17_21_5199)) )
| ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_5199,Y) )
| ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_5199,Y) ),
inference(tautology,[status(thm)],[]) ).
tff(176,plain,
( ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_5199,Y) ),
inference(unit_resolution,[status(thm)],[175,174]) ).
tff(177,plain,
( ~ cp1(i2003_11_14_17_21_5199)
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_5199))
| ~ rr(i2003_11_14_17_21_5199,tptp_fun_Y_0(i2003_11_14_17_21_5199))
| cp1(i2003_11_14_17_21_5199) ),
inference(tautology,[status(thm)],[]) ).
tff(178,plain,
cp1(i2003_11_14_17_21_5199),
inference(unit_resolution,[status(thm)],[177,82]) ).
tff(179,plain,
( ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_5199,Y) )
| ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_5199,Y) ),
inference(tautology,[status(thm)],[]) ).
tff(180,plain,
( ~ ( ~ cp1(i2003_11_14_17_21_5199)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_5199,Y) )
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_5199,Y) ),
inference(unit_resolution,[status(thm)],[179,178]) ).
tff(181,plain,
! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_5199,Y),
inference(unit_resolution,[status(thm)],[180,176]) ).
tff(182,plain,
( ~ ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_5199,Y)
| ~ ra_Px1(i2003_11_14_17_21_5199,tptp_fun_Y0_2(i2003_11_14_17_21_5199)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(183,plain,
$false,
inference(unit_resolution,[status(thm)],[182,181,153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS121+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:11:42 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------