TSTP Solution File: KRS112+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS112+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 Sep 17 17:44:48 EDT 2022
% Result : Unsatisfiable 0.11s 0.29s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 110
% Syntax : Number of formulae : 247 ( 52 unt; 18 typ; 0 def)
% Number of atoms : 1826 ( 88 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 3158 (1650 ~;1162 |; 167 &)
% ( 164 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 89 ( 89 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 17 >; 5 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 615 ( 547 !; 20 ?; 615 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px1_type,type,
ra_Px1: ( $i * $i ) > $o ).
tff(tptp_fun_Y0_3_type,type,
tptp_fun_Y0_3: $i > $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_21_19256_type,type,
i2003_11_14_17_21_19256: $i ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(tptp_fun_Y_5_type,type,
tptp_fun_Y_5: $i > $i ).
tff(rf1_type,type,
rf1: ( $i * $i ) > $o ).
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(cowlThing_type,type,
cowlThing: $i > $o ).
tff(ca_Vx3_type,type,
ca_Vx3: $i > $o ).
tff(rinvF1_type,type,
rinvF1: ( $i * $i ) > $o ).
tff(cp_type,type,
cp: $i > $o ).
tff(rf_type,type,
rf: ( $i * $i ) > $o ).
tff(ca_Ax2_type,type,
ca_Ax2: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(cpxcomp_type,type,
cpxcomp: $i > $o ).
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $i > $i ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cowlThing(tptp_fun_Y_5(X)) ) )
<=> ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) ) )),
rewrite(
( ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) ) )
<=> ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )),
( ( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cowlThing(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) ) ) )
<=> ( ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) )),
rewrite(
( ( ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) )),
( ( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cowlThing(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [X: $i] :
( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cowlThing(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) ) )
<=> ! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(10,plain,
! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i] :
( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cowlThing(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) ) ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_19256,Y)
| ~ cowlThing(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_19256,Y)
| ~ cowlThing(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_19256,Y)
| ~ cowlThing(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[16,14]) ).
tff(18,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_19256,Y)
| ~ cowlThing(Y) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cowlThing(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) ) ),
inference(unit_resolution,[status(thm)],[19,13]) ).
tff(21,plain,
( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_19256,Y) ) )
| ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(tautology,[status(thm)],]) ).
tff(22,plain,
( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
^ [X: $i,Y: $i] :
refl(
( ( rinvF1(X,Y)
<=> rf1(Y,X) )
<=> ( rinvF1(X,Y)
<=> rf1(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
tff(27,plain,
! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [X: $i,Y: $i] :
( rinvF1(X,Y)
<=> rf1(Y,X) )
| ( rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256)
<=> rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256)
<=> rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) ) )),
rewrite(
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) )),
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
^ [X: $i] :
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& ca_Ax2(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& ca_Ax2(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& ca_Ax2(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(43,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& ca_Ax2(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& rf(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& ca_Ax2(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[46,36]) ).
tff(48,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ rf(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_19256,Y) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_19256,Y) ) ) ),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_19256)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf1(i2003_11_14_17_21_19256,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_19256,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256)) ) ),
inference(tautology,[status(thm)],]) ).
tff(51,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256)) ) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( cUnsatisfiable(i2003_11_14_17_21_19256)
<=> cUnsatisfiable(i2003_11_14_17_21_19256) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
cUnsatisfiable(i2003_11_14_17_21_19256),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
tff(54,plain,
cUnsatisfiable(i2003_11_14_17_21_19256),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256)) ) ),
inference(tautology,[status(thm)],]) ).
tff(56,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_19256)
| ~ ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256)) ) )
| ~ ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256)) ) ),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
~ ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256)) ),
inference(unit_resolution,[status(thm)],[56,51]) ).
tff(58,plain,
( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ),
inference(tautology,[status(thm)],]) ).
tff(59,plain,
rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
( ~ ( rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256)
<=> rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) )
| rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256)
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) ),
inference(tautology,[status(thm)],]) ).
tff(61,plain,
( ~ ( rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256)
<=> rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256)) )
| rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256) ),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256),
inference(unit_resolution,[status(thm)],[61,31]) ).
tff(63,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
<=> ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) )),
( ( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ( ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) )),
rewrite(
( ( ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) )),
( ( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
^ [X: $i] :
rewrite(
( ( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [X: $i] :
( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
<=> ! [X: $i] :
( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
^ [X: $i] :
rewrite(
( ( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( rinvF1(X,Y)
=> ca_Vx3(Y) ) ) )
<=> ( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(76,plain,
( ! [X: $i] :
( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( rinvF1(X,Y)
=> ca_Vx3(Y) ) ) )
<=> ! [X: $i] :
( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,axiom,
! [X: $i] :
( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( rinvF1(X,Y)
=> ca_Vx3(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(78,plain,
! [X: $i] :
( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [X: $i] :
( ca_Ax2(X)
<=> ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cpxcomp(X)
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ),
inference(modus_ponens,[status(thm)],[80,73]) ).
tff(82,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ),
inference(modus_ponens,[status(thm)],[81,71]) ).
tff(83,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) ) ),
inference(modus_ponens,[status(thm)],[82,69]) ).
tff(84,plain,
! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[83,64]) ).
tff(85,plain,
( ~ ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ cpxcomp(X)
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF1(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ cpxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) ) ) ) )
| ~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_19256)))
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_19256)))
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) ) ),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_19256)))
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(88,plain,
( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) ),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256)) ),
inference(tautology,[status(thm)],]) ).
tff(90,plain,
ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[89,57]) ).
tff(91,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(92,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) )
| ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ) ),
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ),
inference(unit_resolution,[status(thm)],[92,88]) ).
tff(94,plain,
( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) )
| ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ) ),
inference(tautology,[status(thm)],]) ).
tff(95,plain,
! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) ),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
( ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) )
| ca_Vx3(i2003_11_14_17_21_19256)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256) )
<=> ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) )
| ca_Vx3(i2003_11_14_17_21_19256)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) )
| ca_Vx3(i2003_11_14_17_21_19256)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) )
| ca_Vx3(i2003_11_14_17_21_19256)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
ca_Vx3(i2003_11_14_17_21_19256),
inference(unit_resolution,[status(thm)],[98,95,62]) ).
tff(100,plain,
( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(tautology,[status(thm)],]) ).
tff(101,plain,
( ~ ( ~ ca_Vx3(i2003_11_14_17_21_19256)
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) )
| ~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(unit_resolution,[status(thm)],[100,99]) ).
tff(102,plain,
~ ( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(unit_resolution,[status(thm)],[101,22]) ).
tff(103,plain,
( ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| ~ cowlThing(tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(tautology,[status(thm)],]) ).
tff(104,plain,
rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ rs(X,Y)
| rf1(X,Y) )
<=> ( ~ rs(X,Y)
| rf1(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( rs(X,Y)
=> rf1(X,Y) )
<=> ( ~ rs(X,Y)
| rf1(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(109,plain,
( ! [X: $i,Y: $i] :
( rs(X,Y)
=> rf1(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,axiom,
! [X: $i,Y: $i] :
( rs(X,Y)
=> rf1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
tff(111,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[113,106]) ).
tff(115,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[117,114,104]) ).
tff(119,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(
( ( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
<=> ( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(120,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( rf1(X,Y)
& rf1(X,Z) )
<=> ~ ( ~ rf1(X,Z)
| ~ rf1(X,Y) ) )),
( ~ ( rf1(X,Y)
& rf1(X,Z) )
<=> ~ ~ ( ~ rf1(X,Z)
| ~ rf1(X,Y) ) )),
rewrite(
( ~ ~ ( ~ rf1(X,Z)
| ~ rf1(X,Y) )
<=> ( ~ rf1(X,Z)
| ~ rf1(X,Y) ) )),
( ~ ( rf1(X,Y)
& rf1(X,Z) )
<=> ( ~ rf1(X,Z)
| ~ rf1(X,Y) ) )),
( ( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ( ~ rf1(X,Z)
| ~ rf1(X,Y)
| ( Y = Z ) ) )),
rewrite(
( ( ~ rf1(X,Z)
| ~ rf1(X,Y)
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) ) )),
( ( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(122,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(
( ( ( rf1(X,Y)
& rf1(X,Z) )
=> ( Y = Z ) )
<=> ( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ) )),
inference(bind,[status(th)],]) ).
tff(125,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rf1(X,Y)
& rf1(X,Z) )
=> ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rf1(X,Y)
& rf1(X,Z) )
=> ( Y = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(127,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[128]) ).
tff(130,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[129,122]) ).
tff(131,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[130,120]) ).
tff(132,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
( ( ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) )
<=> ( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(transitivity,[status(thm)],[134,132]) ).
tff(136,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(quant_inst,[status(thm)],]) ).
tff(137,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256) )
| ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256),
inference(unit_resolution,[status(thm)],[137,131,59,118]) ).
tff(139,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ rs(X,Y)
| rf(X,Y) )
<=> ( ~ rs(X,Y)
| rf(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(140,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(142,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( rs(X,Y)
=> rf(X,Y) )
<=> ( ~ rs(X,Y)
| rf(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(143,plain,
( ! [X: $i,Y: $i] :
( rs(X,Y)
=> rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,axiom,
! [X: $i,Y: $i] :
( rs(X,Y)
=> rf(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
tff(145,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[145,141]) ).
tff(147,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(skolemize,[status(sab)],[146]) ).
tff(148,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[147,140]) ).
tff(149,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(150,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(quant_inst,[status(thm)],]) ).
tff(151,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256))
| rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[151,148,104]) ).
tff(153,plain,
( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256)) ),
inference(tautology,[status(thm)],]) ).
tff(154,plain,
rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[153,57]) ).
tff(155,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(
( ( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
<=> ( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(156,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( rf(X,Y)
& rf(X,Z) )
<=> ~ ( ~ rf(X,Z)
| ~ rf(X,Y) ) )),
( ~ ( rf(X,Y)
& rf(X,Z) )
<=> ~ ~ ( ~ rf(X,Z)
| ~ rf(X,Y) ) )),
rewrite(
( ~ ~ ( ~ rf(X,Z)
| ~ rf(X,Y) )
<=> ( ~ rf(X,Z)
| ~ rf(X,Y) ) )),
( ~ ( rf(X,Y)
& rf(X,Z) )
<=> ( ~ rf(X,Z)
| ~ rf(X,Y) ) )),
( ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ( ~ rf(X,Z)
| ~ rf(X,Y)
| ( Y = Z ) ) )),
rewrite(
( ( ~ rf(X,Z)
| ~ rf(X,Y)
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ) )),
( ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(158,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,Z)
| ~ rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,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(160,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(161,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)],[160]) ).
tff(162,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(163,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[163,159]) ).
tff(165,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[164]) ).
tff(166,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(modus_ponens,[status(thm)],[165,158]) ).
tff(167,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(modus_ponens,[status(thm)],[166,156]) ).
tff(168,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(169,plain,
( ( ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) )
<=> ( ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(170,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ) ),
inference(transitivity,[status(thm)],[170,168]) ).
tff(172,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(quant_inst,[status(thm)],]) ).
tff(173,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ( tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256) )
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_5(i2003_11_14_17_21_19256)) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
tptp_fun_Y_5(i2003_11_14_17_21_19256) = tptp_fun_Y_1(i2003_11_14_17_21_19256),
inference(unit_resolution,[status(thm)],[173,167,154,152]) ).
tff(175,plain,
tptp_fun_Y_1(i2003_11_14_17_21_19256) = tptp_fun_Y_5(i2003_11_14_17_21_19256),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
tptp_fun_Y_1(i2003_11_14_17_21_19256) = tptp_fun_Y_0(i2003_11_14_17_21_19256),
inference(transitivity,[status(thm)],[175,138]) ).
tff(177,plain,
( ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256)))
<=> ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256)))
<=> ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(180,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[179]) ).
tff(181,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(182,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[181]) ).
tff(183,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[182,180]) ).
tff(184,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) )
<=> ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )),
( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
rewrite(
( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(185,plain,
( ! [X: $i] :
( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[184]) ).
tff(186,plain,
( ! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) )
<=> ! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(187,axiom,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(188,plain,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
! [X: $i] :
( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(skolemize,[status(sab)],[188]) ).
tff(190,plain,
! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[189,185]) ).
tff(191,plain,
! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[190,183]) ).
tff(192,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
| ~ ( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) )
| ~ ( cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y0) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(193,plain,
~ ( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) )
| ~ ( cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y0) ) ),
inference(unit_resolution,[status(thm)],[192,191]) ).
tff(194,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) )
| ~ ( cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y0) )
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ),
inference(tautology,[status(thm)],]) ).
tff(195,plain,
( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ),
inference(unit_resolution,[status(thm)],[194,193]) ).
tff(196,plain,
( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF1(tptp_fun_Y_0(i2003_11_14_17_21_19256),Y) )
| cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256)) ),
inference(tautology,[status(thm)],]) ).
tff(197,plain,
cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[196,93]) ).
tff(198,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) )
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ),
inference(tautology,[status(thm)],]) ).
tff(199,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) )
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ),
inference(unit_resolution,[status(thm)],[198,197]) ).
tff(200,plain,
ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))),
inference(unit_resolution,[status(thm)],[199,195]) ).
tff(201,plain,
ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))),
inference(modus_ponens,[status(thm)],[200,178]) ).
tff(202,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(203,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[202]) ).
tff(204,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(205,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) ),
inference(quant_intro,[status(thm)],[204]) ).
tff(206,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(207,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) ),
inference(quant_intro,[status(thm)],[206]) ).
tff(208,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) ),
inference(transitivity,[status(thm)],[207,205]) ).
tff(209,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
<=> ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )),
( ( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) )),
rewrite(
( ( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) )),
( ( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(210,plain,
( ! [X: $i] :
( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) ),
inference(quant_intro,[status(thm)],[209]) ).
tff(211,plain,
( ! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(212,axiom,
! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(213,plain,
! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
inference(modus_ponens,[status(thm)],[212,211]) ).
tff(214,plain,
! [X: $i] :
( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ),
inference(skolemize,[status(sab)],[213]) ).
tff(215,plain,
! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ),
inference(modus_ponens,[status(thm)],[214,210]) ).
tff(216,plain,
! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ),
inference(modus_ponens,[status(thm)],[215,208]) ).
tff(217,plain,
! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ),
inference(modus_ponens,[status(thm)],[216,203]) ).
tff(218,plain,
( ~ ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
| ~ ( ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y_2(tptp_fun_Y_1(i2003_11_14_17_21_19256))) )
| ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(219,plain,
~ ( ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y_2(tptp_fun_Y_1(i2003_11_14_17_21_19256))) )
| ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) ) ),
inference(unit_resolution,[status(thm)],[218,217]) ).
tff(220,plain,
( ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y_2(tptp_fun_Y_1(i2003_11_14_17_21_19256))) )
| ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) ),
inference(tautology,[status(thm)],]) ).
tff(221,plain,
( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) ),
inference(unit_resolution,[status(thm)],[220,219]) ).
tff(222,plain,
( ~ rf1(i2003_11_14_17_21_19256,tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_19256))
| ~ rf(i2003_11_14_17_21_19256,tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| cp(tptp_fun_Y_1(i2003_11_14_17_21_19256)) ),
inference(tautology,[status(thm)],]) ).
tff(223,plain,
cp(tptp_fun_Y_1(i2003_11_14_17_21_19256)),
inference(unit_resolution,[status(thm)],[222,57]) ).
tff(224,plain,
( ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) ),
inference(tautology,[status(thm)],]) ).
tff(225,plain,
( ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_19256))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) )
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y) ),
inference(unit_resolution,[status(thm)],[224,223]) ).
tff(226,plain,
! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y),
inference(unit_resolution,[status(thm)],[225,221]) ).
tff(227,plain,
( ~ ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),Y)
| ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))) ),
inference(quant_inst,[status(thm)],]) ).
tff(228,plain,
~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_19256),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_19256))),
inference(unit_resolution,[status(thm)],[227,226]) ).
tff(229,plain,
$false,
inference(unit_resolution,[status(thm)],[228,201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : KRS112+1 : TPTP v8.1.0. Released v3.1.0.
% 0.02/0.07 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.06/0.26 % Computer : n017.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Thu Sep 1 08:58:37 EDT 2022
% 0.06/0.26 % CPUTime :
% 0.06/0.26 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.06/0.26 Usage: tptp [options] [-file:]file
% 0.06/0.26 -h, -? prints this message.
% 0.06/0.26 -smt2 print SMT-LIB2 benchmark.
% 0.06/0.26 -m, -model generate model.
% 0.06/0.26 -p, -proof generate proof.
% 0.06/0.26 -c, -core generate unsat core of named formulas.
% 0.06/0.26 -st, -statistics display statistics.
% 0.06/0.26 -t:timeout set timeout (in second).
% 0.06/0.26 -smt2status display status in smt2 format instead of SZS.
% 0.06/0.26 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.06/0.26 -<param>:<value> configuration parameter and value.
% 0.06/0.26 -o:<output-file> file to place output in.
% 0.11/0.29 % SZS status Unsatisfiable
% 0.11/0.29 % SZS output start Proof
% See solution above
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