TSTP Solution File: KRS072+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS072+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:44:36 EDT 2022
% Result : Unsatisfiable 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 53
% Syntax : Number of formulae : 109 ( 23 unt; 13 typ; 0 def)
% Number of atoms : 1102 ( 158 equ)
% Maximal formula atoms : 32 ( 11 avg)
% Number of connectives : 1755 ( 786 ~; 741 |; 142 &)
% ( 74 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 37 ( 37 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 12 >; 2 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 322 ( 289 !; 18 ?; 322 :)
% Comments :
%------------------------------------------------------------------------------
tff(tptp_fun_Z_1_type,type,
tptp_fun_Z_1: $i > $i ).
tff(i2003_11_14_17_18_50190_type,type,
i2003_11_14_17_18_50190: $i ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(rinvR_type,type,
rinvR: ( $i * $i ) > $o ).
tff(cp1_type,type,
cp1: $i > $o ).
tff(cp2_type,type,
cp2: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Z1_2_type,type,
tptp_fun_Z1_2: $i > $i ).
tff(tptp_fun_Z0_3_type,type,
tptp_fun_Z0_3: $i > $i ).
tff(cp5_type,type,
cp5: $i > $o ).
tff(cp4_type,type,
cp4: $i > $o ).
tff(cp3_type,type,
cp3: $i > $o ).
tff(1,plain,
^ [X: $i,Y: $i] :
refl(
( ( rinvR(X,Y)
<=> rr(Y,X) )
<=> ( rinvR(X,Y)
<=> rr(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(5,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
| ( rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
<=> rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
( rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
<=> rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(tptp_fun_Y_0(X),Z0)
& rr(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& cp2(X) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) ) )),
rewrite(
( ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ ( rr(Y,tptp_fun_Z0_3(Y))
& rr(Y,tptp_fun_Z1_2(Y)) )
| ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) ) )
| ! [Z: $i] :
~ ( rr(Y,Z)
& cp1(Z) ) ) )
<=> ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(tptp_fun_Y_0(X),Z0)
& rr(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ ( rr(Y,tptp_fun_Z0_3(Y))
& rr(Y,tptp_fun_Z1_2(Y)) )
| ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) ) )
| ! [Z: $i] :
~ ( rr(Y,Z)
& cp1(Z) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ) )),
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(tptp_fun_Y_0(X),Z0)
& rr(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ ( rr(Y,tptp_fun_Z0_3(Y))
& rr(Y,tptp_fun_Z1_2(Y)) )
| ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) ) )
| ! [Z: $i] :
~ ( rr(Y,Z)
& cp1(Z) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(tptp_fun_Y_0(X),Z0)
& rr(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ ( rr(Y,tptp_fun_Z0_3(Y))
& rr(Y,tptp_fun_Z1_2(Y)) )
| ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) ) )
| ! [Z: $i] :
~ ( rr(Y,Z)
& cp1(Z) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
^ [X: $i] :
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(tptp_fun_Y_0(X),Z0)
& rr(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ ( rr(Y,tptp_fun_Z0_3(Y))
& rr(Y,tptp_fun_Z1_2(Y)) )
| ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) ) )
| ! [Z: $i] :
~ ( rr(Y,Z)
& cp1(Z) ) )
| ~ cp2(X) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(tptp_fun_Y_0(X),Z0)
& rr(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ ( rr(Y,tptp_fun_Z0_3(Y))
& rr(Y,tptp_fun_Z1_2(Y)) )
| ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) ) )
| ! [Z: $i] :
~ ( rr(Y,Z)
& cp1(Z) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(tptp_fun_Y_0(X),Z0)
& rr(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ ( rr(Y,tptp_fun_Z0_3(Y))
& rr(Y,tptp_fun_Z1_2(Y)) )
| ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) ) )
| ! [Z: $i] :
~ ( rr(Y,Z)
& cp1(Z) ) )
| ~ cp2(X) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(tptp_fun_Y_0(X),Z0)
& rr(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ ( rr(Y,tptp_fun_Z0_3(Y))
& rr(Y,tptp_fun_Z1_2(Y)) )
| ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) ) )
| ! [Z: $i] :
~ ( rr(Y,Z)
& cp1(Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvR(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(Y,Z0)
& rr(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z) ) )
& cp2(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvR(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(Y,Z0)
& rr(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z) ) )
& cp2(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
^ [X: $i] :
rewrite(
( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvR(X,Y)
& ! [Z0: $i,Z1: $i] :
( ( rr(Y,Z0)
& rr(Y,Z1) )
=> ( Z0 = Z1 ) )
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z) ) )
& cp2(X) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvR(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(Y,Z0)
& rr(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z) ) )
& cp2(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvR(X,Y)
& ! [Z0: $i,Z1: $i] :
( ( rr(Y,Z0)
& rr(Y,Z1) )
=> ( Z0 = Z1 ) )
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z) ) )
& cp2(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvR(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(Y,Z0)
& rr(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z) ) )
& cp2(X) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvR(X,Y)
& ! [Z0: $i,Z1: $i] :
( ( rr(Y,Z0)
& rr(Y,Z1) )
=> ( Z0 = Z1 ) )
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z) ) )
& cp2(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(23,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvR(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(Y,Z0)
& rr(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z) ) )
& cp2(X) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvR(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(Y,Z0)
& rr(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rr(Y,Z)
& cp1(Z) ) )
& cp2(X) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(tptp_fun_Y_0(X),Z0)
& rr(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ ( rr(Y,tptp_fun_Z0_3(Y))
& rr(Y,tptp_fun_Z1_2(Y)) )
| ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) ) )
| ! [Z: $i] :
~ ( rr(Y,Z)
& cp1(Z) ) )
| ~ cp2(X) ) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rr(tptp_fun_Y_0(X),Z0)
& rr(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cp1(tptp_fun_Z_1(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ ( rr(Y,tptp_fun_Z0_3(Y))
& rr(Y,tptp_fun_Z1_2(Y)) )
| ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) ) )
| ! [Z: $i] :
~ ( rr(Y,Z)
& cp1(Z) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ),
inference(modus_ponens,[status(thm)],[26,16]) ).
tff(28,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,14]) ).
tff(29,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(X),Z0)
| ~ rr(tptp_fun_Y_0(X),Z1) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cp1(tptp_fun_Z_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| ~ ( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_50190)
| ~ cp2(i2003_11_14_17_18_50190)
| ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_18_50190,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| ~ ( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_50190)
| ~ cp2(i2003_11_14_17_18_50190)
| ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_18_50190,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| ~ ( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_50190)
| ~ cp2(i2003_11_14_17_18_50190)
| ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_18_50190,Y)
| ~ ( ( tptp_fun_Z0_3(Y) = tptp_fun_Z1_2(Y) )
| ~ rr(Y,tptp_fun_Z0_3(Y))
| ~ rr(Y,tptp_fun_Z1_2(Y)) )
| ! [Z: $i] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| ~ ( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ) ),
inference(tautology,[status(thm)],]) ).
tff(32,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| ~ ( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ) ),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
( cUnsatisfiable(i2003_11_14_17_18_50190)
<=> cUnsatisfiable(i2003_11_14_17_18_50190) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
cUnsatisfiable(i2003_11_14_17_18_50190),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(35,plain,
cUnsatisfiable(i2003_11_14_17_18_50190),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| ~ ( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| ~ ( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ) ),
inference(tautology,[status(thm)],]) ).
tff(37,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| ~ ( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ) )
| ~ ( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ) ),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
~ ( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ),
inference(unit_resolution,[status(thm)],[37,32]) ).
tff(39,plain,
( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190)) ),
inference(tautology,[status(thm)],]) ).
tff(40,plain,
rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190)),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ ( rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
<=> rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) )
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) ),
inference(tautology,[status(thm)],]) ).
tff(42,plain,
( ~ ( rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
<=> rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) )
| rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) ),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190),
inference(unit_resolution,[status(thm)],[42,9]) ).
tff(44,plain,
( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190)) ),
inference(tautology,[status(thm)],]) ).
tff(45,plain,
rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190)),
inference(unit_resolution,[status(thm)],[44,38]) ).
tff(46,plain,
( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) ) ),
inference(tautology,[status(thm)],]) ).
tff(47,plain,
! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) ),
inference(unit_resolution,[status(thm)],[46,38]) ).
tff(48,plain,
( ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190)
| ( tptp_fun_Z_1(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 ) )
<=> ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190)
| ( tptp_fun_Z_1(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ( ( tptp_fun_Z_1(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) )
<=> ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190)
| ( tptp_fun_Z_1(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ( tptp_fun_Z_1(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) )
<=> ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190)
| ( tptp_fun_Z_1(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 ) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ( tptp_fun_Z_1(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) )
<=> ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190)
| ( tptp_fun_Z_1(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 ) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ( tptp_fun_Z_1(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190)
| ( tptp_fun_Z_1(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
tptp_fun_Z_1(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190,
inference(unit_resolution,[status(thm)],[53,47,45,43]) ).
tff(55,plain,
i2003_11_14_17_18_50190 = tptp_fun_Z_1(i2003_11_14_17_18_50190),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ),
inference(tautology,[status(thm)],]) ).
tff(57,plain,
cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190)),
inference(unit_resolution,[status(thm)],[56,38]) ).
tff(58,plain,
^ [X: $i] :
refl(
( ( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
<=> ( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
<=> ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
<=> ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ~ ( cp3(X)
| cp2(X)
| cp4(X)
| cp5(X) )
<=> ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )),
( ( cp1(X)
=> ~ ( cp3(X)
| cp2(X)
| cp4(X)
| cp5(X) ) )
<=> ( cp1(X)
=> ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) )),
rewrite(
( ( cp1(X)
=> ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
<=> ( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) )),
( ( cp1(X)
=> ~ ( cp3(X)
| cp2(X)
| cp4(X)
| cp5(X) ) )
<=> ( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [X: $i] :
( cp1(X)
=> ~ ( cp3(X)
| cp2(X)
| cp4(X)
| cp5(X) ) )
<=> ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [X: $i] :
( cp1(X)
=> ~ ( cp3(X)
| cp2(X)
| cp4(X)
| cp5(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(64,plain,
! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( ( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ ( cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp3(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp4(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp5(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ) )
<=> ( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ ( cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp3(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp4(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp5(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ ( cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp3(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp4(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp5(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ ( cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp3(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp4(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp5(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
~ ( cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp3(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp4(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp5(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ),
inference(unit_resolution,[status(thm)],[70,67,57]) ).
tff(72,plain,
( cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp3(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp4(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp5(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190)) ),
inference(tautology,[status(thm)],]) ).
tff(73,plain,
~ cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190)),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
( ~ cp2(i2003_11_14_17_18_50190)
| ~ rinvR(i2003_11_14_17_18_50190,tptp_fun_Y_0(i2003_11_14_17_18_50190))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z0)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),Z1) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_18_50190),tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ~ cp1(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| cp2(i2003_11_14_17_18_50190) ),
inference(tautology,[status(thm)],]) ).
tff(75,plain,
cp2(i2003_11_14_17_18_50190),
inference(unit_resolution,[status(thm)],[74,38]) ).
tff(76,plain,
^ [A: $i,B: $i] :
refl(
( ( cp2(B)
| ( A != B )
| ~ cp2(A) )
<=> ( cp2(B)
| ( A != B )
| ~ cp2(A) ) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
<=> ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
^ [A: $i,B: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( A = B )
& cp2(A) )
<=> ~ ( ( A != B )
| ~ cp2(A) ) )),
( ~ ( ( A = B )
& cp2(A) )
<=> ~ ~ ( ( A != B )
| ~ cp2(A) ) )),
rewrite(
( ~ ~ ( ( A != B )
| ~ cp2(A) )
<=> ( ( A != B )
| ~ cp2(A) ) )),
( ~ ( ( A = B )
& cp2(A) )
<=> ( ( A != B )
| ~ cp2(A) ) )),
( ( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) )
<=> ( cp2(B)
| ( A != B )
| ~ cp2(A) ) )),
rewrite(
( ( cp2(B)
| ( A != B )
| ~ cp2(A) )
<=> ( cp2(B)
| ( A != B )
| ~ cp2(A) ) )),
( ( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) )
<=> ( cp2(B)
| ( A != B )
| ~ cp2(A) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [A: $i,B: $i] :
( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) )
<=> ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [A: $i,B: $i] :
( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) )
<=> ! [A: $i,B: $i] :
( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
^ [A: $i,B: $i] :
rewrite(
( ( ( ( A = B )
& cp2(A) )
=> cp2(B) )
<=> ( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [A: $i,B: $i] :
( ( ( A = B )
& cp2(A) )
=> cp2(B) )
<=> ! [A: $i,B: $i] :
( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& cp2(A) )
=> cp2(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2_substitution_1) ).
tff(84,plain,
! [A: $i,B: $i] :
( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [A: $i,B: $i] :
( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [A: $i,B: $i] :
( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) ),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) ),
inference(modus_ponens,[status(thm)],[87,77]) ).
tff(89,plain,
( ( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| ~ cp2(i2003_11_14_17_18_50190)
| cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ( i2003_11_14_17_18_50190 != tptp_fun_Z_1(i2003_11_14_17_18_50190) ) )
<=> ( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| ~ cp2(i2003_11_14_17_18_50190)
| cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ( i2003_11_14_17_18_50190 != tptp_fun_Z_1(i2003_11_14_17_18_50190) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ( i2003_11_14_17_18_50190 != tptp_fun_Z_1(i2003_11_14_17_18_50190) )
| ~ cp2(i2003_11_14_17_18_50190) )
<=> ( ~ cp2(i2003_11_14_17_18_50190)
| cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ( i2003_11_14_17_18_50190 != tptp_fun_Z_1(i2003_11_14_17_18_50190) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ( i2003_11_14_17_18_50190 != tptp_fun_Z_1(i2003_11_14_17_18_50190) )
| ~ cp2(i2003_11_14_17_18_50190) )
<=> ( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| ~ cp2(i2003_11_14_17_18_50190)
| cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ( i2003_11_14_17_18_50190 != tptp_fun_Z_1(i2003_11_14_17_18_50190) ) ) ),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
( ( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ( i2003_11_14_17_18_50190 != tptp_fun_Z_1(i2003_11_14_17_18_50190) )
| ~ cp2(i2003_11_14_17_18_50190) )
<=> ( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| ~ cp2(i2003_11_14_17_18_50190)
| cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ( i2003_11_14_17_18_50190 != tptp_fun_Z_1(i2003_11_14_17_18_50190) ) ) ),
inference(transitivity,[status(thm)],[91,89]) ).
tff(93,plain,
( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ( i2003_11_14_17_18_50190 != tptp_fun_Z_1(i2003_11_14_17_18_50190) )
| ~ cp2(i2003_11_14_17_18_50190) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| ~ cp2(i2003_11_14_17_18_50190)
| cp2(tptp_fun_Z_1(i2003_11_14_17_18_50190))
| ( i2003_11_14_17_18_50190 != tptp_fun_Z_1(i2003_11_14_17_18_50190) ) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
i2003_11_14_17_18_50190 != tptp_fun_Z_1(i2003_11_14_17_18_50190),
inference(unit_resolution,[status(thm)],[94,88,75,73]) ).
tff(96,plain,
$false,
inference(unit_resolution,[status(thm)],[95,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : KRS072+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 09:29:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.40 % SZS status Unsatisfiable
% 0.18/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------