TSTP Solution File: KRS077+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS077+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 17:44:37 EDT 2022
% Result : Unsatisfiable 0.14s 0.33s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 53
% Syntax : Number of formulae : 110 ( 22 unt; 11 typ; 0 def)
% Number of atoms : 1356 ( 172 equ)
% Maximal formula atoms : 40 ( 13 avg)
% Number of connectives : 2245 (1037 ~; 946 |; 168 &)
% ( 82 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 49 ( 49 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 10 >; 3 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 463 ( 423 !; 18 ?; 463 :)
% Comments :
%------------------------------------------------------------------------------
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_19_09372_type,type,
i2003_11_14_17_19_09372: $i ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(rinvS_type,type,
rinvS: ( $i * $i ) > $o ).
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(cp_type,type,
cp: $i > $o ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Z_4_type,type,
tptp_fun_Z_4: $i > $i ).
tff(tptp_fun_Y1_2_type,type,
tptp_fun_Y1_2: $i > $i ).
tff(tptp_fun_Y0_3_type,type,
tptp_fun_Y0_3: $i > $i ).
tff(1,plain,
^ [X: $i,Y: $i] :
refl(
( ( rinvS(X,Y)
<=> rs(Y,X) )
<=> ( rinvS(X,Y)
<=> rs(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(5,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) )
| ( rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
<=> rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
( rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
<=> rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) ),
inference(transitivity,[status(thm)],[15,13]) ).
tff(17,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) ) )),
trans(
monotonicity(
rewrite(
( ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
<=> ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rs(X,Y)
& cp(Y) )
<=> ~ ( ~ cp(Y)
| ~ rs(X,Y) ) )),
( ~ ( rs(X,Y)
& cp(Y) )
<=> ~ ~ ( ~ cp(Y)
| ~ rs(X,Y) ) )),
rewrite(
( ~ ~ ( ~ cp(Y)
| ~ rs(X,Y) )
<=> ( ~ cp(Y)
| ~ rs(X,Y) ) )),
( ~ ( rs(X,Y)
& cp(Y) )
<=> ( ~ cp(Y)
| ~ rs(X,Y) ) ))),
( ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) )
<=> ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) )),
( ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) )
<=> ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )),
rewrite(
( ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) )
<=> ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )),
( ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) )
<=> ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) )),
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
^ [X: $i] :
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ~ ~ cp(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ~ ~ cp(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [X: $i] :
rewrite(
( ( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( rinvS(Y,Z)
=> cp(Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( rinvS(Y,Z)
=> cp(Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( rinvS(Y,Z)
=> cp(Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(25,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ~ ~ cp(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ),
inference(modus_ponens,[status(thm)],[28,18]) ).
tff(30,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) ) ),
inference(modus_ponens,[status(thm)],[29,16]) ).
tff(31,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[30,11]) ).
tff(32,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| cp(i2003_11_14_17_19_09372)
| ~ ( ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372)) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| cp(i2003_11_14_17_19_09372)
| ~ ( ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372)) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) ) ) ),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| cp(i2003_11_14_17_19_09372)
| ~ ( ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372)) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(35,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ) ),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
( cUnsatisfiable(i2003_11_14_17_19_09372)
<=> cUnsatisfiable(i2003_11_14_17_19_09372) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
cUnsatisfiable(i2003_11_14_17_19_09372),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(38,plain,
cUnsatisfiable(i2003_11_14_17_19_09372),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(40,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ) )
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ) ),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
~ ( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ),
inference(unit_resolution,[status(thm)],[40,35]) ).
tff(42,plain,
( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ),
inference(tautology,[status(thm)],]) ).
tff(43,plain,
rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ ( rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
<=> rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) )
| rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ),
inference(tautology,[status(thm)],]) ).
tff(45,plain,
( ~ ( rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
<=> rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) )
| rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372),
inference(unit_resolution,[status(thm)],[45,9]) ).
tff(47,plain,
( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ),
inference(tautology,[status(thm)],]) ).
tff(48,plain,
! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ),
inference(unit_resolution,[status(thm)],[47,41]) ).
tff(49,plain,
( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(i2003_11_14_17_19_09372) ),
inference(tautology,[status(thm)],]) ).
tff(50,plain,
~ cp(i2003_11_14_17_19_09372),
inference(unit_resolution,[status(thm)],[49,41]) ).
tff(51,plain,
( ( ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| cp(i2003_11_14_17_19_09372)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) )
<=> ( ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| cp(i2003_11_14_17_19_09372)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| cp(i2003_11_14_17_19_09372)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
( ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| cp(i2003_11_14_17_19_09372)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372),
inference(unit_resolution,[status(thm)],[53,50,48]) ).
tff(55,plain,
^ [A: $i,B: $i,C: $i] :
refl(
( ( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) )
<=> ( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [A: $i,B: $i,C: $i] :
( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) )
<=> ! [A: $i,B: $i,C: $i] :
( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
^ [A: $i,B: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( A = B )
& rinvS(A,C) )
<=> ~ ( ( A != B )
| ~ rinvS(A,C) ) )),
( ~ ( ( A = B )
& rinvS(A,C) )
<=> ~ ~ ( ( A != B )
| ~ rinvS(A,C) ) )),
rewrite(
( ~ ~ ( ( A != B )
| ~ rinvS(A,C) )
<=> ( ( A != B )
| ~ rinvS(A,C) ) )),
( ~ ( ( A = B )
& rinvS(A,C) )
<=> ( ( A != B )
| ~ rinvS(A,C) ) )),
( ( ~ ( ( A = B )
& rinvS(A,C) )
| rinvS(B,C) )
<=> ( ( A != B )
| ~ rinvS(A,C)
| rinvS(B,C) ) )),
rewrite(
( ( ( A != B )
| ~ rinvS(A,C)
| rinvS(B,C) )
<=> ( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) ) )),
( ( ~ ( ( A = B )
& rinvS(A,C) )
| rinvS(B,C) )
<=> ( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [A: $i,B: $i,C: $i] :
( ~ ( ( A = B )
& rinvS(A,C) )
| rinvS(B,C) )
<=> ! [A: $i,B: $i,C: $i] :
( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [A: $i,B: $i,C: $i] :
( ~ ( ( A = B )
& rinvS(A,C) )
| rinvS(B,C) )
<=> ! [A: $i,B: $i,C: $i] :
( ~ ( ( A = B )
& rinvS(A,C) )
| rinvS(B,C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
^ [A: $i,B: $i,C: $i] :
rewrite(
( ( ( ( A = B )
& rinvS(A,C) )
=> rinvS(B,C) )
<=> ( ~ ( ( A = B )
& rinvS(A,C) )
| rinvS(B,C) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& rinvS(A,C) )
=> rinvS(B,C) )
<=> ! [A: $i,B: $i,C: $i] :
( ~ ( ( A = B )
& rinvS(A,C) )
| rinvS(B,C) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& rinvS(A,C) )
=> rinvS(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rinvS_substitution_1) ).
tff(63,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ( A = B )
& rinvS(A,C) )
| rinvS(B,C) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ( A = B )
& rinvS(A,C) )
| rinvS(B,C) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ( A = B )
& rinvS(A,C) )
| rinvS(B,C) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [A: $i,B: $i,C: $i] :
( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
! [A: $i,B: $i,C: $i] :
( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) ),
inference(modus_ponens,[status(thm)],[66,56]) ).
tff(68,plain,
( ( ~ ! [A: $i,B: $i,C: $i] :
( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) )
| rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ~ rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) != tptp_fun_Y_0(i2003_11_14_17_19_09372) ) )
<=> ( ~ ! [A: $i,B: $i,C: $i] :
( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) )
| rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ~ rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) != tptp_fun_Y_0(i2003_11_14_17_19_09372) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) != tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) )
<=> ( rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ~ rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) != tptp_fun_Y_0(i2003_11_14_17_19_09372) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( ~ ! [A: $i,B: $i,C: $i] :
( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) )
| rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) != tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) )
<=> ( ~ ! [A: $i,B: $i,C: $i] :
( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) )
| rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ~ rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) != tptp_fun_Y_0(i2003_11_14_17_19_09372) ) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [A: $i,B: $i,C: $i] :
( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) )
| rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) != tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) )
<=> ( ~ ! [A: $i,B: $i,C: $i] :
( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) )
| rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ~ rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) != tptp_fun_Y_0(i2003_11_14_17_19_09372) ) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [A: $i,B: $i,C: $i] :
( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) )
| rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) != tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [A: $i,B: $i,C: $i] :
( rinvS(B,C)
| ( A != B )
| ~ rinvS(A,C) )
| rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ~ rinvS(tptp_fun_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) != tptp_fun_Y_0(i2003_11_14_17_19_09372) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
tptp_fun_Y_1(i2003_11_14_17_19_09372) != tptp_fun_Y_0(i2003_11_14_17_19_09372),
inference(unit_resolution,[status(thm)],[73,67,54,46]) ).
tff(75,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ rs(X,Y)
| rr(X,Y) )
<=> ( ~ rs(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(76,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( rs(X,Y)
=> rr(X,Y) )
<=> ( ~ rs(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [X: $i,Y: $i] :
( rs(X,Y)
=> rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [X: $i,Y: $i] :
( rs(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(81,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)),
inference(unit_resolution,[status(thm)],[87,84,43]) ).
tff(89,plain,
( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ),
inference(tautology,[status(thm)],]) ).
tff(90,plain,
! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ),
inference(unit_resolution,[status(thm)],[89,41]) ).
tff(91,plain,
( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372)) ),
inference(tautology,[status(thm)],]) ).
tff(92,plain,
rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372)),
inference(unit_resolution,[status(thm)],[91,41]) ).
tff(93,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ( ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) )
<=> ( ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ) ),
inference(transitivity,[status(thm)],[95,93]) ).
tff(97,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
$false,
inference(unit_resolution,[status(thm)],[98,92,90,88,74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : KRS077+1 : TPTP v8.1.0. Released v3.1.0.
% 0.00/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.29 % Computer : n027.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Thu Sep 1 09:45:18 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.29 Usage: tptp [options] [-file:]file
% 0.09/0.29 -h, -? prints this message.
% 0.09/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.29 -m, -model generate model.
% 0.09/0.29 -p, -proof generate proof.
% 0.09/0.29 -c, -core generate unsat core of named formulas.
% 0.09/0.29 -st, -statistics display statistics.
% 0.09/0.29 -t:timeout set timeout (in second).
% 0.09/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.29 -<param>:<value> configuration parameter and value.
% 0.09/0.29 -o:<output-file> file to place output in.
% 0.14/0.33 % SZS status Unsatisfiable
% 0.14/0.33 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------