TSTP Solution File: KRS193+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS193+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 17:45:09 EDT 2022
% Result : Theorem 0.13s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 44
% Syntax : Number of formulae : 95 ( 21 unt; 9 typ; 0 def)
% Number of atoms : 650 ( 0 equ)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 1134 ( 602 ~; 442 |; 18 &)
% ( 66 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 32 ( 32 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 7 >; 7 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 321 ( 289 !; 4 ?; 321 :)
% Comments :
%------------------------------------------------------------------------------
tff(model_type,type,
model: ( $i * $i ) > $o ).
tff(tptp_fun_Ax_21_type,type,
tptp_fun_Ax_21: ( $i * $i ) > $i ).
tff(cax_type,type,
cax: $i ).
tff(thm_type,type,
thm: $i ).
tff(status_type,type,
status: ( $i * $i * $i ) > $o ).
tff(tptp_fun_C_20_type,type,
tptp_fun_C_20: ( $i * $i ) > $i ).
tff(tptp_fun_I1_0_type,type,
tptp_fun_I1_0: $i > $i ).
tff(isa_type,type,
isa: ( $i * $i ) > $o ).
tff(tptp_fun_I1_3_type,type,
tptp_fun_I1_3: ( $i * $i ) > $i ).
tff(1,plain,
^ [Ax: $i,C: $i] :
rewrite(
( ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) )
<=> ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ~ status(Ax,C,cax)
| ! [I1: $i] : ~ model(I1,Ax) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ~ status(Ax,C,cax)
| ! [I1: $i] : ~ model(I1,Ax) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [Ax: $i,C: $i] :
refl(
( ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) )
<=> ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [Ax: $i,C: $i] :
rewrite(
( ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) )
<=> ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [Ax: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) )
<=> ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) )),
( ( ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
& ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) )
<=> ( ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
& ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) ) )),
rewrite(
( ( ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
& ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) )
<=> ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) ) )),
( ( ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
& ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) )
<=> ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [Ax: $i,C: $i] :
( ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
& ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [Ax: $i,C: $i] :
( ~ ? [I1: $i] : model(I1,Ax)
<=> status(Ax,C,cax) )
<=> ! [Ax: $i,C: $i] :
( ~ ? [I1: $i] : model(I1,Ax)
<=> status(Ax,C,cax) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
! [Ax: $i,C: $i] :
( ~ ? [I1: $i] : model(I1,Ax)
<=> status(Ax,C,cax) ),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax',cax) ).
tff(12,plain,
! [Ax: $i,C: $i] :
( ~ ? [I1: $i] : model(I1,Ax)
<=> status(Ax,C,cax) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [Ax: $i,C: $i] :
( ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
& ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ! [I1: $i] : ~ model(I1,Ax)
| ~ status(Ax,C,cax) ) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ~ status(Ax,C,cax)
| ! [I1: $i] : ~ model(I1,Ax) ) ),
inference(modus_ponens,[status(thm)],[15,2]) ).
tff(17,plain,
( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
| status(Ax,C,cax) )
| ~ ( ~ status(Ax,C,cax)
| ! [I1: $i] : ~ model(I1,Ax) ) )
| ~ ( ~ ( model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
~ ( ~ ( model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) ) ),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ( model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) )
| ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) ),
inference(tautology,[status(thm)],]) ).
tff(20,plain,
( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) ),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
^ [S1: $i,S2: $i] :
rewrite(
( ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) )
<=> ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ~ isa(S1,S2)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [S1: $i,S2: $i] :
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) )
<=> ! [S1: $i,S2: $i] :
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ~ isa(S1,S2)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) ) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
^ [S1: $i,S2: $i] :
refl(
( ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) )
<=> ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [S1: $i,S2: $i] :
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) )
<=> ! [S1: $i,S2: $i] :
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
^ [S1: $i,S2: $i] :
rewrite(
( ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) )
<=> ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [S1: $i,S2: $i] :
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) )
<=> ! [S1: $i,S2: $i] :
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [S1: $i,S2: $i] :
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) )
<=> ! [S1: $i,S2: $i] :
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) ) ),
inference(transitivity,[status(thm)],[26,24]) ).
tff(28,plain,
^ [S1: $i,S2: $i] :
trans(
monotonicity(
rewrite(
( ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) )
<=> ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) )),
( ( ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
& ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) )
<=> ( ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
& ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) ) )),
rewrite(
( ( ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
& ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) )
<=> ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) ) )),
( ( ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
& ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) )
<=> ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [S1: $i,S2: $i] :
( ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
& ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) )
<=> ! [S1: $i,S2: $i] :
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [S1: $i,S2: $i] :
( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
<=> isa(S1,S2) )
<=> ! [S1: $i,S2: $i] :
( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
<=> isa(S1,S2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
^ [S1: $i,S2: $i] :
rewrite(
( ( ! [Ax: $i,C: $i] :
( status(Ax,C,S1)
=> status(Ax,C,S2) )
<=> isa(S1,S2) )
<=> ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
<=> isa(S1,S2) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [S1: $i,S2: $i] :
( ! [Ax: $i,C: $i] :
( status(Ax,C,S1)
=> status(Ax,C,S2) )
<=> isa(S1,S2) )
<=> ! [S1: $i,S2: $i] :
( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
<=> isa(S1,S2) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [S1: $i,S2: $i] :
( ! [Ax: $i,C: $i] :
( status(Ax,C,S1)
=> status(Ax,C,S2) )
<=> isa(S1,S2) ),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax',isa) ).
tff(34,plain,
! [S1: $i,S2: $i] :
( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
<=> isa(S1,S2) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [S1: $i,S2: $i] :
( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
<=> isa(S1,S2) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [S1: $i,S2: $i] :
( ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
& ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [S1: $i,S2: $i] :
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
! [S1: $i,S2: $i] :
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) ),
inference(modus_ponens,[status(thm)],[37,27]) ).
tff(39,plain,
! [S1: $i,S2: $i] :
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ~ isa(S1,S2)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) ) ) ),
inference(modus_ponens,[status(thm)],[38,22]) ).
tff(40,plain,
( ~ ! [S1: $i,S2: $i] :
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
| status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
| isa(S1,S2) )
| ~ ( ~ isa(S1,S2)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) ) ) )
| ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
| isa(cax,thm) )
| ~ ( ~ isa(cax,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,cax)
| status(Ax,C,thm) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
| isa(cax,thm) )
| ~ ( ~ isa(cax,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,cax)
| status(Ax,C,thm) ) ) ),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
| isa(cax,thm) )
| ~ ( ~ isa(cax,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,cax)
| status(Ax,C,thm) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
| isa(cax,thm) ),
inference(tautology,[status(thm)],]) ).
tff(43,plain,
( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
| isa(cax,thm) ),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ isa(cax,thm)
<=> ~ isa(cax,thm) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
~ isa(cax,thm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isa_cax_thm) ).
tff(46,plain,
~ isa(cax,thm),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
| isa(cax,thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
| isa(cax,thm) ),
inference(tautology,[status(thm)],]) ).
tff(48,plain,
( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
| isa(cax,thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) ) ),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) ),
inference(unit_resolution,[status(thm)],[48,43]) ).
tff(50,plain,
( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm)
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax) ),
inference(tautology,[status(thm)],]) ).
tff(51,plain,
status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) )
| ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) ),
inference(tautology,[status(thm)],]) ).
tff(53,plain,
( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) ),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)),
inference(unit_resolution,[status(thm)],[53,20]) ).
tff(55,plain,
^ [Ax: $i,C: $i] :
rewrite(
( ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) )
<=> ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ~ status(Ax,C,thm)
| ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ~ status(Ax,C,thm)
| ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) ) ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
^ [Ax: $i,C: $i] :
refl(
( ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) )
<=> ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
^ [Ax: $i,C: $i] :
rewrite(
( ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) )
<=> ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
^ [Ax: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) )
<=> ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) )),
( ( ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
& ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) )
<=> ( ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
& ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) ) )),
rewrite(
( ( ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
& ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) )
<=> ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) ) )),
( ( ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
& ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) )
<=> ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [Ax: $i,C: $i] :
( ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
& ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [Ax: $i,C: $i] :
( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
<=> status(Ax,C,thm) )
<=> ! [Ax: $i,C: $i] :
( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
<=> status(Ax,C,thm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
^ [Ax: $i,C: $i] :
rewrite(
( ( ! [I1: $i] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) )
<=> ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
<=> status(Ax,C,thm) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [Ax: $i,C: $i] :
( ! [I1: $i] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) )
<=> ! [Ax: $i,C: $i] :
( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
<=> status(Ax,C,thm) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,axiom,
! [Ax: $i,C: $i] :
( ! [I1: $i] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax',thm) ).
tff(68,plain,
! [Ax: $i,C: $i] :
( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
<=> status(Ax,C,thm) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [Ax: $i,C: $i] :
( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
<=> status(Ax,C,thm) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
! [Ax: $i,C: $i] :
( ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
& ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
| ~ status(Ax,C,thm) ) ),
inference(modus_ponens,[status(thm)],[71,61]) ).
tff(73,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ~ status(Ax,C,thm)
| ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) ) ) ),
inference(modus_ponens,[status(thm)],[72,56]) ).
tff(74,plain,
( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
| model(tptp_fun_I1_3(C,Ax),C) )
| status(Ax,C,thm) )
| ~ ( ~ status(Ax,C,thm)
| ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) ) ) )
| ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,cax))
| model(I1,tptp_fun_C_20(thm,cax)) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,cax))
| model(I1,tptp_fun_C_20(thm,cax)) ) ) ),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,cax))
| model(I1,tptp_fun_C_20(thm,cax)) ) )
| ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) ),
inference(tautology,[status(thm)],]) ).
tff(77,plain,
( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) ),
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm)
| ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) ),
inference(tautology,[status(thm)],]) ).
tff(79,plain,
~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm),
inference(unit_resolution,[status(thm)],[78,49]) ).
tff(80,plain,
( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
| ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) ),
inference(tautology,[status(thm)],]) ).
tff(81,plain,
( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
| status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
| ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) ) ),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) ),
inference(unit_resolution,[status(thm)],[81,77]) ).
tff(83,plain,
( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax)) ),
inference(tautology,[status(thm)],]) ).
tff(84,plain,
model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax)),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
( ~ ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax))
| ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax)) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
$false,
inference(unit_resolution,[status(thm)],[85,84,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS193+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 09:42:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.42 % SZS status Theorem
% 0.13/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------