TSTP Solution File: KRS187+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS187+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 17:45:07 EDT 2022
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 47
% Syntax : Number of formulae : 101 ( 22 unt; 10 typ; 0 def)
% Number of atoms : 784 ( 0 equ)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 1410 ( 758 ~; 535 |; 39 &)
% ( 72 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 41 ( 41 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 384 ( 350 !; 4 ?; 384 :)
% Comments :
%------------------------------------------------------------------------------
tff(model_type,type,
model: ( $i * $i ) > $o ).
tff(tptp_fun_C_20_type,type,
tptp_fun_C_20: ( $i * $i ) > $i ).
tff(tac_type,type,
tac: $i ).
tff(thm_type,type,
thm: $i ).
tff(tptp_fun_Ax_21_type,type,
tptp_fun_Ax_21: ( $i * $i ) > $i ).
tff(tptp_fun_I1_0_type,type,
tptp_fun_I1_0: $i > $i ).
tff(status_type,type,
status: ( $i * $i * $i ) > $o ).
tff(tptp_fun_I2_5_type,type,
tptp_fun_I2_5: $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(
( ~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) )
<=> ~ ( ~ ( status(Ax,C,tac)
| ~ model(tptp_fun_I2_5(C),C)
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,tac)
| ~ model(tptp_fun_I2_5(C),C)
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [Ax: $i,C: $i] :
refl(
( ~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) )
<=> ~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [Ax: $i,C: $i] :
rewrite(
( ~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) )
<=> ~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [Ax: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
<=> ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) ) )),
trans(
monotonicity(
rewrite(
( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] : model(I2,C) )
<=> ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) )),
( ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] : model(I2,C) )
| ~ status(Ax,C,tac) )
<=> ( ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) )
| ~ status(Ax,C,tac) ) )),
rewrite(
( ( ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) )
| ~ status(Ax,C,tac) )
<=> ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) )),
( ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] : model(I2,C) )
| ~ status(Ax,C,tac) )
<=> ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) )),
( ( ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] : model(I2,C) )
| ~ status(Ax,C,tac) ) )
<=> ( ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
& ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) ) )),
rewrite(
( ( ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
& ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) )
<=> ~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) ) )),
( ( ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] : model(I2,C) )
| ~ status(Ax,C,tac) ) )
<=> ~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [Ax: $i,C: $i] :
( ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] : model(I2,C) )
| ~ status(Ax,C,tac) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [Ax: $i,C: $i] :
rewrite(
( ( ( ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C)
| status(Ax,C,tac) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] : model(I2,C) )
| ~ status(Ax,C,tac) ) )
<=> ( ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] : model(I2,C) )
| ~ status(Ax,C,tac) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Ax: $i,C: $i] :
( ( ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C)
| status(Ax,C,tac) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] : model(I2,C) )
| ~ status(Ax,C,tac) ) )
<=> ! [Ax: $i,C: $i] :
( ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] : model(I2,C) )
| ~ status(Ax,C,tac) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] : model(I2,C) )
<=> status(Ax,C,tac) )
<=> ! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] : model(I2,C) )
<=> status(Ax,C,tac) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] : model(I2,C) )
<=> status(Ax,C,tac) ),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax',tac) ).
tff(14,plain,
! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] : model(I2,C) )
<=> status(Ax,C,tac) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Ax: $i,C: $i] :
( ( ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C)
| status(Ax,C,tac) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] : model(I2,C) )
| ~ status(Ax,C,tac) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Ax: $i,C: $i] :
( ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] : model(I2,C) )
| ~ status(Ax,C,tac) ) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,tac)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ model(tptp_fun_I2_5(C),C) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) ),
inference(modus_ponens,[status(thm)],[17,7]) ).
tff(19,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,tac)
| ~ model(tptp_fun_I2_5(C),C)
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) ),
inference(modus_ponens,[status(thm)],[18,2]) ).
tff(20,plain,
( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,tac)
| ~ model(tptp_fun_I2_5(C),C)
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,tac)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] : model(I2,C) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| ~ model(tptp_fun_I2_5(tptp_fun_C_20(thm,tac)),tptp_fun_C_20(thm,tac))
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,tac)) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| ~ ! [I2: $i] : model(I2,tptp_fun_C_20(thm,tac)) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
~ ( ~ ( status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| ~ model(tptp_fun_I2_5(tptp_fun_C_20(thm,tac)),tptp_fun_C_20(thm,tac))
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,tac)) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| ~ ! [I2: $i] : model(I2,tptp_fun_C_20(thm,tac)) ) ) ),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
( ~ ( status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| ~ model(tptp_fun_I2_5(tptp_fun_C_20(thm,tac)),tptp_fun_C_20(thm,tac))
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,tac)) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| ~ ! [I2: $i] : model(I2,tptp_fun_C_20(thm,tac)) ) )
| ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| ~ ! [I2: $i] : model(I2,tptp_fun_C_20(thm,tac)) ) ),
inference(tautology,[status(thm)],]) ).
tff(23,plain,
( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| ~ ! [I2: $i] : model(I2,tptp_fun_C_20(thm,tac)) ) ),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,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(25,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)],[24]) ).
tff(26,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(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(quant_intro,[status(thm)],[26]) ).
tff(28,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(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] :
~ ( ~ ( ~ ( ~ 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)],[29,27]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,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(35,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)],[34]) ).
tff(36,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(37,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)],[36,35]) ).
tff(38,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)],[37,33]) ).
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) )
& ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) ),
inference(skolemize,[status(sab)],[38]) ).
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) )
| ~ ( ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) )
| ~ isa(S1,S2) ) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,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)],[40,30]) ).
tff(42,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)],[41,25]) ).
tff(43,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,tac),tptp_fun_C_20(thm,tac),tac)
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) )
| isa(tac,thm) )
| ~ ( ~ isa(tac,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,tac)
| status(Ax,C,thm) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) )
| isa(tac,thm) )
| ~ ( ~ isa(tac,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,tac)
| status(Ax,C,thm) ) ) ),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) )
| isa(tac,thm) )
| ~ ( ~ isa(tac,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,tac)
| status(Ax,C,thm) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) )
| isa(tac,thm) ),
inference(tautology,[status(thm)],]) ).
tff(46,plain,
( ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) )
| isa(tac,thm) ),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
( ~ isa(tac,thm)
<=> ~ isa(tac,thm) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
~ isa(tac,thm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isa_tac_thm) ).
tff(49,plain,
~ isa(tac,thm),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) )
| isa(tac,thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) )
| isa(tac,thm) ),
inference(tautology,[status(thm)],]) ).
tff(51,plain,
( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) )
| isa(tac,thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) ) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) ),
inference(unit_resolution,[status(thm)],[51,46]) ).
tff(53,plain,
( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm)
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac) ),
inference(tautology,[status(thm)],]) ).
tff(54,plain,
status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| ~ ! [I2: $i] : model(I2,tptp_fun_C_20(thm,tac)) ) )
| ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| ~ ! [I2: $i] : model(I2,tptp_fun_C_20(thm,tac)) ) ),
inference(tautology,[status(thm)],]) ).
tff(56,plain,
( ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| ~ ! [I2: $i] : model(I2,tptp_fun_C_20(thm,tac)) ) )
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| ~ ! [I2: $i] : model(I2,tptp_fun_C_20(thm,tac)) ) ),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| ~ ! [I2: $i] : model(I2,tptp_fun_C_20(thm,tac)) ),
inference(unit_resolution,[status(thm)],[56,23]) ).
tff(58,plain,
( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| ~ ! [I2: $i] : model(I2,tptp_fun_C_20(thm,tac))
| ! [I2: $i] : model(I2,tptp_fun_C_20(thm,tac)) ),
inference(tautology,[status(thm)],]) ).
tff(59,plain,
! [I2: $i] : model(I2,tptp_fun_C_20(thm,tac)),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,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(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) )
| ~ ( ~ status(Ax,C,thm)
| ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) ) ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,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(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] :
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(65,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)],[64]) ).
tff(66,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)],[65,63]) ).
tff(67,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(68,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)],[67]) ).
tff(69,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(70,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(71,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)],[70]) ).
tff(72,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(73,plain,
! [Ax: $i,C: $i] :
( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
<=> status(Ax,C,thm) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [Ax: $i,C: $i] :
( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
<=> status(Ax,C,thm) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,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)],[74]) ).
tff(76,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)],[75,68]) ).
tff(77,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)],[76,66]) ).
tff(78,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)],[77,61]) ).
tff(79,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,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_C_20(thm,tac)) )
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,tac))
| model(I1,tptp_fun_C_20(thm,tac)) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_C_20(thm,tac)) )
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,tac))
| model(I1,tptp_fun_C_20(thm,tac)) ) ) ),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_C_20(thm,tac)) )
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,tac))
| model(I1,tptp_fun_C_20(thm,tac)) ) )
| ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_C_20(thm,tac)) )
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) ),
inference(tautology,[status(thm)],]) ).
tff(82,plain,
( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_C_20(thm,tac)) )
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) ),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
( ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),tac)
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm)
| ~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) ),
inference(tautology,[status(thm)],]) ).
tff(84,plain,
~ status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm),
inference(unit_resolution,[status(thm)],[83,52]) ).
tff(85,plain,
( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_C_20(thm,tac)) )
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) )
| ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_C_20(thm,tac)) )
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) ),
inference(tautology,[status(thm)],]) ).
tff(86,plain,
( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_C_20(thm,tac)) )
| status(tptp_fun_Ax_21(thm,tac),tptp_fun_C_20(thm,tac),thm) )
| ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_C_20(thm,tac)) ) ),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_C_20(thm,tac)) ),
inference(unit_resolution,[status(thm)],[86,82]) ).
tff(88,plain,
( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_Ax_21(thm,tac))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_C_20(thm,tac))
| ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_C_20(thm,tac)) ),
inference(tautology,[status(thm)],]) ).
tff(89,plain,
~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_C_20(thm,tac)),
inference(unit_resolution,[status(thm)],[88,87]) ).
tff(90,plain,
( ~ ! [I2: $i] : model(I2,tptp_fun_C_20(thm,tac))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,tac),tptp_fun_Ax_21(thm,tac)),tptp_fun_C_20(thm,tac)) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
$false,
inference(unit_resolution,[status(thm)],[90,89,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS187+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Sep 1 09:53:16 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.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------