%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS188+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 Jun 21 05:13:32 AM UTC 2025
% Result : Theorem 0.16s 0.36s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 46
% Syntax : Number of formulae : 113 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 1510 ( 0 equ)
% Maximal formula atoms : 48 ( 13 avg)
% Number of connectives : 2779 (1433 ~;1146 |; 95 &)
% ( 96 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 51 ( 51 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 594 ( 543 !; 18 ?; 594 :)
% Comments :
%------------------------------------------------------------------------------
tff(model_type,type,
model: ( $i * $i ) > $o ).
tff(tptp_fun_C_20_type,type,
tptp_fun_C_20: ( $i * $i ) > $i ).
tff(wec_type,type,
wec: $i ).
tff(thm_type,type,
thm: $i ).
tff(tptp_fun_Ax_21_type,type,
tptp_fun_Ax_21: ( $i * $i ) > $i ).
tff(tptp_fun_I3_6_type,type,
tptp_fun_I3_6: ( $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_7_type,type,
tptp_fun_I2_7: ( $i * $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,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) )
<=> ~ ( ~ ( status(Ax,C,wec)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax)
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax)
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [Ax: $i,C: $i] :
refl(( ~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) )
<=> ~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [Ax: $i,C: $i] :
rewrite(( ~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) )
<=> ~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [Ax: $i,C: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [I3: $i] :
trans(monotonicity(rewrite(( ( model(I3,C)
& ~ model(I3,Ax) )
<=> ~ ( ~ model(I3,C)
| model(I3,Ax) ) )),
( ~ ( model(I3,C)
& ~ model(I3,Ax) )
<=> ~ ~ ( ~ model(I3,C)
| model(I3,Ax) ) )),
rewrite(( ~ ~ ( ~ model(I3,C)
| model(I3,Ax) )
<=> ( ~ model(I3,C)
| model(I3,Ax) ) )),
( ~ ( model(I3,C)
& ~ model(I3,Ax) )
<=> ( ~ model(I3,C)
| model(I3,Ax) ) ))),
( ! [I3: $i] :
~ ( model(I3,C)
& ~ model(I3,Ax) )
<=> ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )),
( ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
~ ( model(I3,C)
& ~ model(I3,Ax) ) )
<=> ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) ) )),
rewrite(( ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
<=> ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) ) )),
( ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
~ ( model(I3,C)
& ~ model(I3,Ax) ) )
<=> ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) ) )),
rewrite(( ( ~ status(Ax,C,wec)
| ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& model(tptp_fun_I3_6(C,Ax),C)
& ~ model(tptp_fun_I3_6(C,Ax),Ax) ) )
<=> ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) )),
( ( ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
~ ( model(I3,C)
& ~ model(I3,Ax) ) )
& ( ~ status(Ax,C,wec)
| ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& model(tptp_fun_I3_6(C,Ax),C)
& ~ model(tptp_fun_I3_6(C,Ax),Ax) ) ) )
<=> ( ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
& ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) ) )),
rewrite(( ( ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
& ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) )
<=> ~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) ) )),
( ( ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
~ ( model(I3,C)
& ~ model(I3,Ax) ) )
& ( ~ status(Ax,C,wec)
| ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& model(tptp_fun_I3_6(C,Ax),C)
& ~ model(tptp_fun_I3_6(C,Ax),Ax) ) ) )
<=> ~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [Ax: $i,C: $i] :
( ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
~ ( model(I3,C)
& ~ model(I3,Ax) ) )
& ( ~ status(Ax,C,wec)
| ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& model(tptp_fun_I3_6(C,Ax),C)
& ~ model(tptp_fun_I3_6(C,Ax),Ax) ) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [Ax: $i,C: $i] :
rewrite(( ( ( ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
~ ( model(I3,C)
& ~ model(I3,Ax) )
| status(Ax,C,wec) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& model(tptp_fun_I3_6(C,Ax),C)
& ~ model(tptp_fun_I3_6(C,Ax),Ax) )
| ~ status(Ax,C,wec) ) )
<=> ( ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
~ ( model(I3,C)
& ~ model(I3,Ax) ) )
& ( ~ status(Ax,C,wec)
| ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& model(tptp_fun_I3_6(C,Ax),C)
& ~ model(tptp_fun_I3_6(C,Ax),Ax) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Ax: $i,C: $i] :
( ( ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
~ ( model(I3,C)
& ~ model(I3,Ax) )
| status(Ax,C,wec) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& model(tptp_fun_I3_6(C,Ax),C)
& ~ model(tptp_fun_I3_6(C,Ax),Ax) )
| ~ status(Ax,C,wec) ) )
<=> ! [Ax: $i,C: $i] :
( ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
~ ( model(I3,C)
& ~ model(I3,Ax) ) )
& ( ~ status(Ax,C,wec)
| ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& model(tptp_fun_I3_6(C,Ax),C)
& ~ model(tptp_fun_I3_6(C,Ax),Ax) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& ? [I3: $i] :
( model(I3,C)
& ~ model(I3,Ax) ) )
<=> status(Ax,C,wec) )
<=> ! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& ? [I3: $i] :
( model(I3,C)
& ~ model(I3,Ax) ) )
<=> status(Ax,C,wec) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [Ax: $i,C: $i] :
rewrite(( ( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] :
( model(I2,Ax)
=> model(I2,C) )
& ? [I3: $i] :
( model(I3,C)
& ~ model(I3,Ax) ) )
<=> status(Ax,C,wec) )
<=> ( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& ? [I3: $i] :
( model(I3,C)
& ~ model(I3,Ax) ) )
<=> status(Ax,C,wec) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] :
( model(I2,Ax)
=> model(I2,C) )
& ? [I3: $i] :
( model(I3,C)
& ~ model(I3,Ax) ) )
<=> status(Ax,C,wec) )
<=> ! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& ? [I3: $i] :
( model(I3,C)
& ~ model(I3,Ax) ) )
<=> status(Ax,C,wec) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] :
( model(I2,Ax)
=> model(I2,C) )
& ? [I3: $i] :
( model(I3,C)
& ~ model(I3,Ax) ) )
<=> status(Ax,C,wec) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax',wec) ).
tff(16,plain,
! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& ? [I3: $i] :
( model(I3,C)
& ~ model(I3,Ax) ) )
<=> status(Ax,C,wec) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& ? [I3: $i] :
( model(I3,C)
& ~ model(I3,Ax) ) )
<=> status(Ax,C,wec) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [Ax: $i,C: $i] :
( ( ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
~ ( model(I3,C)
& ~ model(I3,Ax) )
| status(Ax,C,wec) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& model(tptp_fun_I3_6(C,Ax),C)
& ~ model(tptp_fun_I3_6(C,Ax),Ax) )
| ~ status(Ax,C,wec) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [Ax: $i,C: $i] :
( ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
~ ( model(I3,C)
& ~ model(I3,Ax) ) )
& ( ~ status(Ax,C,wec)
| ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
& model(tptp_fun_I3_6(C,Ax),C)
& ~ model(tptp_fun_I3_6(C,Ax),Ax) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) )
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax)
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax)
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ! [I3: $i] :
( ~ model(I3,tptp_fun_C_20(thm,wec))
| model(I3,tptp_fun_Ax_21(thm,wec)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,wec))
| ~ ( ~ model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ) ) ) )
<=> ( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax)
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ! [I3: $i] :
( ~ model(I3,tptp_fun_C_20(thm,wec))
| model(I3,tptp_fun_Ax_21(thm,wec)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,wec))
| ~ ( ~ model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ( ~ ( status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,wec))
| ! [I3: $i] :
( ~ model(I3,tptp_fun_C_20(thm,wec))
| model(I3,tptp_fun_Ax_21(thm,wec)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) ) ) ) )
<=> ~ ( ~ ( status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ! [I3: $i] :
( ~ model(I3,tptp_fun_C_20(thm,wec))
| model(I3,tptp_fun_Ax_21(thm,wec)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,wec))
| ~ ( ~ model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax)
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,wec))
| ! [I3: $i] :
( ~ model(I3,tptp_fun_C_20(thm,wec))
| model(I3,tptp_fun_Ax_21(thm,wec)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) ) ) ) ) )
<=> ( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax)
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ! [I3: $i] :
( ~ model(I3,tptp_fun_C_20(thm,wec))
| model(I3,tptp_fun_Ax_21(thm,wec)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,wec))
| ~ ( ~ model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax)
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,wec))
| ! [I3: $i] :
( ~ model(I3,tptp_fun_C_20(thm,wec))
| model(I3,tptp_fun_Ax_21(thm,wec)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) ) ) ) ) )
<=> ( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax)
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ! [I3: $i] :
( ~ model(I3,tptp_fun_C_20(thm,wec))
| model(I3,tptp_fun_Ax_21(thm,wec)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,wec))
| ~ ( ~ model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax)
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,wec))
| ! [I3: $i] :
( ~ model(I3,tptp_fun_C_20(thm,wec))
| model(I3,tptp_fun_Ax_21(thm,wec)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,wec)
| ~ ( ~ model(tptp_fun_I2_7(C,Ax),Ax)
| model(tptp_fun_I2_7(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax)
| ! [I3: $i] :
( ~ model(I3,C)
| model(I3,Ax) ) )
| ~ ( ~ status(Ax,C,wec)
| ~ ( model(tptp_fun_I3_6(C,Ax),Ax)
| ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ model(tptp_fun_I3_6(C,Ax),C)
| ~ ! [I2: $i] :
( ~ model(I2,Ax)
| model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ! [I3: $i] :
( ~ model(I3,tptp_fun_C_20(thm,wec))
| model(I3,tptp_fun_Ax_21(thm,wec)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,wec))
| ~ ( ~ model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ! [I3: $i] :
( ~ model(I3,tptp_fun_C_20(thm,wec))
| model(I3,tptp_fun_Ax_21(thm,wec)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,wec))
| ~ ( ~ model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ! [I3: $i] :
( ~ model(I3,tptp_fun_C_20(thm,wec))
| model(I3,tptp_fun_Ax_21(thm,wec)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,wec))
| ~ ( ~ model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I2_7(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ) )
| ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(31,plain,
( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,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(33,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)],[32]) ).
tff(34,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(35,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)],[34]) ).
tff(36,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(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) ) )
<=> ! [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)],[36]) ).
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) ) )
<=> ! [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)],[37,35]) ).
tff(39,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(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) ) )
<=> ! [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)],[39]) ).
tff(41,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(42,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(43,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)],[42]) ).
tff(44,axiom,
! [S1: $i,S2: $i] :
( ! [Ax: $i,C: $i] :
( status(Ax,C,S1)
=> status(Ax,C,S2) )
<=> isa(S1,S2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax',isa) ).
tff(45,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)],[44,43]) ).
tff(46,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)],[45,41]) ).
tff(47,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)],[46]) ).
tff(48,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)],[47,40]) ).
tff(49,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)],[48,38]) ).
tff(50,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)],[49,33]) ).
tff(51,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) ) ) )
| ~ ( ~ ( ~ isa(wec,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,wec)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) ) ) )
<=> ( ~ ! [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) ) ) )
| ~ ( ~ ( ~ isa(wec,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,wec)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) )
| ~ ( ~ isa(wec,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,wec)
| status(Ax,C,thm) ) ) )
<=> ~ ( ~ ( ~ isa(wec,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,wec)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,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,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) )
| ~ ( ~ isa(wec,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,wec)
| status(Ax,C,thm) ) ) ) )
<=> ( ~ ! [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) ) ) )
| ~ ( ~ ( ~ isa(wec,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,wec)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) ) ) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,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,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) )
| ~ ( ~ isa(wec,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,wec)
| status(Ax,C,thm) ) ) ) )
<=> ( ~ ! [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) ) ) )
| ~ ( ~ ( ~ isa(wec,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,wec)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) ) ) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,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,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) )
| ~ ( ~ isa(wec,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,wec)
| status(Ax,C,thm) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,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) ) ) )
| ~ ( ~ ( ~ isa(wec,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,wec)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) ) ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
~ ( ~ ( ~ isa(wec,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,wec)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) ) ),
inference(unit_resolution,[status(thm)],[56,50]) ).
tff(58,plain,
( ~ ( ~ isa(wec,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,wec)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) ),
inference(tautology,[status(thm)],[]) ).
tff(59,plain,
( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) ),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
( ~ isa(wec,thm)
<=> ~ isa(wec,thm) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
~ isa(wec,thm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isa_wec_thm) ).
tff(62,plain,
~ isa(wec,thm),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) ),
inference(tautology,[status(thm)],[]) ).
tff(64,plain,
( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| isa(wec,thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) ) ),
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) ),
inference(unit_resolution,[status(thm)],[64,59]) ).
tff(66,plain,
( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec) ),
inference(tautology,[status(thm)],[]) ).
tff(67,plain,
status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec),
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,plain,
( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ) )
| ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(69,plain,
( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| ~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ) )
| ~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ) ),
inference(unit_resolution,[status(thm)],[68,67]) ).
tff(70,plain,
~ ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ),
inference(unit_resolution,[status(thm)],[69,31]) ).
tff(71,plain,
( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I3_6(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(72,plain,
! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) ),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,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(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) )
| ~ ( ! [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)],[73]) ).
tff(75,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(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) ) )
<=> ! [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)],[75]) ).
tff(77,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(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) )
| ~ ( ! [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)],[77]) ).
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) )
| ~ ( ! [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)],[78,76]) ).
tff(80,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(81,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)],[80]) ).
tff(82,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(83,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(84,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)],[83]) ).
tff(85,axiom,
! [Ax: $i,C: $i] :
( ! [I1: $i] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax',thm) ).
tff(86,plain,
! [Ax: $i,C: $i] :
( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
<=> status(Ax,C,thm) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [Ax: $i,C: $i] :
( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
<=> status(Ax,C,thm) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,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)],[87]) ).
tff(89,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)],[88,81]) ).
tff(90,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)],[89,79]) ).
tff(91,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)],[90,74]) ).
tff(92,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) ) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,wec))
| model(I1,tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),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) ) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,wec))
| model(I1,tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,wec))
| model(I1,tptp_fun_C_20(thm,wec)) ) ) )
<=> ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,wec))
| model(I1,tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,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,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,wec))
| model(I1,tptp_fun_C_20(thm,wec)) ) ) ) )
<=> ( ~ ! [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) ) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,wec))
| model(I1,tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) ) ) ) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,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,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,wec))
| model(I1,tptp_fun_C_20(thm,wec)) ) ) ) )
<=> ( ~ ! [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) ) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,wec))
| model(I1,tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) ) ) ) ),
inference(transitivity,[status(thm)],[94,92]) ).
tff(96,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,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,wec))
| model(I1,tptp_fun_C_20(thm,wec)) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,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) ) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,wec))
| model(I1,tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) ) ) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,wec))
| model(I1,tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) ) ),
inference(unit_resolution,[status(thm)],[97,91]) ).
tff(99,plain,
( ~ ( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,wec))
| model(I1,tptp_fun_C_20(thm,wec)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) ),
inference(tautology,[status(thm)],[]) ).
tff(100,plain,
( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) ),
inference(unit_resolution,[status(thm)],[99,98]) ).
tff(101,plain,
( ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),wec)
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm)
| ~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) ),
inference(tautology,[status(thm)],[]) ).
tff(102,plain,
~ status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm),
inference(unit_resolution,[status(thm)],[101,65]) ).
tff(103,plain,
( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) ),
inference(tautology,[status(thm)],[]) ).
tff(104,plain,
( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
| status(tptp_fun_Ax_21(thm,wec),tptp_fun_C_20(thm,wec),thm) )
| ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) ) ),
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) ),
inference(unit_resolution,[status(thm)],[104,100]) ).
tff(106,plain,
( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) ),
inference(tautology,[status(thm)],[]) ).
tff(107,plain,
~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)),
inference(unit_resolution,[status(thm)],[106,105]) ).
tff(108,plain,
( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)) ),
inference(tautology,[status(thm)],[]) ).
tff(109,plain,
model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec)),
inference(unit_resolution,[status(thm)],[108,105]) ).
tff(110,plain,
( ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) )
<=> ( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [I2: $i] :
( ~ model(I2,tptp_fun_Ax_21(thm,wec))
| model(I2,tptp_fun_C_20(thm,wec)) )
| ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_Ax_21(thm,wec))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,wec),tptp_fun_Ax_21(thm,wec)),tptp_fun_C_20(thm,wec)) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
$false,
inference(unit_resolution,[status(thm)],[112,109,107,72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : KRS188+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.10/0.10 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n014.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Jun 19 19:12:24 EDT 2025
% 0.10/0.31 % CPUTime :
% 0.16/0.36 % SZS status Theorem
% 0.16/0.36 % SZS output start Proof
% See solution above
% 0.17/0.42 % E exiting
%------------------------------------------------------------------------------