%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS186+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.11s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 45
% Syntax : Number of formulae : 110 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 1233 ( 0 equ)
% Maximal formula atoms : 32 ( 11 avg)
% Number of connectives : 2237 (1161 ~; 808 |; 39 &)
% ( 223 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 47 ( 47 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 510 ( 476 !; 4 ?; 510 :)
% Comments :
%------------------------------------------------------------------------------
tff(model_type,type,
model: ( $i * $i ) > $o ).
tff(tptp_fun_C_20_type,type,
tptp_fun_C_20: ( $i * $i ) > $i ).
tff(eqv_type,type,
eqv: $i ).
tff(thm_type,type,
thm: $i ).
tff(tptp_fun_I1_3_type,type,
tptp_fun_I1_3: ( $i * $i ) > $i ).
tff(tptp_fun_Ax_21_type,type,
tptp_fun_Ax_21: ( $i * $i ) > $i ).
tff(status_type,type,
status: ( $i * $i * $i ) > $o ).
tff(isa_type,type,
isa: ( $i * $i ) > $o ).
tff(tptp_fun_I1_0_type,type,
tptp_fun_I1_0: $i > $i ).
tff(tptp_fun_I2_4_type,type,
tptp_fun_I2_4: ( $i * $i ) > $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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)],[3]) ).
tff(5,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(6,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)],[5]) ).
tff(7,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)],[6,4]) ).
tff(8,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(9,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)],[8]) ).
tff(10,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(11,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(12,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)],[11]) ).
tff(13,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(14,plain,
! [Ax: $i,C: $i] :
( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
<=> status(Ax,C,thm) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Ax: $i,C: $i] :
( ! [I1: $i] :
( ~ model(I1,Ax)
| model(I1,C) )
<=> status(Ax,C,thm) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,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)],[15]) ).
tff(17,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)],[16,9]) ).
tff(18,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)],[17,7]) ).
tff(19,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)],[18,2]) ).
tff(20,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,eqv),tptp_fun_C_20(thm,eqv),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| model(I1,tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),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,eqv),tptp_fun_C_20(thm,eqv),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| model(I1,tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| model(I1,tptp_fun_C_20(thm,eqv)) ) ) )
<=> ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| model(I1,tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,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,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| model(I1,tptp_fun_C_20(thm,eqv)) ) ) ) )
<=> ( ~ ! [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,eqv),tptp_fun_C_20(thm,eqv),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| model(I1,tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) ) ) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,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,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| model(I1,tptp_fun_C_20(thm,eqv)) ) ) ) )
<=> ( ~ ! [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,eqv),tptp_fun_C_20(thm,eqv),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| model(I1,tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) ) ) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,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,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| model(I1,tptp_fun_C_20(thm,eqv)) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,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,eqv),tptp_fun_C_20(thm,eqv),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| model(I1,tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) ) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| model(I1,tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) ) ),
inference(unit_resolution,[status(thm)],[25,19]) ).
tff(27,plain,
( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm)
| ! [I1: $i] :
( ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| model(I1,tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) ),
inference(tautology,[status(thm)],[]) ).
tff(28,plain,
( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) ),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,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(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) )
| ~ ( ~ isa(S1,S2)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) ) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,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(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] :
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(34,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)],[33]) ).
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(transitivity,[status(thm)],[34,32]) ).
tff(36,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(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] :
( ! [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(39,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(40,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)],[39]) ).
tff(41,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(42,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)],[41,40]) ).
tff(43,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)],[42,38]) ).
tff(44,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)],[43]) ).
tff(45,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)],[44,37]) ).
tff(46,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)],[45,35]) ).
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) )
| ~ ( ~ isa(S1,S2)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) ) ) ),
inference(modus_ponens,[status(thm)],[46,30]) ).
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) )
| ~ ( ~ isa(S1,S2)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) ) ) )
| ~ ( ~ ( ~ isa(eqv,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,eqv)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,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(eqv,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,eqv)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) )
| ~ ( ~ isa(eqv,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,eqv)
| status(Ax,C,thm) ) ) )
<=> ~ ( ~ ( ~ isa(eqv,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,eqv)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) ) ) ),
inference(rewrite,[status(thm)],[]) ).
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) ) ) )
| ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) )
| ~ ( ~ isa(eqv,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,eqv)
| 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(eqv,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,eqv)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) ) ) ) ),
inference(monotonicity,[status(thm)],[49]) ).
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) ) ) )
| ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) )
| ~ ( ~ isa(eqv,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,eqv)
| 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(eqv,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,eqv)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) ) ) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,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,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) )
| ~ ( ~ isa(eqv,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,eqv)
| status(Ax,C,thm) ) ) ) ),
inference(quant_inst,[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) ) ) )
| ~ ( ~ ( ~ isa(eqv,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,eqv)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) ) ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
~ ( ~ ( ~ isa(eqv,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,eqv)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) ) ),
inference(unit_resolution,[status(thm)],[53,47]) ).
tff(55,plain,
( ~ ( ~ isa(eqv,thm)
| ! [Ax: $i,C: $i] :
( ~ status(Ax,C,eqv)
| status(Ax,C,thm) ) )
| ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) ),
inference(tautology,[status(thm)],[]) ).
tff(56,plain,
( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) ),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
( ~ isa(eqv,thm)
<=> ~ isa(eqv,thm) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
~ isa(eqv,thm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isa_eqv_thm) ).
tff(59,plain,
~ isa(eqv,thm),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) ),
inference(tautology,[status(thm)],[]) ).
tff(61,plain,
( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| isa(eqv,thm) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) ) ),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) ),
inference(unit_resolution,[status(thm)],[61,56]) ).
tff(63,plain,
( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm)
| ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) ),
inference(tautology,[status(thm)],[]) ).
tff(64,plain,
~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm),
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) ),
inference(tautology,[status(thm)],[]) ).
tff(66,plain,
( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm) )
| ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) ) ),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) ),
inference(unit_resolution,[status(thm)],[66,28]) ).
tff(68,plain,
( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv))
| ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) ),
inference(tautology,[status(thm)],[]) ).
tff(69,plain,
~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)),
inference(unit_resolution,[status(thm)],[68,67]) ).
tff(70,plain,
( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv)) ),
inference(tautology,[status(thm)],[]) ).
tff(71,plain,
model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv)),
inference(unit_resolution,[status(thm)],[70,67]) ).
tff(72,plain,
( ~ ( model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) ),
inference(tautology,[status(thm)],[]) ).
tff(73,plain,
~ ( model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) ),
inference(unit_resolution,[status(thm)],[72,71,69]) ).
tff(74,plain,
^ [Ax: $i,C: $i] :
rewrite(( ~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
<=> ~ ( ~ ( status(Ax,C,eqv)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
^ [Ax: $i,C: $i] :
refl(( ~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
<=> ~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
^ [Ax: $i,C: $i] :
rewrite(( ~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
<=> ~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) ) ),
inference(transitivity,[status(thm)],[79,77]) ).
tff(81,plain,
^ [Ax: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
<=> ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )),
( ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
<=> ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) ) )),
rewrite(( ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
<=> ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) ) )),
( ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
<=> ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) ) )),
trans(monotonicity(rewrite(( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
<=> ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) )),
( ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
| ~ status(Ax,C,eqv) )
<=> ( ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
| ~ status(Ax,C,eqv) ) )),
rewrite(( ( ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
| ~ status(Ax,C,eqv) )
<=> ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )),
( ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
| ~ status(Ax,C,eqv) )
<=> ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )),
( ( ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
| ~ status(Ax,C,eqv) ) )
<=> ( ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
& ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) ) )),
rewrite(( ( ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
& ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
<=> ~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) ) )),
( ( ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
| ~ status(Ax,C,eqv) ) )
<=> ~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [Ax: $i,C: $i] :
( ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
| ~ status(Ax,C,eqv) ) )
<=> ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
^ [Ax: $i,C: $i] :
rewrite(( ( ( ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
| status(Ax,C,eqv) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
| ~ status(Ax,C,eqv) ) )
<=> ( ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
| ~ status(Ax,C,eqv) ) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [Ax: $i,C: $i] :
( ( ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
| status(Ax,C,eqv) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
| ~ status(Ax,C,eqv) ) )
<=> ! [Ax: $i,C: $i] :
( ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
| ~ status(Ax,C,eqv) ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
<=> status(Ax,C,eqv) )
<=> ! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
<=> status(Ax,C,eqv) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,axiom,
! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
<=> status(Ax,C,eqv) ),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax',eqv) ).
tff(87,plain,
! [Ax: $i,C: $i] :
( ( ? [I1: $i] : model(I1,Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
<=> status(Ax,C,eqv) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [Ax: $i,C: $i] :
( ( ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
| status(Ax,C,eqv) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
| ~ status(Ax,C,eqv) ) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [Ax: $i,C: $i] :
( ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
& ( ( model(tptp_fun_I1_0(Ax),Ax)
& ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) )
| ~ status(Ax,C,eqv) ) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ! [I1: $i] : ~ model(I1,Ax)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) ) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) ),
inference(modus_ponens,[status(thm)],[90,80]) ).
tff(92,plain,
! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) ),
inference(modus_ponens,[status(thm)],[91,75]) ).
tff(93,plain,
( ( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| ~ ( model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ) ) )
<=> ( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| ~ ( model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ~ ( ~ ( status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,eqv)) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ) )
<=> ~ ( ~ ( status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| ~ ( model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,eqv)) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ) ) )
<=> ( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| ~ ( model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,eqv)) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ) ) )
<=> ( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| ~ ( model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[95,93]) ).
tff(97,plain,
( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) )
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,eqv)) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [Ax: $i,C: $i] :
~ ( ~ ( status(Ax,C,eqv)
| ~ ( model(tptp_fun_I2_4(C,Ax),Ax)
<=> model(tptp_fun_I2_4(C,Ax),C) )
| ! [I1: $i] : ~ model(I1,Ax) )
| ~ ( ~ status(Ax,C,eqv)
| ~ ( ~ model(tptp_fun_I1_0(Ax),Ax)
| ~ ! [I2: $i] :
( model(I2,Ax)
<=> model(I2,C) ) ) ) )
| ~ ( ~ ( status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| ~ ( model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
~ ( ~ ( status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| ~ ( model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ) ),
inference(unit_resolution,[status(thm)],[98,92]) ).
tff(100,plain,
( ~ ( status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,eqv))
| ~ ( model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I2_4(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) ) )
| ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) )
| ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(101,plain,
( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ),
inference(unit_resolution,[status(thm)],[100,99]) ).
tff(102,plain,
( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),thm)
| status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv) ),
inference(tautology,[status(thm)],[]) ).
tff(103,plain,
status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv),
inference(unit_resolution,[status(thm)],[102,62]) ).
tff(104,plain,
( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) )
| ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(105,plain,
( ~ ( ~ status(tptp_fun_Ax_21(thm,eqv),tptp_fun_C_20(thm,eqv),eqv)
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) )
| ~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ) ),
inference(unit_resolution,[status(thm)],[104,103]) ).
tff(106,plain,
~ ( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ),
inference(unit_resolution,[status(thm)],[105,101]) ).
tff(107,plain,
( ~ model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
| ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) )
| ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(108,plain,
! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) ),
inference(unit_resolution,[status(thm)],[107,106]) ).
tff(109,plain,
( ~ ! [I2: $i] :
( model(I2,tptp_fun_Ax_21(thm,eqv))
<=> model(I2,tptp_fun_C_20(thm,eqv)) )
| ( model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_Ax_21(thm,eqv))
<=> model(tptp_fun_I1_3(tptp_fun_C_20(thm,eqv),tptp_fun_Ax_21(thm,eqv)),tptp_fun_C_20(thm,eqv)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
$false,
inference(unit_resolution,[status(thm)],[109,108,73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KRS186+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n002.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:13:46 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.39 % SZS status Theorem
% 0.11/0.39 % SZS output start Proof
% See solution above
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------