%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV888-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:36:17 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 20 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 31 ~; 27 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Natural_Oevalc_type,type,
c_Natural_Oevalc: ( $i * $i * $i ) > $o ).
tff(v_xa_type,type,
v_xa: $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_Com_Ocom_OBODY_type,type,
c_Com_Ocom_OBODY: $i > $i ).
tff(v_pn_type,type,
v_pn: $i ).
tff(c_Option_Othe_type,type,
c_Option_Othe: ( $i * $i ) > $i ).
tff(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
tff(c_Com_Obody_type,type,
c_Com_Obody: $i > $i ).
tff(1,plain,
( ~ c_Natural_Oevalc(c_Com_Ocom_OBODY(v_pn),v_x,v_xa)
<=> ~ c_Natural_Oevalc(c_Com_Ocom_OBODY(v_pn),v_x,v_xa) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_Natural_Oevalc(c_Com_Ocom_OBODY(v_pn),v_x,v_xa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(3,plain,
~ c_Natural_Oevalc(c_Com_Ocom_OBODY(v_pn),v_x,v_xa),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_x,v_xa)
<=> c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_x,v_xa) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_x,v_xa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(6,plain,
c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_x,v_xa),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_s0: $i,V_pn: $i,V_s1: $i] :
refl(( ( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) )
<=> ( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_s0: $i,V_pn: $i,V_s1: $i] :
( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) )
<=> ! [V_s0: $i,V_pn: $i,V_s1: $i] :
( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_s0: $i,V_pn: $i,V_s1: $i] :
( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) )
<=> ! [V_s0: $i,V_pn: $i,V_s1: $i] :
( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [V_s0: $i,V_pn: $i,V_s1: $i] :
rewrite(( ( c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1)
| ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1) )
<=> ( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_s0: $i,V_pn: $i,V_s1: $i] :
( c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1)
| ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1) )
<=> ! [V_s0: $i,V_pn: $i,V_s1: $i] :
( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_s0: $i,V_pn: $i,V_s1: $i] :
( c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1)
| ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).
tff(13,plain,
! [V_s0: $i,V_pn: $i,V_s1: $i] :
( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_s0: $i,V_pn: $i,V_s1: $i] :
( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_s0: $i,V_pn: $i,V_s1: $i] :
( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_s0: $i,V_pn: $i,V_s1: $i] :
( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_s0: $i,V_pn: $i,V_s1: $i] :
( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) )
| ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_x,v_xa)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(v_pn),v_x,v_xa) )
<=> ( ~ ! [V_s0: $i,V_pn: $i,V_s1: $i] :
( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) )
| ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_x,v_xa)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(v_pn),v_x,v_xa) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [V_s0: $i,V_pn: $i,V_s1: $i] :
( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) )
| ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_x,v_xa)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(v_pn),v_x,v_xa) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V_s0: $i,V_pn: $i,V_s1: $i] :
( ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_s1)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(V_pn),V_s0,V_s1) )
| ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_x,v_xa)
| c_Natural_Oevalc(c_Com_Ocom_OBODY(v_pn),v_x,v_xa) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
$false,
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV888-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % 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 : Fri Jun 20 11:00:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% See solution above
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------