%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV821-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:36:10 AM UTC 2025
% Result : Unsatisfiable 0.53s 0.75s
% Output : Proof 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 36 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 78 ( 40 ~; 28 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 78 ( 69 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Suc_type,type,
c_Suc: $i > $i ).
tff(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1_type,type,
c_Natural_Osko__Natural__Xevaln__elim__cases__6__1: ( $i * $i * $i * $i ) > $i ).
tff(v_xb_type,type,
v_xb: $i ).
tff(v_xa_type,type,
v_xa: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(v_pn_type,type,
v_pn: $i ).
tff(c_Natural_Oevaln_type,type,
c_Natural_Oevaln: ( $i * $i * $i * $i ) > $o ).
tff(c_Com_Ocom_OBODY_type,type,
c_Com_Ocom_OBODY: $i > $i ).
tff(1,plain,
( c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_HOL_Ozero__class_Ozero(tc_nat),v_xb)
<=> c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_HOL_Ozero__class_Ozero(tc_nat),v_xb) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_HOL_Ozero__class_Ozero(tc_nat),v_xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(3,plain,
c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_HOL_Ozero__class_Ozero(tc_nat),v_xb),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
refl(( ( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) )
<=> ( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) )
<=> ! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) )
<=> ! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
rewrite(( ( ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1) )
<=> ( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1) )
<=> ! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_0) ).
tff(10,plain,
! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_HOL_Ozero__class_Ozero(tc_nat),v_xb)
| ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_HOL_Ozero__class_Ozero(tc_nat),v_xa,v_xb)) ) )
<=> ( ~ ! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_HOL_Ozero__class_Ozero(tc_nat),v_xb)
| ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_HOL_Ozero__class_Ozero(tc_nat),v_xa,v_xb)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_HOL_Ozero__class_Ozero(tc_nat),v_xb)
| ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_HOL_Ozero__class_Ozero(tc_nat),v_xa,v_xb)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_n: $i,V_P: $i,V_s1: $i,V_s: $i] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1)
| ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) ) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_HOL_Ozero__class_Ozero(tc_nat),v_xb)
| ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_HOL_Ozero__class_Ozero(tc_nat),v_xa,v_xb)) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_HOL_Ozero__class_Ozero(tc_nat),v_xa,v_xb)),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [V_nat_H: $i] :
refl(( ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) )
<=> ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_nat_H: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) )
<=> ! [V_nat_H: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_nat_H: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) )
<=> ! [V_nat_H: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [V_nat_H: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
tff(22,plain,
! [V_nat_H: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_nat_H: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_nat_H: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [V_nat_H: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) )
| ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_HOL_Ozero__class_Ozero(tc_nat),v_xa,v_xb)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,24,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWV821-1 : TPTP v9.0.0. Released v4.1.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 10:54:32 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.53/0.75 % SZS status Unsatisfiable
% 0.53/0.75 % SZS output start Proof
% See solution above
% 0.60/0.80 % E exiting
%------------------------------------------------------------------------------