%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV860-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:36:14 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.50s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 25 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 20 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 57 ( 26 ~; 22 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 36 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_xb_type,type,
v_xb: $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_P_type,type,
v_P: $i ).
tff(v_xa_type,type,
v_xa: $i ).
tff(c_Natural_Oevaln_type,type,
c_Natural_Oevaln: ( $i * $i * $i * $i ) > $o ).
tff(v_n_type,type,
v_n: $i ).
tff(c_Com_Ocom_OSKIP_type,type,
c_Com_Ocom_OSKIP: $i ).
tff(1,plain,
( c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb)
<=> c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(3,plain,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_n: $i,V_t: $i,V_s: $i] :
refl(( ( ( V_t = V_s )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) )
<=> ( ( V_t = V_s )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_n: $i,V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) )
<=> ! [V_n: $i,V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_n: $i,V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) )
<=> ! [V_n: $i,V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_n: $i,V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
tff(8,plain,
! [V_n: $i,V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_n: $i,V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_n: $i,V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_n: $i,V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) )
| ( v_xb = v_xa )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb) )
<=> ( ~ ! [V_n: $i,V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) )
| ( v_xb = v_xa )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V_n: $i,V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) )
| ( v_xb = v_xa )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V_n: $i,V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) )
| ( v_xb = v_xa )
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
v_xb = v_xa,
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
hAPP(hAPP(v_P,v_x),v_xb) = hAPP(hAPP(v_P,v_x),v_xa),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( hBOOL(hAPP(hAPP(v_P,v_x),v_xb))
<=> hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
<=> hBOOL(hAPP(hAPP(v_P,v_x),v_xb)) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
<=> hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(20,plain,
hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
hBOOL(hAPP(hAPP(v_P,v_x),v_xb)),
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,plain,
( ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xb))
<=> ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xb)) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
~ hBOOL(hAPP(hAPP(v_P,v_x),v_xb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(24,plain,
~ hBOOL(hAPP(hAPP(v_P,v_x),v_xb)),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
$false,
inference(unit_resolution,[status(thm)],[24,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWV860-1 : TPTP v9.0.0. Released v4.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.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
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 10:59:20 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.50 % SZS status Unsatisfiable
% 0.18/0.50 % SZS output start Proof
% See solution above
% 0.18/0.52 % E exiting
%------------------------------------------------------------------------------