%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV875-1 : 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 05:36:15 AM UTC 2025
% Result : Unsatisfiable 0.61s 0.80s
% Output : Proof 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 1 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 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 : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 9 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_Natural_Oevalc_type,type,
c_Natural_Oevalc: $i > $i ).
tff(c_Com_Ocom_OSKIP_type,type,
c_Com_Ocom_OSKIP: $i ).
tff(1,plain,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x))
<=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_s: $i] :
refl(( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s))
<=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_s: $i] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s))
<=> ! [V_s: $i] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_s: $i] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s))
<=> ! [V_s: $i] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_s: $i] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
tff(8,plain,
! [V_s: $i] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_s: $i] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_s: $i] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [V_s: $i] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
$false,
inference(unit_resolution,[status(thm)],[11,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV875-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 10:59:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.61/0.80 % SZS status Unsatisfiable
% 0.61/0.80 % SZS output start Proof
% See solution above
% 0.61/0.81 % E exiting
%------------------------------------------------------------------------------