%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV866-1 : 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 05:36:14 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 41 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 75 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 93 ( 46 ~; 33 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 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 : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 55 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Com_Ocom_OSemi_type,type,
c_Com_Ocom_OSemi: ( $i * $i ) > $i ).
tff(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1_type,type,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1: $i ).
tff(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1_type,type,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1: $i ).
tff(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2_type,type,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2: $i ).
tff(v_s_H_type,type,
v_s_H: $i ).
tff(c_Hoare__Mirabelle_Ostate__not__singleton_type,type,
c_Hoare__Mirabelle_Ostate__not__singleton: $o ).
tff(1,plain,
( ( v_s_H = c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) )
<=> ( c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_s_H ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( ! [V_Z_H: $i] : ( V_Z_H = v_s_H )
<=> ! [V_Z_H: $i] : ( V_Z_H = v_s_H ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
! [V_Z_H: $i] : ( V_Z_H = v_s_H ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(4,plain,
! [V_Z_H: $i] : ( V_Z_H = v_s_H ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
! [V_Z_H: $i] : ( V_Z_H = v_s_H ),
inference(skolemize,[status(sab)],[4]) ).
tff(6,plain,
( ~ ! [V_Z_H: $i] : ( V_Z_H = v_s_H )
| ( c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) = v_s_H ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(7,plain,
c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) = v_s_H,
inference(unit_resolution,[status(thm)],[6,5]) ).
tff(8,plain,
( ( c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) = c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) )
<=> ( v_s_H = c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ( c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) = c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) )
<=> ( c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_s_H ) ),
inference(transitivity,[status(thm)],[8,1]) ).
tff(10,plain,
( ( c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_s_H )
<=> ( c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) = c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) ) ),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [V_Z_H: $i] : ( V_Z_H = v_s_H )
| ( c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_s_H ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_s_H,
inference(unit_resolution,[status(thm)],[11,5]) ).
tff(13,plain,
c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) = c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1),
inference(modus_ponens,[status(thm)],[12,10]) ).
tff(14,plain,
( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 )
<=> ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(15,plain,
( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
<=> ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 ) ),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
<=> ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( c_Hoare__Mirabelle_Ostate__not__singleton
<=> c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(19,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
<=> ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_state__not__singleton__def__raw_0) ).
tff(22,plain,
( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(modus_ponens,[status(thm)],[22,20]) ).
tff(24,plain,
( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(modus_ponens,[status(thm)],[23,20]) ).
tff(25,plain,
( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(modus_ponens,[status(thm)],[25,20]) ).
tff(27,plain,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,
inference(unit_resolution,[status(thm)],[26,19]) ).
tff(28,plain,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,
inference(modus_ponens,[status(thm)],[27,16]) ).
tff(29,plain,
^ [V_com1: $i,V_com1_H: $i,V_com2_H: $i,V_com2: $i] :
refl(( ( ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) )
| ( V_com1 = V_com1_H ) )
<=> ( ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) )
| ( V_com1 = V_com1_H ) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [V_com1: $i,V_com1_H: $i,V_com2_H: $i,V_com2: $i] :
( ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) )
| ( V_com1 = V_com1_H ) )
<=> ! [V_com1: $i,V_com1_H: $i,V_com2_H: $i,V_com2: $i] :
( ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) )
| ( V_com1 = V_com1_H ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [V_com1: $i,V_com1_H: $i,V_com2_H: $i,V_com2: $i] :
( ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) )
| ( V_com1 = V_com1_H ) )
<=> ! [V_com1: $i,V_com1_H: $i,V_com2_H: $i,V_com2: $i] :
( ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) )
| ( V_com1 = V_com1_H ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [V_com1: $i,V_com1_H: $i,V_com2_H: $i,V_com2: $i] :
( ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) )
| ( V_com1 = V_com1_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
tff(33,plain,
! [V_com1: $i,V_com1_H: $i,V_com2_H: $i,V_com2: $i] :
( ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) )
| ( V_com1 = V_com1_H ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [V_com1: $i,V_com1_H: $i,V_com2_H: $i,V_com2: $i] :
( ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) )
| ( V_com1 = V_com1_H ) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [V_com1: $i,V_com1_H: $i,V_com2_H: $i,V_com2: $i] :
( ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) )
| ( V_com1 = V_com1_H ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ( ~ ! [V_com1: $i,V_com1_H: $i,V_com2_H: $i,V_com2: $i] :
( ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) )
| ( V_com1 = V_com1_H ) )
| ( c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) != c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) )
| ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 ) )
<=> ( ~ ! [V_com1: $i,V_com1_H: $i,V_com2_H: $i,V_com2: $i] :
( ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) )
| ( V_com1 = V_com1_H ) )
| ( c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) != c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) )
| ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [V_com1: $i,V_com1_H: $i,V_com2_H: $i,V_com2: $i] :
( ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) )
| ( V_com1 = V_com1_H ) )
| ( c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) != c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) )
| ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [V_com1: $i,V_com1_H: $i,V_com2_H: $i,V_com2: $i] :
( ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) )
| ( V_com1 = V_com1_H ) )
| ( c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) != c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) )
| ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ( c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) != c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) )
| ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 ) ),
inference(unit_resolution,[status(thm)],[38,35]) ).
tff(40,plain,
c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) != c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1),
inference(unit_resolution,[status(thm)],[39,28]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV866-1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 10:58:48 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.42 % SZS status Unsatisfiable
% 0.22/0.42 % SZS output start Proof
% See solution above
% 0.22/0.43 % E exiting
%------------------------------------------------------------------------------