%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV817-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.15s 0.40s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 25 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 19 ~; 10 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 7 ( 7 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
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_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1_type,type,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1: $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_Hoare__Mirabelle_Ostate__not__singleton_type,type,
c_Hoare__Mirabelle_Ostate__not__singleton: $o ).
tff(1,plain,
( ( v_x = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
<=> ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_x ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( ! [V_s: $i] : ( V_s = v_x )
<=> ! [V_s: $i] : ( V_s = v_x ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
! [V_s: $i] : ( V_s = v_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(4,plain,
! [V_s: $i] : ( V_s = v_x ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
! [V_s: $i] : ( V_s = v_x ),
inference(skolemize,[status(sab)],[4]) ).
tff(6,plain,
( ~ ! [V_s: $i] : ( V_s = v_x )
| ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 = v_x ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(7,plain,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 = v_x,
inference(unit_resolution,[status(thm)],[6,5]) ).
tff(8,plain,
( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
<=> ( v_x = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,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_x ) ),
inference(transitivity,[status(thm)],[8,1]) ).
tff(10,plain,
( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_x )
<=> ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 ) ),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [V_s: $i] : ( V_s = v_x )
| ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_x ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_x,
inference(unit_resolution,[status(thm)],[11,5]) ).
tff(13,plain,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,
inference(modus_ponens,[status(thm)],[12,10]) ).
tff(14,plain,
( c_Hoare__Mirabelle_Ostate__not__singleton
<=> c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(16,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,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(18,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(19,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)],[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 ),
inference(modus_ponens,[status(thm)],[19,17]) ).
tff(21,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)],[20,17]) ).
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)],[21,17]) ).
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)],[22,17]) ).
tff(24,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)],[23,16]) ).
tff(25,plain,
$false,
inference(unit_resolution,[status(thm)],[24,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SWV817-1 : TPTP v9.0.0. Released v4.1.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 10:53:56 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.15/0.40 % SZS status Unsatisfiable
% 0.15/0.40 % SZS output start Proof
% See solution above
% 0.23/0.41 % E exiting
%------------------------------------------------------------------------------