TSTP Solution File: SWV817-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV817-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 : Thu Sep 29 15:24:37 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 30 ( 11 unt; 4 typ; 0 def)
% Number of atoms : 47 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 28 ~; 11 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 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 : 4 ( 1 usr; 3 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_s: $i] : ( V_s = v_x )
<=> ! [V_s: $i] : ( V_s = v_x ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
! [V_s: $i] : ( V_s = v_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(3,plain,
! [V_s: $i] : ( V_s = v_x ),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
! [V_s: $i] : ( V_s = v_x ),
inference(skolemize,[status(sab)],[3]) ).
tff(5,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(6,plain,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_x,
inference(unit_resolution,[status(thm)],[5,4]) ).
tff(7,plain,
v_x = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,
inference(symmetry,[status(thm)],[6]) ).
tff(8,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(9,plain,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 = v_x,
inference(unit_resolution,[status(thm)],[8,4]) ).
tff(10,plain,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,
inference(transitivity,[status(thm)],[9,7]) ).
tff(11,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__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
| $false )
<=> ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(15,plain,
( c_Hoare__Mirabelle_Ostate__not__singleton
<=> $true ),
inference(iff_true,[status(thm)],[14]) ).
tff(16,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
<=> ~ $true ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
<=> $false ),
inference(transitivity,[status(thm)],[16,13]) ).
tff(18,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 )
| $false ) ),
inference(monotonicity,[status(thm)],[17]) ).
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 )
<=> ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 ) ),
inference(transitivity,[status(thm)],[18,12]) ).
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,
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,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)],[24,11]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV817-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.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 : Sun Sep 4 08:29:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------