TSTP Solution File: SWW375+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW375+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 20:58:26 EDT 2022
% Result : Theorem 5.19s 3.92s
% Output : Proof 5.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 25
% Syntax : Number of formulae : 40 ( 10 unt; 12 typ; 0 def)
% Number of atoms : 136 ( 50 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 141 ( 57 ~; 51 |; 0 &)
% ( 22 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 50 ( 42 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_y_type,type,
v_y: $i ).
tff(c_Com_OWT_type,type,
c_Com_OWT: $i ).
tff(c_Option_Ooption_OSome_type,type,
c_Option_Ooption_OSome: $i > $i ).
tff(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
tff(v_pn_type,type,
v_pn: $i ).
tff(c_Com_Obodies_type,type,
c_Com_Obodies: $i ).
tff(c_Map_Omap__of_type,type,
c_Map_Omap__of: ( $i * $i ) > $i ).
tff(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
tff(c_Com_Obody_type,type,
c_Com_Obody: $i ).
tff(c_Com_OWT__bodies_type,type,
c_Com_OWT__bodies: $o ).
tff(1,plain,
( ~ hBOOL(hAPP(c_Com_OWT,v_y))
<=> ~ hBOOL(hAPP(c_Com_OWT,v_y)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ hBOOL(hAPP(c_Com_OWT,v_y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
tff(3,plain,
~ hBOOL(hAPP(c_Com_OWT,v_y)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) )
<=> ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) )
<=> ( hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
tff(7,plain,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
^ [V_b: $i,V_pn: $i] :
refl(
( ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) )
<=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) )
<=> ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [V_b: $i,V_pn: $i] :
rewrite(
( ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) )
<=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) )
<=> ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) )
<=> ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
^ [V_b: $i,V_pn: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(asserted(c_Com_OWT__bodies),
( c_Com_OWT__bodies
<=> $true )),
( ~ c_Com_OWT__bodies
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ c_Com_OWT__bodies
<=> $false )),
( ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies )
<=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| $false ) )),
rewrite(
( ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| $false )
<=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ) )),
( ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies )
<=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies )
<=> ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
^ [V_b: $i,V_pn: $i] :
trans(
monotonicity(
rewrite(
( ( ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
=> hBOOL(hAPP(c_Com_OWT,V_b)) )
<=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ) )),
( ( c_Com_OWT__bodies
=> ( ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
=> hBOOL(hAPP(c_Com_OWT,V_b)) ) )
<=> ( c_Com_OWT__bodies
=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ) ) )),
rewrite(
( ( c_Com_OWT__bodies
=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ) )
<=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ) )),
( ( c_Com_OWT__bodies
=> ( ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
=> hBOOL(hAPP(c_Com_OWT,V_b)) ) )
<=> ( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [V_b: $i,V_pn: $i] :
( c_Com_OWT__bodies
=> ( ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
=> hBOOL(hAPP(c_Com_OWT,V_b)) ) )
<=> ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [V_b: $i,V_pn: $i] :
( c_Com_OWT__bodies
=> ( ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
=> hBOOL(hAPP(c_Com_OWT,V_b)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT__bodiesD) ).
tff(19,plain,
! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ),
inference(modus_ponens,[status(thm)],[20,13]) ).
tff(22,plain,
! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ),
inference(modus_ponens,[status(thm)],[21,12]) ).
tff(23,plain,
! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) ),
inference(modus_ponens,[status(thm)],[23,10]) ).
tff(25,plain,
( ( ~ ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) )
| hBOOL(hAPP(c_Com_OWT,v_y))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) )
<=> ( ~ ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) )
| hBOOL(hAPP(c_Com_OWT,v_y))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) )
| hBOOL(hAPP(c_Com_OWT,v_y))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [V_b: $i,V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) ) )
| hBOOL(hAPP(c_Com_OWT,v_y))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
$false,
inference(unit_resolution,[status(thm)],[27,24,8,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW375+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 15:55:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 5.19/3.92 % SZS status Theorem
% 5.19/3.92 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------