TSTP Solution File: SWC254-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC254-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 : Tue Sep 20 11:56:34 EDT 2022
% Result : Unsatisfiable 0.18s 0.44s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 37
% Syntax : Number of formulae : 69 ( 12 unt; 11 typ; 0 def)
% Number of atoms : 275 ( 59 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 386 ( 183 ~; 165 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 5 >; 2 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 42 ( 38 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(singletonP_type,type,
singletonP: $i > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(1,plain,
( ( ~ singletonP(sk3)
| $false )
<=> ~ singletonP(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(7,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[8,3]) ).
tff(10,plain,
( neq(sk4,nil)
<=> $true ),
inference(iff_true,[status(thm)],[9]) ).
tff(11,plain,
( ~ neq(sk4,nil)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ~ neq(sk4,nil)
<=> $false ),
inference(transitivity,[status(thm)],[11,2]) ).
tff(13,plain,
( ( ~ singletonP(sk3)
| ~ neq(sk4,nil) )
<=> ( ~ singletonP(sk3)
| $false ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( ~ singletonP(sk3)
| ~ neq(sk4,nil) )
<=> ~ singletonP(sk3) ),
inference(transitivity,[status(thm)],[13,1]) ).
tff(15,plain,
( ( ~ singletonP(sk1)
| ~ neq(sk4,nil) )
<=> ( ~ singletonP(sk3)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ( ~ singletonP(sk1)
| ~ neq(sk4,nil) )
<=> ( ~ singletonP(sk1)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
( ~ singletonP(sk1)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
tff(18,plain,
( ~ singletonP(sk1)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ singletonP(sk3)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
~ singletonP(sk3),
inference(modus_ponens,[status(thm)],[19,14]) ).
tff(21,plain,
( ( $false
| ( cons(sk5,nil) = sk3 ) )
<=> ( cons(sk5,nil) = sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) )
<=> ( $false
| ( cons(sk5,nil) = sk3 ) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(23,plain,
( ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) )
<=> ( cons(sk5,nil) = sk3 ) ),
inference(transitivity,[status(thm)],[22,21]) ).
tff(24,plain,
( ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) )
<=> ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
tff(27,plain,
( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
cons(sk5,nil) = sk3,
inference(modus_ponens,[status(thm)],[28,23]) ).
tff(30,plain,
( ( ssItem(sk5)
| $false )
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| $false ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(32,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ssItem(sk5) ),
inference(transitivity,[status(thm)],[31,30]) ).
tff(33,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(35,plain,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[35,32]) ).
tff(37,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
tff(40,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[40,37]) ).
tff(42,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( cons(U,nil) != V )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ( cons(U,nil) != V )
| ~ ssList(V) ) )),
rewrite(
( ( ~ ssItem(U)
| ( cons(U,nil) != V )
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V )
| singletonP(V) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V )
| singletonP(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [V: $i,U: $i] :
( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,axiom,
! [V: $i,U: $i] :
( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause116) ).
tff(48,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(modus_ponens,[status(thm)],[50,43]) ).
tff(52,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != sk3 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( ~ ssItem(sk5)
| ~ ssList(sk3)
| singletonP(sk3)
| ( cons(sk5,nil) != sk3 ) )
<=> ( singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| singletonP(sk3)
| ( cons(sk5,nil) != sk3 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != sk3 ) ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| singletonP(sk3)
| ( cons(sk5,nil) != sk3 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != sk3 ) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| singletonP(sk3)
| ( cons(sk5,nil) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != sk3 ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
$false,
inference(unit_resolution,[status(thm)],[57,51,41,36,29,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC254-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.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 : Sat Sep 3 23:13:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.18/0.44 % SZS status Unsatisfiable
% 0.18/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------