TSTP Solution File: SWC127-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC127-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 11:55:26 EDT 2022
% Result : Unsatisfiable 0.18s 0.43s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 35
% Syntax : Number of formulae : 70 ( 20 unt; 9 typ; 0 def)
% Number of atoms : 211 ( 29 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 244 ( 102 ~; 108 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 34 ( 30 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(singletonP_type,type,
singletonP: $i > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk4_type,type,
sk4: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(1,plain,
( ( ~ neq(sk3,nil)
| $false )
<=> ~ neq(sk3,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( segmentP(sk4,sk3)
<=> segmentP(sk4,sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
segmentP(sk4,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(5,plain,
segmentP(sk4,sk3),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
( segmentP(sk4,sk3)
<=> $true ),
inference(iff_true,[status(thm)],[5]) ).
tff(7,plain,
( ~ segmentP(sk4,sk3)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ~ segmentP(sk4,sk3)
<=> $false ),
inference(transitivity,[status(thm)],[7,2]) ).
tff(9,plain,
( ( ~ neq(sk3,nil)
| ~ segmentP(sk4,sk3) )
<=> ( ~ neq(sk3,nil)
| $false ) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ( ~ neq(sk3,nil)
| ~ segmentP(sk4,sk3) )
<=> ~ neq(sk3,nil) ),
inference(transitivity,[status(thm)],[9,1]) ).
tff(11,plain,
( ( ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) )
<=> ( ~ neq(sk3,nil)
| ~ segmentP(sk4,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) )
<=> ( ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
( ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(14,plain,
( ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
( ~ neq(sk3,nil)
| ~ segmentP(sk4,sk3) ),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
~ neq(sk3,nil),
inference(modus_ponens,[status(thm)],[15,10]) ).
tff(17,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(20,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
tff(28,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(34,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
sk3 = nil,
inference(unit_resolution,[status(thm)],[37,34,31,21,16]) ).
tff(39,plain,
nil = sk3,
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( singletonP(nil)
<=> singletonP(sk3) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( singletonP(sk3)
<=> singletonP(nil) ),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ( singletonP(sk3)
| $false )
<=> singletonP(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(46,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[46,43]) ).
tff(48,plain,
( neq(sk4,nil)
<=> $true ),
inference(iff_true,[status(thm)],[47]) ).
tff(49,plain,
( ~ neq(sk4,nil)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
( ~ neq(sk4,nil)
<=> $false ),
inference(transitivity,[status(thm)],[49,2]) ).
tff(51,plain,
( ( singletonP(sk3)
| ~ neq(sk4,nil) )
<=> ( singletonP(sk3)
| $false ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( singletonP(sk3)
| ~ neq(sk4,nil) )
<=> singletonP(sk3) ),
inference(transitivity,[status(thm)],[51,42]) ).
tff(53,plain,
( ( singletonP(sk3)
| ~ neq(sk4,nil) )
<=> ( singletonP(sk3)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,axiom,
( singletonP(sk3)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(55,plain,
( singletonP(sk3)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
singletonP(sk3),
inference(modus_ponens,[status(thm)],[55,52]) ).
tff(57,plain,
singletonP(nil),
inference(modus_ponens,[status(thm)],[56,41]) ).
tff(58,plain,
( ~ singletonP(nil)
<=> ~ singletonP(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause11) ).
tff(60,plain,
~ singletonP(nil),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
$false,
inference(unit_resolution,[status(thm)],[60,57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWC127-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sat Sep 3 21:47:45 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.32 Usage: tptp [options] [-file:]file
% 0.12/0.32 -h, -? prints this message.
% 0.12/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.32 -m, -model generate model.
% 0.12/0.32 -p, -proof generate proof.
% 0.12/0.32 -c, -core generate unsat core of named formulas.
% 0.12/0.32 -st, -statistics display statistics.
% 0.12/0.32 -t:timeout set timeout (in second).
% 0.12/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.32 -<param>:<value> configuration parameter and value.
% 0.12/0.32 -o:<output-file> file to place output in.
% 0.18/0.43 % SZS status Unsatisfiable
% 0.18/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------