TSTP Solution File: SWC339-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC339-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 11:57:12 EDT 2022
% Result : Unsatisfiable 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 36
% Syntax : Number of formulae : 66 ( 15 unt; 9 typ; 0 def)
% Number of atoms : 403 ( 0 equ)
% Maximal formula atoms : 23 ( 7 avg)
% Number of connectives : 637 ( 318 ~; 279 |; 0 &)
% ( 40 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 27 ( 27 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 97 ( 88 !; 0 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(totalorderedP_type,type,
totalorderedP: $i > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(1,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
tff(4,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| segmentP(U,U) )
<=> ( ~ ssList(U)
| segmentP(U,U) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause57) ).
tff(10,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
segmentP(sk3,sk3),
inference(unit_resolution,[status(thm)],[15,12,5]) ).
tff(17,plain,
( ( $false
| ~ segmentP(app(app(sk5,sk3),sk6),sk3) )
<=> ~ segmentP(app(app(sk5,sk3),sk6),sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( totalorderedP(sk3)
<=> totalorderedP(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
totalorderedP(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(21,plain,
totalorderedP(sk3),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( totalorderedP(sk3)
<=> $true ),
inference(iff_true,[status(thm)],[21]) ).
tff(23,plain,
( ~ totalorderedP(sk3)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ~ totalorderedP(sk3)
<=> $false ),
inference(transitivity,[status(thm)],[23,18]) ).
tff(25,plain,
( ( ~ totalorderedP(sk3)
| ~ segmentP(app(app(sk5,sk3),sk6),sk3) )
<=> ( $false
| ~ segmentP(app(app(sk5,sk3),sk6),sk3) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ totalorderedP(sk3)
| ~ segmentP(app(app(sk5,sk3),sk6),sk3) )
<=> ~ segmentP(app(app(sk5,sk3),sk6),sk3) ),
inference(transitivity,[status(thm)],[25,17]) ).
tff(27,plain,
( ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) )
<=> ( ~ totalorderedP(sk3)
| ~ segmentP(app(app(sk5,sk3),sk6),sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) )
<=> ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) )
<=> ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
( ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(31,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[31,28]) ).
tff(33,plain,
( ~ totalorderedP(sk3)
| ~ segmentP(app(app(sk5,sk3),sk6),sk3) ),
inference(modus_ponens,[status(thm)],[32,27]) ).
tff(34,plain,
~ segmentP(app(app(sk5,sk3),sk6),sk3),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
( ssList(sk6)
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(37,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(40,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ segmentP(U,V)
| ~ ssList(W) )
<=> ( ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) )
<=> ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) ) )),
rewrite(
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(V) ) )),
rewrite(
( ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(app(app(X,U),W),V) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(app(app(X,U),W),V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause172) ).
tff(47,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ segmentP(sk3,sk3) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ segmentP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ ssList(sk6) )
<=> ( segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ segmentP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ ssList(sk6) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ segmentP(sk3,sk3) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ ssList(sk6) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ segmentP(sk3,sk3) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ ssList(sk6) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ segmentP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
$false,
inference(unit_resolution,[status(thm)],[56,50,5,40,37,34,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SWC339-1 : TPTP v8.1.0. Released v2.4.0.
% 0.05/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n006.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sun Sep 4 00:10:08 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Unsatisfiable
% 0.14/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------