TSTP Solution File: SWC094-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC094-1 : 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 11:55:12 EDT 2022
% Result : Unsatisfiable 0.18s 0.44s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 26
% Syntax : Number of formulae : 52 ( 15 unt; 6 typ; 0 def)
% Number of atoms : 313 ( 121 equ)
% Maximal formula atoms : 19 ( 6 avg)
% Number of connectives : 528 ( 277 ~; 226 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 92 ( 82 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
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/sandbox/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)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(10,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
app(nil,sk3) = sk3,
inference(unit_resolution,[status(thm)],[15,12,5]) ).
tff(17,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(19,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(nil)
| ( app(nil,nil) = nil ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(nil)
| ( app(nil,nil) = nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(nil)
| ( app(nil,nil) = nil ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
app(nil,nil) = nil,
inference(unit_resolution,[status(thm)],[22,19,12]) ).
tff(24,plain,
app(app(nil,nil),sk3) = app(nil,sk3),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
app(app(nil,nil),sk3) = sk3,
inference(transitivity,[status(thm)],[24,16]) ).
tff(26,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [B: $i,A: $i,C: $i] :
rewrite(
( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk1 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk1 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk1 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk1 )
| ( app(A,C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk1 )
| ( app(A,C) != sk2 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk1 )
| ( app(A,C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk1 )
| ( app(A,C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk1 )
| ( app(A,C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk1 )
| ( app(A,C) != sk2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(34,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[35,29]) ).
tff(37,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[37,27]) ).
tff(39,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( app(nil,sk3) != sk3 )
| ( app(app(nil,nil),sk3) != sk3 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( app(nil,sk3) != sk3 )
| ( app(app(nil,nil),sk3) != sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,sk3) != sk3 )
| ( app(app(nil,nil),sk3) != sk3 ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk3)
| ( app(nil,sk3) != sk3 )
| ( app(app(nil,nil),sk3) != sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) )
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,sk3) != sk3 )
| ( app(app(nil,nil),sk3) != sk3 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( app(nil,sk3) != sk3 )
| ( app(app(nil,nil),sk3) != sk3 ) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) )
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,sk3) != sk3 )
| ( app(app(nil,nil),sk3) != sk3 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( app(nil,sk3) != sk3 )
| ( app(app(nil,nil),sk3) != sk3 ) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) )
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,sk3) != sk3 )
| ( app(app(nil,nil),sk3) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( app(nil,sk3) != sk3 )
| ( app(app(nil,nil),sk3) != sk3 ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
app(app(nil,nil),sk3) != sk3,
inference(unit_resolution,[status(thm)],[44,19,5,38,16]) ).
tff(46,plain,
$false,
inference(unit_resolution,[status(thm)],[45,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWC094-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n014.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 21:29:00 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
%------------------------------------------------------------------------------