TSTP Solution File: SWC007-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC007-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 11:54:35 EDT 2022
% Result : Unsatisfiable 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 35
% Syntax : Number of formulae : 72 ( 20 unt; 7 typ; 0 def)
% Number of atoms : 376 ( 150 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 601 ( 309 ~; 258 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 19 ( 19 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 113 ( 100 !; 0 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk4_type,type,
sk4: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(nil_type,type,
nil: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(1,plain,
( ssList(sk2)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ssList(sk2)
<=> ssList(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
tff(4,plain,
ssList(sk2),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( app(U,sk3) = U ) )
<=> ( ~ ssList(U)
| ( app(U,sk3) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,sk3) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,sk3) = U ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ( ~ ssList(U)
| ( app(U,sk3) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,sk3) = U ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,sk3) = U ) ),
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,sk3) = U ) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,sk3) = U ) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,sk3) = U ) )
| ~ ssList(sk4)
| ( app(sk4,sk3) = sk4 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,sk3) = U ) )
| ~ ssList(sk4)
| ( app(sk4,sk3) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,sk3) = U ) )
| ~ ssList(sk4)
| ( app(sk4,sk3) = sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,sk3) = U ) )
| ~ ssList(sk4)
| ( app(sk4,sk3) = sk4 ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
app(sk4,sk3) = sk4,
inference(unit_resolution,[status(thm)],[18,15,5]) ).
tff(20,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( app(sk3,U) = U ) )
<=> ( ~ ssList(U)
| ( app(sk3,U) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(sk3,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(sk3,U) = U ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(sk3,U) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(sk3,U) = U ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(26,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(sk3,U) = U ) ),
inference(modus_ponens,[status(thm)],[26,23]) ).
tff(28,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(sk3,U) = U ) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(sk3,U) = U ) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(sk3,U) = U ) )
| ~ ssList(sk4)
| ( app(sk3,sk4) = sk4 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(sk3,U) = U ) )
| ~ ssList(sk4)
| ( app(sk3,sk4) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(sk3,U) = U ) )
| ~ ssList(sk4)
| ( app(sk3,sk4) = sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(sk3,U) = U ) )
| ~ ssList(sk4)
| ( app(sk3,sk4) = sk4 ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
app(sk3,sk4) = sk4,
inference(unit_resolution,[status(thm)],[32,29,5]) ).
tff(34,plain,
app(app(sk3,sk4),sk3) = app(sk4,sk3),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
app(app(sk3,sk4),sk3) = sk4,
inference(transitivity,[status(thm)],[34,19]) ).
tff(36,plain,
( ssList(nil)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(39,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[39,36]) ).
tff(41,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(sk3,U) = U ) )
| ~ ssList(sk3)
| ( app(sk3,sk3) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(sk3,U) = U ) )
| ~ ssList(sk3)
| ( app(sk3,sk3) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(sk3,U) = U ) )
| ~ ssList(sk3)
| ( app(sk3,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(sk3,U) = U ) )
| ~ ssList(sk3)
| ( app(sk3,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
app(sk3,sk3) = sk3,
inference(unit_resolution,[status(thm)],[43,40,29]) ).
tff(45,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
^ [B: $i,A: $i,C: $i] :
rewrite(
( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,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) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(53,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[54,48]) ).
tff(56,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[56,46]) ).
tff(58,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ( app(sk3,sk3) != sk3 )
| ( app(app(sk3,sk4),sk3) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ( app(sk3,sk3) != sk3 )
| ( app(app(sk3,sk4),sk3) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( ~ ssList(sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ( app(sk3,sk3) != sk3 )
| ( app(app(sk3,sk4),sk3) != sk4 ) )
<=> ( ~ ssList(sk3)
| ~ ssList(sk4)
| ( app(sk3,sk3) != sk3 )
| ( app(app(sk3,sk4),sk3) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) )
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ( app(sk3,sk3) != sk3 )
| ( app(app(sk3,sk4),sk3) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ( app(sk3,sk3) != sk3 )
| ( app(app(sk3,sk4),sk3) != sk4 ) ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) )
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ( app(sk3,sk3) != sk3 )
| ( app(app(sk3,sk4),sk3) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ( app(sk3,sk3) != sk3 )
| ( app(app(sk3,sk4),sk3) != sk4 ) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) )
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ( app(sk3,sk3) != sk3 )
| ( app(app(sk3,sk4),sk3) != sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk3 )
| ( app(app(A,B),C) != sk4 ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ( app(sk3,sk3) != sk3 )
| ( app(app(sk3,sk4),sk3) != sk4 ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
app(app(sk3,sk4),sk3) != sk4,
inference(unit_resolution,[status(thm)],[63,40,5,57,44]) ).
tff(65,plain,
$false,
inference(unit_resolution,[status(thm)],[64,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC007-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 20:34:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.45 % SZS status Unsatisfiable
% 0.21/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------