TSTP Solution File: SWC095-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC095-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 11:55:13 EDT 2022
% Result : Unsatisfiable 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 24
% Syntax : Number of formulae : 45 ( 10 unt; 7 typ; 0 def)
% Number of atoms : 282 ( 86 equ)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 486 ( 257 ~; 200 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 8 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 75 ( 66 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk7_type,type,
sk7: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(1,plain,
( ssList(sk7)
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(3,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ssList(sk6)
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(6,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(9,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,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) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,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) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,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(15,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(16,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)],[15]) ).
tff(17,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_7) ).
tff(18,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)],[17,16]) ).
tff(19,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)],[18,14]) ).
tff(20,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) ),
inference(modus_ponens,[status(thm)],[19,13]) ).
tff(21,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) ),
inference(modus_ponens,[status(thm)],[21,11]) ).
tff(23,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ ssList(sk7)
| ~ ssList(sk5)
| ~ ssList(sk6)
| $false
| $false )
<=> ( ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ( app(app(sk5,sk6),sk7) = app(app(sk5,sk6),sk7) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( app(app(sk5,sk6),sk7) != app(app(sk5,sk6),sk7) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ( app(app(sk5,sk6),sk7) != app(app(sk5,sk6),sk7) )
<=> $false ),
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,plain,
( ( app(sk5,sk7) = app(sk5,sk7) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( app(sk5,sk7) != app(sk5,sk7) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( app(sk5,sk7) != app(sk5,sk7) )
<=> $false ),
inference(transitivity,[status(thm)],[30,25]) ).
tff(32,plain,
( ( ~ ssList(sk7)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ( app(sk5,sk7) != app(sk5,sk7) )
| ( app(app(sk5,sk6),sk7) != app(app(sk5,sk6),sk7) ) )
<=> ( ~ ssList(sk7)
| ~ ssList(sk5)
| ~ ssList(sk6)
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[31,28]) ).
tff(33,plain,
( ( ~ ssList(sk7)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ( app(sk5,sk7) != app(sk5,sk7) )
| ( app(app(sk5,sk6),sk7) != app(app(sk5,sk6),sk7) ) )
<=> ( ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7) ) ),
inference(transitivity,[status(thm)],[32,24]) ).
tff(34,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) )
| ~ ssList(sk7)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ( app(sk5,sk7) != app(sk5,sk7) )
| ( app(app(sk5,sk6),sk7) != app(app(sk5,sk6),sk7) ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) )
| ~ ssList(sk7)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ( app(sk5,sk7) != app(sk5,sk7) )
| ( app(app(sk5,sk6),sk7) != app(app(sk5,sk6),sk7) ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7) ) ),
inference(transitivity,[status(thm)],[34,23]) ).
tff(36,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) )
| ~ ssList(sk7)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ( app(sk5,sk7) != app(sk5,sk7) )
| ( app(app(sk5,sk6),sk7) != app(app(sk5,sk6),sk7) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != app(sk5,sk7) )
| ( app(app(A,B),C) != app(app(sk5,sk6),sk7) ) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
$false,
inference(unit_resolution,[status(thm)],[37,22,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC095-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 21:14:04 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.46 % SZS status Unsatisfiable
% 0.21/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------