TSTP Solution File: SYN589-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN589-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 : Thu Sep 29 23:56:32 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 30
% Syntax : Number of formulae : 41 ( 9 unt; 18 typ; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 136 ( 64 ~; 60 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 9 >; 4 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(p7_type,type,
p7: ( $i * $i ) > $o ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(f9_type,type,
f9: ( $i * $i ) > $i ).
tff(f10_type,type,
f10: ( $i * $i ) > $i ).
tff(c22_type,type,
c22: $i ).
tff(f11_type,type,
f11: $i > $i ).
tff(f3_type,type,
f3: $i > $i ).
tff(f4_type,type,
f4: $i > $i ).
tff(f5_type,type,
f5: $i > $i ).
tff(c17_type,type,
c17: $i ).
tff(c24_type,type,
c24: $i ).
tff(c25_type,type,
c25: $i ).
tff(c23_type,type,
c23: $i ).
tff(f12_type,type,
f12: $i > $i ).
tff(c19_type,type,
c19: $i ).
tff(c21_type,type,
c21: $i ).
tff(c18_type,type,
c18: $i ).
tff(c20_type,type,
c20: $i ).
tff(1,plain,
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
<=> ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p7_26) ).
tff(3,plain,
~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))))
<=> p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_25) ).
tff(6,plain,
p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
<=> p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_24) ).
tff(9,plain,
p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X25: $i,X27: $i,X26: $i] :
refl(
( ( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) )
<=> ( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) )
<=> ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) )
<=> ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X25: $i,X27: $i,X26: $i] :
trans(
monotonicity(
rewrite(
( ( p7(X26,X27)
| ~ p7(X25,X26) )
<=> ( p7(X26,X27)
| ~ p7(X25,X26) ) )),
( ( p7(X26,X27)
| ~ p7(X25,X26)
| ~ p7(X25,X27) )
<=> ( p7(X26,X27)
| ~ p7(X25,X26)
| ~ p7(X25,X27) ) )),
rewrite(
( ( p7(X26,X27)
| ~ p7(X25,X26)
| ~ p7(X25,X27) )
<=> ( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ) )),
( ( p7(X26,X27)
| ~ p7(X25,X26)
| ~ p7(X25,X27) )
<=> ( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X26)
| ~ p7(X25,X27) )
<=> ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X26)
| ~ p7(X25,X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_14) ).
tff(16,plain,
! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) )
| p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) )
<=> ( ~ ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) )
| p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) )
| p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) )
| p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN589-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 05:57:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------