TSTP Solution File: SYN593-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN593-1 : TPTP v8.1.0. Released v2.5.0.
% 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 : Thu Sep 29 23:56:33 EDT 2022
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 36
% Syntax : Number of formulae : 52 ( 15 unt; 17 typ; 0 def)
% Number of atoms : 318 ( 0 equ)
% Maximal formula atoms : 24 ( 9 avg)
% Number of connectives : 367 ( 104 ~; 239 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 7 ( 3 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 11 >; 5 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 84 ( 76 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(p12_type,type,
p12: ( $i * $i ) > $o ).
tff(f13_type,type,
f13: $i > $i ).
tff(c18_type,type,
c18: $i ).
tff(p15_type,type,
p15: ( $i * $i ) > $o ).
tff(f4_type,type,
f4: ( $i * $i ) > $i ).
tff(f11_type,type,
f11: $i > $i ).
tff(f6_type,type,
f6: ( $i * $i ) > $i ).
tff(f7_type,type,
f7: $i > $i ).
tff(f8_type,type,
f8: $i > $i ).
tff(f9_type,type,
f9: $i > $i ).
tff(c17_type,type,
c17: $i ).
tff(f10_type,type,
f10: $i > $i ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(c20_type,type,
c20: $i ).
tff(c19_type,type,
c19: $i ).
tff(c16_type,type,
c16: $i ).
tff(c21_type,type,
c21: $i ).
tff(1,plain,
^ [X6: $i,X7: $i,X5: $i,X8: $i] :
refl(
( ( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) )
<=> ( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) )
<=> ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) )
<=> ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [X6: $i,X7: $i,X5: $i,X8: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p3(X7,X8)
| p12(f13(X5),f13(c18))
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5) )
<=> ( p3(X7,X8)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ) )),
( ( p3(X7,X8)
| p12(f13(X5),f13(c18))
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5) )
<=> ( p3(X7,X8)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18))
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5) ) )),
rewrite(
( ( p3(X7,X8)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18))
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5) )
<=> ( p3(X7,X8)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ) )),
( ( p3(X7,X8)
| p12(f13(X5),f13(c18))
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5) )
<=> ( p3(X7,X8)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ) )),
( ( p3(X7,X8)
| p12(f13(X5),f13(c18))
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5) )
<=> ( p3(X7,X8)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18))
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5) ) )),
rewrite(
( ( p3(X7,X8)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18))
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5) )
<=> ( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ) )),
( ( p3(X7,X8)
| p12(f13(X5),f13(c18))
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5) )
<=> ( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ) )),
( ( p3(X7,X8)
| p12(f13(X5),f13(c18))
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5) )
<=> ( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18))
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5) ) )),
rewrite(
( ( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18))
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5) )
<=> ( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ) )),
( ( p3(X7,X8)
| p12(f13(X5),f13(c18))
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5) )
<=> ( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| p12(f13(X5),f13(c18))
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5) )
<=> ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| p12(f13(X5),f13(c18))
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_27) ).
tff(7,plain,
! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
<=> ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p15_24) ).
tff(13,plain,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
<=> ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p15_23) ).
tff(16,plain,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
<=> p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_19) ).
tff(19,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
<=> p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_18) ).
tff(22,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ~ p12(f13(c20),f13(c18))
<=> ~ p12(f13(c20),f13(c18)) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
~ p12(f13(c20),f13(c18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p12_6) ).
tff(25,plain,
~ p12(f13(c20),f13(c18)),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ~ p3(c21,c19)
<=> ~ p3(c21,c19) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
~ p3(c21,c19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p3_5) ).
tff(28,plain,
~ p3(c21,c19),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) )
| p3(c21,c19)
| p12(f13(c20),f13(c18))
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) )
<=> ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) )
| p3(c21,c19)
| p12(f13(c20),f13(c18))
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( p3(c21,c19)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
| p12(f13(c20),f13(c18)) )
<=> ( p3(c21,c19)
| p12(f13(c20),f13(c18))
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) )
| p3(c21,c19)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
| p12(f13(c20),f13(c18)) )
<=> ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) )
| p3(c21,c19)
| p12(f13(c20),f13(c18))
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) )
| p3(c21,c19)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
| p12(f13(c20),f13(c18)) )
<=> ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) )
| p3(c21,c19)
| p12(f13(c20),f13(c18))
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) )
| p3(c21,c19)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
| p12(f13(c20),f13(c18)) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p3(X7,X8)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
| ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
| p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
| p12(f13(X5),f13(c18)) )
| p3(c21,c19)
| p12(f13(c20),f13(c18))
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
$false,
inference(unit_resolution,[status(thm)],[34,28,25,22,19,16,13,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN593-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 05:53:50 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------