TSTP Solution File: SYN638-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN638-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 23:56:43 EDT 2022
% Result : Unsatisfiable 1.14s 1.01s
% Output : Proof 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 46
% Syntax : Number of formulae : 85 ( 26 unt; 14 typ; 0 def)
% Number of atoms : 348 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 468 ( 217 ~; 213 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 26 ( 26 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 207 ( 185 !; 0 ?; 207 :)
% Comments :
%------------------------------------------------------------------------------
tff(p4_type,type,
p4: ( $i * $i ) > $o ).
tff(f16_type,type,
f16: $i > $i ).
tff(f17_type,type,
f17: ( $i * $i ) > $i ).
tff(f5_type,type,
f5: ( $i * $i * $i ) > $i ).
tff(c29_type,type,
c29: $i ).
tff(c26_type,type,
c26: $i ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(f9_type,type,
f9: ( $i * $i ) > $i ).
tff(c28_type,type,
c28: $i ).
tff(f10_type,type,
f10: $i > $i ).
tff(c25_type,type,
c25: $i ).
tff(f11_type,type,
f11: $i > $i ).
tff(c27_type,type,
c27: $i ).
tff(p22_type,type,
p22: ( $i * $i ) > $o ).
tff(1,plain,
^ [X51: $i] :
refl(
( p4(f5(f8(f11(c25),f9(f10(c25),c28)),X51,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X51,c29))
<=> p4(f5(f8(f11(c25),f9(f10(c25),c28)),X51,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X51,c29)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X51: $i] : p4(f5(f8(f11(c25),f9(f10(c25),c28)),X51,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X51,c29))
<=> ! [X51: $i] : p4(f5(f8(f11(c25),f9(f10(c25),c28)),X51,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X51,c29)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X51: $i] : p4(f5(f8(f11(c25),f9(f10(c25),c28)),X51,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X51,c29))
<=> ! [X51: $i] : p4(f5(f8(f11(c25),f9(f10(c25),c28)),X51,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X51,c29)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X51: $i] : p4(f5(f8(f11(c25),f9(f10(c25),c28)),X51,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X51,c29)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_39) ).
tff(5,plain,
! [X51: $i] : p4(f5(f8(f11(c25),f9(f10(c25),c28)),X51,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X51,c29)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X51: $i] : p4(f5(f8(f11(c25),f9(f10(c25),c28)),X51,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X51,c29)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X51: $i] : p4(f5(f8(f11(c25),f9(f10(c25),c28)),X51,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X51,c29)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X51: $i] : p4(f5(f8(f11(c25),f9(f10(c25),c28)),X51,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X51,c29))
| p4(f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p4(f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X36: $i] :
refl(
( p4(X36,X36)
<=> p4(X36,X36) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X36: $i] : p4(X36,X36)
<=> ! [X36: $i] : p4(X36,X36) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X36: $i] : p4(X36,X36)
<=> ! [X36: $i] : p4(X36,X36) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X36: $i] : p4(X36,X36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_4) ).
tff(14,plain,
! [X36: $i] : p4(X36,X36),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X36: $i] : p4(X36,X36),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X36: $i] : p4(X36,X36),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X36: $i] : p4(X36,X36)
| p4(c27,c27) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
p4(c27,c27),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X43: $i,X42: $i,X44: $i,X41: $i] :
refl(
( ( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) )
<=> ( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) )
<=> ! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) )
<=> ! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [X43: $i,X42: $i,X44: $i,X41: $i] :
trans(
monotonicity(
rewrite(
( ( p4(f17(X41,X42),f17(X43,X44))
| ~ p4(X41,X43) )
<=> ( ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) ) )),
( ( p4(f17(X41,X42),f17(X43,X44))
| ~ p4(X41,X43)
| ~ p4(X42,X44) )
<=> ( ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44))
| ~ p4(X42,X44) ) )),
rewrite(
( ( ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44))
| ~ p4(X42,X44) )
<=> ( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) ) )),
( ( p4(f17(X41,X42),f17(X43,X44))
| ~ p4(X41,X43)
| ~ p4(X42,X44) )
<=> ( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [X43: $i,X42: $i,X44: $i,X41: $i] :
( p4(f17(X41,X42),f17(X43,X44))
| ~ p4(X41,X43)
| ~ p4(X42,X44) )
<=> ! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [X43: $i,X42: $i,X44: $i,X41: $i] :
( p4(f17(X41,X42),f17(X43,X44))
| ~ p4(X41,X43)
| ~ p4(X42,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_32) ).
tff(25,plain,
! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( ~ ! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) )
| ~ p4(c27,c27)
| ~ p4(f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))
| p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))) )
<=> ( ~ ! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) )
| ~ p4(c27,c27)
| ~ p4(f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))
| p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ p4(f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))
| ~ p4(c27,c27)
| p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))) )
<=> ( ~ p4(c27,c27)
| ~ p4(f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))
| p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) )
| ~ p4(f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))
| ~ p4(c27,c27)
| p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))) )
<=> ( ~ ! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) )
| ~ p4(c27,c27)
| ~ p4(f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))
| p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) )
| ~ p4(f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))
| ~ p4(c27,c27)
| p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))) )
<=> ( ~ ! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) )
| ~ p4(c27,c27)
| ~ p4(f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))
| p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) )
| ~ p4(f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))
| ~ p4(c27,c27)
| p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [X43: $i,X42: $i,X44: $i,X41: $i] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) )
| ~ p4(c27,c27)
| ~ p4(f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))
| p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),
inference(unit_resolution,[status(thm)],[34,28,18,9]) ).
tff(36,plain,
^ [X39: $i,X40: $i] :
refl(
( ( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) )
<=> ( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X39: $i,X40: $i] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) )
<=> ! [X39: $i,X40: $i] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X39: $i,X40: $i] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) )
<=> ! [X39: $i,X40: $i] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
^ [X39: $i,X40: $i] :
rewrite(
( ( p4(f16(X39),f16(X40))
| ~ p4(X39,X40) )
<=> ( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X39: $i,X40: $i] :
( p4(f16(X39),f16(X40))
| ~ p4(X39,X40) )
<=> ! [X39: $i,X40: $i] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X39: $i,X40: $i] :
( p4(f16(X39),f16(X40))
| ~ p4(X39,X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_12) ).
tff(42,plain,
! [X39: $i,X40: $i] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X39: $i,X40: $i] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X39: $i,X40: $i] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X39: $i,X40: $i] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [X39: $i,X40: $i] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) )
| ~ p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29)))
| p4(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29)))) )
<=> ( ~ ! [X39: $i,X40: $i] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) )
| ~ p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29)))
| p4(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ! [X39: $i,X40: $i] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) )
| ~ p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29)))
| p4(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X39: $i,X40: $i] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) )
| ~ p4(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29)))
| p4(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29)))) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
p4(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29)))),
inference(unit_resolution,[status(thm)],[48,45,35]) ).
tff(50,plain,
( ~ ! [X36: $i] : p4(X36,X36)
| p4(f16(f17(c27,f5(c25,c26,c27))),f16(f17(c27,f5(c25,c26,c27)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
p4(f16(f17(c27,f5(c25,c26,c27))),f16(f17(c27,f5(c25,c26,c27)))),
inference(unit_resolution,[status(thm)],[50,16]) ).
tff(52,plain,
( ~ p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27))))
<=> ~ p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
~ p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p22_41) ).
tff(54,plain,
~ p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27))))
<=> p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27)))) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22_40) ).
tff(57,plain,
p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27)))),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
^ [X22: $i,X21: $i,X20: $i,X23: $i] :
refl(
( ( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) )
<=> ( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [X22: $i,X21: $i,X20: $i,X23: $i] :
( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) )
<=> ! [X22: $i,X21: $i,X20: $i,X23: $i] :
( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [X22: $i,X21: $i,X20: $i,X23: $i] :
( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) )
<=> ! [X22: $i,X21: $i,X20: $i,X23: $i] :
( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
^ [X22: $i,X21: $i,X20: $i,X23: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p22(X20,X21)
| ~ p4(X22,X20) )
<=> ( ~ p4(X22,X20)
| p22(X20,X21) ) )),
( ( p22(X20,X21)
| ~ p4(X22,X20)
| ~ p4(X23,X21) )
<=> ( ~ p4(X22,X20)
| p22(X20,X21)
| ~ p4(X23,X21) ) )),
rewrite(
( ( ~ p4(X22,X20)
| p22(X20,X21)
| ~ p4(X23,X21) )
<=> ( ~ p4(X23,X21)
| ~ p4(X22,X20)
| p22(X20,X21) ) )),
( ( p22(X20,X21)
| ~ p4(X22,X20)
| ~ p4(X23,X21) )
<=> ( ~ p4(X23,X21)
| ~ p4(X22,X20)
| p22(X20,X21) ) )),
( ( p22(X20,X21)
| ~ p4(X22,X20)
| ~ p4(X23,X21)
| ~ p22(X22,X23) )
<=> ( ~ p4(X23,X21)
| ~ p4(X22,X20)
| p22(X20,X21)
| ~ p22(X22,X23) ) )),
rewrite(
( ( ~ p4(X23,X21)
| ~ p4(X22,X20)
| p22(X20,X21)
| ~ p22(X22,X23) )
<=> ( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) ) )),
( ( p22(X20,X21)
| ~ p4(X22,X20)
| ~ p4(X23,X21)
| ~ p22(X22,X23) )
<=> ( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [X22: $i,X21: $i,X20: $i,X23: $i] :
( p22(X20,X21)
| ~ p4(X22,X20)
| ~ p4(X23,X21)
| ~ p22(X22,X23) )
<=> ! [X22: $i,X21: $i,X20: $i,X23: $i] :
( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [X22: $i,X21: $i,X20: $i,X23: $i] :
( p22(X20,X21)
| ~ p4(X22,X20)
| ~ p4(X23,X21)
| ~ p22(X22,X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22_28) ).
tff(64,plain,
! [X22: $i,X21: $i,X20: $i,X23: $i] :
( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [X22: $i,X21: $i,X20: $i,X23: $i] :
( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [X22: $i,X21: $i,X20: $i,X23: $i] :
( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [X22: $i,X21: $i,X20: $i,X23: $i] :
( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( ( ~ ! [X22: $i,X21: $i,X20: $i,X23: $i] :
( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) )
| ~ p4(f16(f17(c27,f5(c25,c26,c27))),f16(f17(c27,f5(c25,c26,c27))))
| ~ p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27))))
| ~ p4(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))))
| p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))) )
<=> ( ~ ! [X22: $i,X21: $i,X20: $i,X23: $i] :
( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) )
| ~ p4(f16(f17(c27,f5(c25,c26,c27))),f16(f17(c27,f5(c25,c26,c27))))
| ~ p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27))))
| ~ p4(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))))
| p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ~ ! [X22: $i,X21: $i,X20: $i,X23: $i] :
( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) )
| ~ p4(f16(f17(c27,f5(c25,c26,c27))),f16(f17(c27,f5(c25,c26,c27))))
| ~ p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27))))
| ~ p4(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))))
| p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
( ~ ! [X22: $i,X21: $i,X20: $i,X23: $i] :
( ~ p4(X23,X21)
| ~ p22(X22,X23)
| ~ p4(X22,X20)
| p22(X20,X21) )
| ~ p4(f16(f17(c27,f5(c25,c26,c27))),f16(f17(c27,f5(c25,c26,c27))))
| ~ p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27))))
| ~ p4(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))))
| p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
$false,
inference(unit_resolution,[status(thm)],[70,67,57,54,51,49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN638-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n016.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 06:39:55 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.
% 1.14/1.01 % SZS status Unsatisfiable
% 1.14/1.01 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------