TSTP Solution File: SYN672-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN672-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 23:56:53 EDT 2022
% Result : Unsatisfiable 0.62s 0.66s
% Output : Proof 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 65
% Syntax : Number of formulae : 119 ( 36 unt; 21 typ; 0 def)
% Number of atoms : 475 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 620 ( 272 ~; 297 |; 0 &)
% ( 51 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 29 ( 29 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 12 >; 12 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 268 ( 240 !; 0 ?; 268 :)
% Comments :
%------------------------------------------------------------------------------
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(f4_type,type,
f4: ( $i * $i ) > $i ).
tff(c40_type,type,
c40: $i ).
tff(f7_type,type,
f7: ( $i * $i ) > $i ).
tff(c35_type,type,
c35: $i ).
tff(c34_type,type,
c34: $i ).
tff(p9_type,type,
p9: ( $i * $i ) > $o ).
tff(f10_type,type,
f10: ( $i * $i ) > $i ).
tff(f14_type,type,
f14: ( $i * $i ) > $i ).
tff(c39_type,type,
c39: $i ).
tff(f12_type,type,
f12: ( $i * $i ) > $i ).
tff(c33_type,type,
c33: $i ).
tff(c32_type,type,
c32: $i ).
tff(c38_type,type,
c38: $i ).
tff(p8_type,type,
p8: ( $i * $i ) > $o ).
tff(p30_type,type,
p30: ( $i * $i ) > $o ).
tff(p31_type,type,
p31: ( $i * $i ) > $o ).
tff(f17_type,type,
f17: ( $i * $i ) > $i ).
tff(c37_type,type,
c37: $i ).
tff(f20_type,type,
f20: ( $i * $i ) > $i ).
tff(c36_type,type,
c36: $i ).
tff(1,plain,
^ [X62: $i] :
refl(
( p3(X62,X62)
<=> p3(X62,X62) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X62: $i] : p3(X62,X62)
<=> ! [X62: $i] : p3(X62,X62) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X62: $i] : p3(X62,X62)
<=> ! [X62: $i] : p3(X62,X62) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X62: $i] : p3(X62,X62),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_6) ).
tff(5,plain,
! [X62: $i] : p3(X62,X62),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X62: $i] : p3(X62,X62),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X62: $i] : p3(X62,X62),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X62: $i] : p3(X62,X62)
| p3(f4(f7(c34,c35),c40),f4(f7(c34,c35),c40)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p3(f4(f7(c34,c35),c40),f4(f7(c34,c35),c40)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X98: $i] :
refl(
( p8(X98,X98)
<=> p8(X98,X98) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X98: $i] : p8(X98,X98)
<=> ! [X98: $i] : p8(X98,X98) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X98: $i] : p8(X98,X98)
<=> ! [X98: $i] : p8(X98,X98) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X98: $i] : p8(X98,X98),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_3) ).
tff(14,plain,
! [X98: $i] : p8(X98,X98),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X98: $i] : p8(X98,X98),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X98: $i] : p8(X98,X98),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X98: $i] : p8(X98,X98)
| p8(f12(c32,c33),f12(c32,c33)) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
p8(f12(c32,c33),f12(c32,c33)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X77: $i,X78: $i] :
refl(
( p3(f4(f7(c34,X77),f14(c38,X78)),f14(X77,X78))
<=> p3(f4(f7(c34,X77),f14(c38,X78)),f14(X77,X78)) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X77: $i,X78: $i] : p3(f4(f7(c34,X77),f14(c38,X78)),f14(X77,X78))
<=> ! [X77: $i,X78: $i] : p3(f4(f7(c34,X77),f14(c38,X78)),f14(X77,X78)) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X77: $i,X78: $i] : p3(f4(f7(c34,X77),f14(c38,X78)),f14(X77,X78))
<=> ! [X77: $i,X78: $i] : p3(f4(f7(c34,X77),f14(c38,X78)),f14(X77,X78)) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [X77: $i,X78: $i] : p3(f4(f7(c34,X77),f14(c38,X78)),f14(X77,X78)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_37) ).
tff(23,plain,
! [X77: $i,X78: $i] : p3(f4(f7(c34,X77),f14(c38,X78)),f14(X77,X78)),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X77: $i,X78: $i] : p3(f4(f7(c34,X77),f14(c38,X78)),f14(X77,X78)),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X77: $i,X78: $i] : p3(f4(f7(c34,X77),f14(c38,X78)),f14(X77,X78)),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [X77: $i,X78: $i] : p3(f4(f7(c34,X77),f14(c38,X78)),f14(X77,X78))
| p3(f4(f7(c34,c35),f14(c38,c39)),f14(c35,c39)) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
p3(f4(f7(c34,c35),f14(c38,c39)),f14(c35,c39)),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
^ [X110: $i,X111: $i,X109: $i,X108: $i] :
refl(
( ( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) )
<=> ( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [X110: $i,X111: $i,X109: $i,X108: $i] :
( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) )
<=> ! [X110: $i,X111: $i,X109: $i,X108: $i] :
( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [X110: $i,X111: $i,X109: $i,X108: $i] :
( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) )
<=> ! [X110: $i,X111: $i,X109: $i,X108: $i] :
( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
^ [X110: $i,X111: $i,X109: $i,X108: $i] :
trans(
monotonicity(
rewrite(
( ( p9(f10(X108,X109),f10(X110,X111))
| ~ p3(X109,X111) )
<=> ( ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) ) )),
( ( p9(f10(X108,X109),f10(X110,X111))
| ~ p3(X109,X111)
| ~ p8(X108,X110) )
<=> ( ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111))
| ~ p8(X108,X110) ) )),
rewrite(
( ( ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111))
| ~ p8(X108,X110) )
<=> ( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) ) )),
( ( p9(f10(X108,X109),f10(X110,X111))
| ~ p3(X109,X111)
| ~ p8(X108,X110) )
<=> ( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [X110: $i,X111: $i,X109: $i,X108: $i] :
( p9(f10(X108,X109),f10(X110,X111))
| ~ p3(X109,X111)
| ~ p8(X108,X110) )
<=> ! [X110: $i,X111: $i,X109: $i,X108: $i] :
( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [X110: $i,X111: $i,X109: $i,X108: $i] :
( p9(f10(X108,X109),f10(X110,X111))
| ~ p3(X109,X111)
| ~ p8(X108,X110) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_42) ).
tff(34,plain,
! [X110: $i,X111: $i,X109: $i,X108: $i] :
( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X110: $i,X111: $i,X109: $i,X108: $i] :
( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [X110: $i,X111: $i,X109: $i,X108: $i] :
( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [X110: $i,X111: $i,X109: $i,X108: $i] :
( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ( ~ ! [X110: $i,X111: $i,X109: $i,X108: $i] :
( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) )
| ~ p8(f12(c32,c33),f12(c32,c33))
| ~ p3(f4(f7(c34,c35),f14(c38,c39)),f14(c35,c39))
| p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39))) )
<=> ( ~ ! [X110: $i,X111: $i,X109: $i,X108: $i] :
( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) )
| ~ p8(f12(c32,c33),f12(c32,c33))
| ~ p3(f4(f7(c34,c35),f14(c38,c39)),f14(c35,c39))
| p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [X110: $i,X111: $i,X109: $i,X108: $i] :
( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) )
| ~ p8(f12(c32,c33),f12(c32,c33))
| ~ p3(f4(f7(c34,c35),f14(c38,c39)),f14(c35,c39))
| p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39))) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [X110: $i,X111: $i,X109: $i,X108: $i] :
( ~ p8(X108,X110)
| ~ p3(X109,X111)
| p9(f10(X108,X109),f10(X110,X111)) )
| ~ p8(f12(c32,c33),f12(c32,c33))
| ~ p3(f4(f7(c34,c35),f14(c38,c39)),f14(c35,c39))
| p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39))) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39))),
inference(unit_resolution,[status(thm)],[40,37,27,18]) ).
tff(42,plain,
^ [X60: $i,X61: $i] :
refl(
( ( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) )
<=> ( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) )
<=> ! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) )
<=> ! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
^ [X60: $i,X61: $i] :
rewrite(
( ( p3(X60,f14(c38,X61))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| ~ p31(f20(c36,X61),f17(c37,X60)) )
<=> ( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [X60: $i,X61: $i] :
( p3(X60,f14(c38,X61))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| ~ p31(f20(c36,X61),f17(c37,X60)) )
<=> ! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,axiom,
! [X60: $i,X61: $i] :
( p3(X60,f14(c38,X61))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| ~ p31(f20(c36,X61),f17(c37,X60)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_53) ).
tff(48,plain,
! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) ),
inference(modus_ponens,[status(thm)],[50,43]) ).
tff(52,plain,
( p31(f20(c36,c39),f17(c37,c40))
<=> p31(f20(c36,c39),f17(c37,c40)) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
p31(f20(c36,c39),f17(c37,c40)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31_19) ).
tff(54,plain,
p31(f20(c36,c39),f17(c37,c40)),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ p3(c40,f14(c38,c39))
<=> ~ p3(c40,f14(c38,c39)) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
~ p3(c40,f14(c38,c39)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p3_18) ).
tff(57,plain,
~ p3(c40,f14(c38,c39)),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
( ( ~ ! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) )
| p3(c40,f14(c38,c39))
| ~ p31(f20(c36,c39),f17(c37,c40))
| p30(f10(f12(c32,c33),f14(c38,c39)),c40) )
<=> ( ~ ! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) )
| p3(c40,f14(c38,c39))
| ~ p31(f20(c36,c39),f17(c37,c40))
| p30(f10(f12(c32,c33),f14(c38,c39)),c40) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( ~ p31(f20(c36,c39),f17(c37,c40))
| p30(f10(f12(c32,c33),f14(c38,c39)),c40)
| p3(c40,f14(c38,c39)) )
<=> ( p3(c40,f14(c38,c39))
| ~ p31(f20(c36,c39),f17(c37,c40))
| p30(f10(f12(c32,c33),f14(c38,c39)),c40) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( ~ ! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) )
| ~ p31(f20(c36,c39),f17(c37,c40))
| p30(f10(f12(c32,c33),f14(c38,c39)),c40)
| p3(c40,f14(c38,c39)) )
<=> ( ~ ! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) )
| p3(c40,f14(c38,c39))
| ~ p31(f20(c36,c39),f17(c37,c40))
| p30(f10(f12(c32,c33),f14(c38,c39)),c40) ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ~ ! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) )
| ~ p31(f20(c36,c39),f17(c37,c40))
| p30(f10(f12(c32,c33),f14(c38,c39)),c40)
| p3(c40,f14(c38,c39)) )
<=> ( ~ ! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) )
| p3(c40,f14(c38,c39))
| ~ p31(f20(c36,c39),f17(c37,c40))
| p30(f10(f12(c32,c33),f14(c38,c39)),c40) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) )
| ~ p31(f20(c36,c39),f17(c37,c40))
| p30(f10(f12(c32,c33),f14(c38,c39)),c40)
| p3(c40,f14(c38,c39)) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [X60: $i,X61: $i] :
( ~ p31(f20(c36,X61),f17(c37,X60))
| p30(f10(f12(c32,c33),f14(c38,X61)),X60)
| p3(X60,f14(c38,X61)) )
| p3(c40,f14(c38,c39))
| ~ p31(f20(c36,c39),f17(c37,c40))
| p30(f10(f12(c32,c33),f14(c38,c39)),c40) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
p30(f10(f12(c32,c33),f14(c38,c39)),c40),
inference(unit_resolution,[status(thm)],[63,57,54,51]) ).
tff(65,plain,
^ [X87: $i,X86: $i] :
refl(
( ( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) )
<=> ( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [X87: $i,X86: $i] :
( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) )
<=> ! [X87: $i,X86: $i] :
( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [X87: $i,X86: $i] :
( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) )
<=> ! [X87: $i,X86: $i] :
( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
^ [X87: $i,X86: $i] :
rewrite(
( ( p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87))
| ~ p30(f10(f12(c32,c33),X86),X87) )
<=> ( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [X87: $i,X86: $i] :
( p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87))
| ~ p30(f10(f12(c32,c33),X86),X87) )
<=> ! [X87: $i,X86: $i] :
( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,axiom,
! [X87: $i,X86: $i] :
( p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87))
| ~ p30(f10(f12(c32,c33),X86),X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30_54) ).
tff(71,plain,
! [X87: $i,X86: $i] :
( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [X87: $i,X86: $i] :
( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
! [X87: $i,X86: $i] :
( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [X87: $i,X86: $i] :
( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
( ( ~ ! [X87: $i,X86: $i] :
( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) )
| ~ p30(f10(f12(c32,c33),f14(c38,c39)),c40)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40)) )
<=> ( ~ ! [X87: $i,X86: $i] :
( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) )
| ~ p30(f10(f12(c32,c33),f14(c38,c39)),c40)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( ~ ! [X87: $i,X86: $i] :
( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) )
| ~ p30(f10(f12(c32,c33),f14(c38,c39)),c40)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40)) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
( ~ ! [X87: $i,X86: $i] :
( ~ p30(f10(f12(c32,c33),X86),X87)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),X86)),f4(f7(c34,c35),X87)) )
| ~ p30(f10(f12(c32,c33),f14(c38,c39)),c40)
| p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40)) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40)),
inference(unit_resolution,[status(thm)],[77,74,64]) ).
tff(79,plain,
( ~ p30(f10(f12(c32,c33),f14(c35,c39)),f4(f7(c34,c35),c40))
<=> ~ p30(f10(f12(c32,c33),f14(c35,c39)),f4(f7(c34,c35),c40)) ),
inference(rewrite,[status(thm)],]) ).
tff(80,axiom,
~ p30(f10(f12(c32,c33),f14(c35,c39)),f4(f7(c34,c35),c40)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p30_40) ).
tff(81,plain,
~ p30(f10(f12(c32,c33),f14(c35,c39)),f4(f7(c34,c35),c40)),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
^ [X82: $i,X83: $i,X85: $i,X84: $i] :
refl(
( ( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) )
<=> ( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) )
<=> ! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) )
<=> ! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
^ [X82: $i,X83: $i,X85: $i,X84: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p30(X82,X83)
| ~ p30(X85,X84) )
<=> ( ~ p30(X85,X84)
| p30(X82,X83) ) )),
( ( p30(X82,X83)
| ~ p30(X85,X84)
| ~ p9(X85,X82) )
<=> ( ~ p30(X85,X84)
| p30(X82,X83)
| ~ p9(X85,X82) ) )),
rewrite(
( ( ~ p30(X85,X84)
| p30(X82,X83)
| ~ p9(X85,X82) )
<=> ( ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) ) )),
( ( p30(X82,X83)
| ~ p30(X85,X84)
| ~ p9(X85,X82) )
<=> ( ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) ) )),
( ( p30(X82,X83)
| ~ p30(X85,X84)
| ~ p9(X85,X82)
| ~ p3(X84,X83) )
<=> ( ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83)
| ~ p3(X84,X83) ) )),
rewrite(
( ( ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83)
| ~ p3(X84,X83) )
<=> ( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) ) )),
( ( p30(X82,X83)
| ~ p30(X85,X84)
| ~ p9(X85,X82)
| ~ p3(X84,X83) )
<=> ( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [X82: $i,X83: $i,X85: $i,X84: $i] :
( p30(X82,X83)
| ~ p30(X85,X84)
| ~ p9(X85,X82)
| ~ p3(X84,X83) )
<=> ! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [X82: $i,X83: $i,X85: $i,X84: $i] :
( p30(X82,X83)
| ~ p30(X85,X84)
| ~ p9(X85,X82)
| ~ p3(X84,X83) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30_39) ).
tff(88,plain,
! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( ( ~ ! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) )
| p30(f10(f12(c32,c33),f14(c35,c39)),f4(f7(c34,c35),c40))
| ~ p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40))
| ~ p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39)))
| ~ p3(f4(f7(c34,c35),c40),f4(f7(c34,c35),c40)) )
<=> ( ~ ! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) )
| p30(f10(f12(c32,c33),f14(c35,c39)),f4(f7(c34,c35),c40))
| ~ p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40))
| ~ p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39)))
| ~ p3(f4(f7(c34,c35),c40),f4(f7(c34,c35),c40)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ( ~ p3(f4(f7(c34,c35),c40),f4(f7(c34,c35),c40))
| ~ p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39)))
| ~ p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40))
| p30(f10(f12(c32,c33),f14(c35,c39)),f4(f7(c34,c35),c40)) )
<=> ( p30(f10(f12(c32,c33),f14(c35,c39)),f4(f7(c34,c35),c40))
| ~ p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40))
| ~ p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39)))
| ~ p3(f4(f7(c34,c35),c40),f4(f7(c34,c35),c40)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ( ~ ! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) )
| ~ p3(f4(f7(c34,c35),c40),f4(f7(c34,c35),c40))
| ~ p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39)))
| ~ p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40))
| p30(f10(f12(c32,c33),f14(c35,c39)),f4(f7(c34,c35),c40)) )
<=> ( ~ ! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) )
| p30(f10(f12(c32,c33),f14(c35,c39)),f4(f7(c34,c35),c40))
| ~ p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40))
| ~ p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39)))
| ~ p3(f4(f7(c34,c35),c40),f4(f7(c34,c35),c40)) ) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ( ~ ! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) )
| ~ p3(f4(f7(c34,c35),c40),f4(f7(c34,c35),c40))
| ~ p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39)))
| ~ p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40))
| p30(f10(f12(c32,c33),f14(c35,c39)),f4(f7(c34,c35),c40)) )
<=> ( ~ ! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) )
| p30(f10(f12(c32,c33),f14(c35,c39)),f4(f7(c34,c35),c40))
| ~ p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40))
| ~ p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39)))
| ~ p3(f4(f7(c34,c35),c40),f4(f7(c34,c35),c40)) ) ),
inference(transitivity,[status(thm)],[94,92]) ).
tff(96,plain,
( ~ ! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) )
| ~ p3(f4(f7(c34,c35),c40),f4(f7(c34,c35),c40))
| ~ p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39)))
| ~ p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40))
| p30(f10(f12(c32,c33),f14(c35,c39)),f4(f7(c34,c35),c40)) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
( ~ ! [X82: $i,X83: $i,X85: $i,X84: $i] :
( ~ p3(X84,X83)
| ~ p9(X85,X82)
| ~ p30(X85,X84)
| p30(X82,X83) )
| p30(f10(f12(c32,c33),f14(c35,c39)),f4(f7(c34,c35),c40))
| ~ p30(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f4(f7(c34,c35),c40))
| ~ p9(f10(f12(c32,c33),f4(f7(c34,c35),f14(c38,c39))),f10(f12(c32,c33),f14(c35,c39)))
| ~ p3(f4(f7(c34,c35),c40),f4(f7(c34,c35),c40)) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
$false,
inference(unit_resolution,[status(thm)],[97,91,81,78,41,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN672-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 05:53:40 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.
% 0.62/0.66 % SZS status Unsatisfiable
% 0.62/0.66 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------