TSTP Solution File: SYN717-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN717-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 23:57:03 EDT 2022
% Result : Unsatisfiable 0.20s 0.51s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 54
% Syntax : Number of formulae : 97 ( 27 unt; 19 typ; 0 def)
% Number of atoms : 436 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 653 ( 321 ~; 287 |; 0 &)
% ( 45 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 26 ( 26 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 11 >; 11 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 272 ( 246 !; 0 ?; 272 :)
% Comments :
%------------------------------------------------------------------------------
tff(p24_type,type,
p24: ( $i * $i ) > $o ).
tff(f25_type,type,
f25: ( $i * $i ) > $i ).
tff(c77_type,type,
c77: $i ).
tff(c75_type,type,
c75: $i ).
tff(c79_type,type,
c79: $i ).
tff(p22_type,type,
p22: ( $i * $i ) > $o ).
tff(p23_type,type,
p23: ( $i * $i ) > $o ).
tff(p20_type,type,
p20: ( $i * $i ) > $o ).
tff(f21_type,type,
f21: ( $i * $i ) > $i ).
tff(c78_type,type,
c78: $i ).
tff(c76_type,type,
c76: $i ).
tff(p60_type,type,
p60: ( $i * $i ) > $o ).
tff(p59_type,type,
p59: ( $i * $i ) > $o ).
tff(c72_type,type,
c72: $i ).
tff(f29_type,type,
f29: ( $i * $i ) > $i ).
tff(f31_type,type,
f31: ( $i * $i ) > $i ).
tff(f33_type,type,
f33: ( $i * $i ) > $i ).
tff(c74_type,type,
c74: $i ).
tff(c73_type,type,
c73: $i ).
tff(1,plain,
^ [X55: $i] :
refl(
( p22(X55,X55)
<=> p22(X55,X55) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X55: $i] : p22(X55,X55)
<=> ! [X55: $i] : p22(X55,X55) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X55: $i] : p22(X55,X55)
<=> ! [X55: $i] : p22(X55,X55) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X55: $i] : p22(X55,X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22_28) ).
tff(5,plain,
! [X55: $i] : p22(X55,X55),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X55: $i] : p22(X55,X55),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X55: $i] : p22(X55,X55),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X55: $i] : p22(X55,X55)
| p22(c75,c75) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p22(c75,c75),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X68: $i,X70: $i,X69: $i,X71: $i] :
refl(
( ( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) )
<=> ( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) )
<=> ! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) )
<=> ! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X68: $i,X70: $i,X69: $i,X71: $i] :
trans(
monotonicity(
rewrite(
( ( p24(f25(X68,X69),f25(X70,X71))
| ~ p22(X68,X70) )
<=> ( ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) ) )),
( ( p24(f25(X68,X69),f25(X70,X71))
| ~ p22(X68,X70)
| ~ p23(X69,X71) )
<=> ( ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71))
| ~ p23(X69,X71) ) )),
rewrite(
( ( ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71))
| ~ p23(X69,X71) )
<=> ( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) ) )),
( ( p24(f25(X68,X69),f25(X70,X71))
| ~ p22(X68,X70)
| ~ p23(X69,X71) )
<=> ( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X68: $i,X70: $i,X69: $i,X71: $i] :
( p24(f25(X68,X69),f25(X70,X71))
| ~ p22(X68,X70)
| ~ p23(X69,X71) )
<=> ! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X68: $i,X70: $i,X69: $i,X71: $i] :
( p24(f25(X68,X69),f25(X70,X71))
| ~ p22(X68,X70)
| ~ p23(X69,X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24_94) ).
tff(16,plain,
! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( p23(c79,c77)
<=> p23(c79,c77) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
p23(c79,c77),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_36) ).
tff(22,plain,
p23(c79,c77),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) )
| ~ p23(c79,c77)
| p24(f25(c75,c79),f25(c75,c77))
| ~ p22(c75,c75) )
<=> ( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) )
| ~ p23(c79,c77)
| p24(f25(c75,c79),f25(c75,c77))
| ~ p22(c75,c75) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ p23(c79,c77)
| ~ p22(c75,c75)
| p24(f25(c75,c79),f25(c75,c77)) )
<=> ( ~ p23(c79,c77)
| p24(f25(c75,c79),f25(c75,c77))
| ~ p22(c75,c75) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) )
| ~ p23(c79,c77)
| ~ p22(c75,c75)
| p24(f25(c75,c79),f25(c75,c77)) )
<=> ( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) )
| ~ p23(c79,c77)
| p24(f25(c75,c79),f25(c75,c77))
| ~ p22(c75,c75) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) )
| ~ p23(c79,c77)
| ~ p22(c75,c75)
| p24(f25(c75,c79),f25(c75,c77)) )
<=> ( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) )
| ~ p23(c79,c77)
| p24(f25(c75,c79),f25(c75,c77))
| ~ p22(c75,c75) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) )
| ~ p23(c79,c77)
| ~ p22(c75,c75)
| p24(f25(c75,c79),f25(c75,c77)) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
( ~ p23(X69,X71)
| ~ p22(X68,X70)
| p24(f25(X68,X69),f25(X70,X71)) )
| ~ p23(c79,c77)
| p24(f25(c75,c79),f25(c75,c77))
| ~ p22(c75,c75) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
p24(f25(c75,c79),f25(c75,c77)),
inference(unit_resolution,[status(thm)],[28,22,19,9]) ).
tff(30,plain,
^ [X48: $i] :
refl(
( p20(X48,X48)
<=> p20(X48,X48) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X48: $i] : p20(X48,X48)
<=> ! [X48: $i] : p20(X48,X48) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X48: $i] : p20(X48,X48)
<=> ! [X48: $i] : p20(X48,X48) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [X48: $i] : p20(X48,X48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20_29) ).
tff(34,plain,
! [X48: $i] : p20(X48,X48),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X48: $i] : p20(X48,X48),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X48: $i] : p20(X48,X48),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [X48: $i] : p20(X48,X48)
| p20(f21(c76,c78),f21(c76,c78)) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
p20(f21(c76,c78),f21(c76,c78)),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
^ [X212: $i,X210: $i,X211: $i,X209: $i] :
refl(
( ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) )
<=> ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) )
<=> ! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) )
<=> ! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
^ [X212: $i,X210: $i,X211: $i,X209: $i] :
rewrite(
( ( ~ p60(f25(c75,X209),f21(c76,X212))
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72) )
<=> ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p60(f25(c75,X209),f21(c76,X212))
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72) )
<=> ! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p60(f25(c75,X209),f21(c76,X212))
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p60_107) ).
tff(45,plain,
! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( p59(f29(c73,f31(f33(c74,c77),c78)),c72)
<=> p59(f29(c73,f31(f33(c74,c77),c78)),c72) ),
inference(rewrite,[status(thm)],]) ).
tff(50,axiom,
p59(f29(c73,f31(f33(c74,c77),c78)),c72),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p59_44) ).
tff(51,plain,
p59(f29(c73,f31(f33(c74,c77),c78)),c72),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) )
| ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
| ~ p60(f25(c75,c77),f21(c76,c78)) )
<=> ( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) )
| ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
| ~ p60(f25(c75,c77),f21(c76,c78)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
| ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
| ~ p60(f25(c75,c77),f21(c76,c78)) )
<=> ( ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
| ~ p60(f25(c75,c77),f21(c76,c78)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) )
| ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
| ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
| ~ p60(f25(c75,c77),f21(c76,c78)) )
<=> ( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) )
| ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
| ~ p60(f25(c75,c77),f21(c76,c78)) ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) )
| ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
| ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
| ~ p60(f25(c75,c77),f21(c76,c78)) )
<=> ( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) )
| ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
| ~ p60(f25(c75,c77),f21(c76,c78)) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,plain,
( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) )
| ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
| ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
| ~ p60(f25(c75,c77),f21(c76,c78)) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
| ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
| ~ p60(f25(c75,X209),f21(c76,X212)) )
| ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
| ~ p60(f25(c75,c77),f21(c76,c78)) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
~ p60(f25(c75,c77),f21(c76,c78)),
inference(unit_resolution,[status(thm)],[57,51,48]) ).
tff(59,plain,
^ [X188: $i,X189: $i,X186: $i,X187: $i] :
refl(
( ( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) )
<=> ( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) )
<=> ! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) )
<=> ! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
^ [X188: $i,X189: $i,X186: $i,X187: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p60(X186,X187)
| ~ p24(X189,X186) )
<=> ( ~ p24(X189,X186)
| p60(X186,X187) ) )),
( ( p60(X186,X187)
| ~ p24(X189,X186)
| ~ p60(X189,X188) )
<=> ( ~ p24(X189,X186)
| p60(X186,X187)
| ~ p60(X189,X188) ) )),
rewrite(
( ( ~ p24(X189,X186)
| p60(X186,X187)
| ~ p60(X189,X188) )
<=> ( ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) ) )),
( ( p60(X186,X187)
| ~ p24(X189,X186)
| ~ p60(X189,X188) )
<=> ( ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) ) )),
( ( p60(X186,X187)
| ~ p24(X189,X186)
| ~ p60(X189,X188)
| ~ p20(X188,X187) )
<=> ( ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187)
| ~ p20(X188,X187) ) )),
rewrite(
( ( ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187)
| ~ p20(X188,X187) )
<=> ( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) ) )),
( ( p60(X186,X187)
| ~ p24(X189,X186)
| ~ p60(X189,X188)
| ~ p20(X188,X187) )
<=> ( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [X188: $i,X189: $i,X186: $i,X187: $i] :
( p60(X186,X187)
| ~ p24(X189,X186)
| ~ p60(X189,X188)
| ~ p20(X188,X187) )
<=> ! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,axiom,
! [X188: $i,X189: $i,X186: $i,X187: $i] :
( p60(X186,X187)
| ~ p24(X189,X186)
| ~ p60(X189,X188)
| ~ p20(X188,X187) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p60_84) ).
tff(65,plain,
! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,plain,
( p60(f25(c75,c79),f21(c76,c78))
<=> p60(f25(c75,c79),f21(c76,c78)) ),
inference(rewrite,[status(thm)],]) ).
tff(70,axiom,
p60(f25(c75,c79),f21(c76,c78)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p60_42) ).
tff(71,plain,
p60(f25(c75,c79),f21(c76,c78)),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( ( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) )
| p60(f25(c75,c77),f21(c76,c78))
| ~ p60(f25(c75,c79),f21(c76,c78))
| ~ p24(f25(c75,c79),f25(c75,c77))
| ~ p20(f21(c76,c78),f21(c76,c78)) )
<=> ( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) )
| p60(f25(c75,c77),f21(c76,c78))
| ~ p60(f25(c75,c79),f21(c76,c78))
| ~ p24(f25(c75,c79),f25(c75,c77))
| ~ p20(f21(c76,c78),f21(c76,c78)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ( ~ p20(f21(c76,c78),f21(c76,c78))
| ~ p60(f25(c75,c79),f21(c76,c78))
| ~ p24(f25(c75,c79),f25(c75,c77))
| p60(f25(c75,c77),f21(c76,c78)) )
<=> ( p60(f25(c75,c77),f21(c76,c78))
| ~ p60(f25(c75,c79),f21(c76,c78))
| ~ p24(f25(c75,c79),f25(c75,c77))
| ~ p20(f21(c76,c78),f21(c76,c78)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) )
| ~ p20(f21(c76,c78),f21(c76,c78))
| ~ p60(f25(c75,c79),f21(c76,c78))
| ~ p24(f25(c75,c79),f25(c75,c77))
| p60(f25(c75,c77),f21(c76,c78)) )
<=> ( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) )
| p60(f25(c75,c77),f21(c76,c78))
| ~ p60(f25(c75,c79),f21(c76,c78))
| ~ p24(f25(c75,c79),f25(c75,c77))
| ~ p20(f21(c76,c78),f21(c76,c78)) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) )
| ~ p20(f21(c76,c78),f21(c76,c78))
| ~ p60(f25(c75,c79),f21(c76,c78))
| ~ p24(f25(c75,c79),f25(c75,c77))
| p60(f25(c75,c77),f21(c76,c78)) )
<=> ( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) )
| p60(f25(c75,c77),f21(c76,c78))
| ~ p60(f25(c75,c79),f21(c76,c78))
| ~ p24(f25(c75,c79),f25(c75,c77))
| ~ p20(f21(c76,c78),f21(c76,c78)) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) )
| ~ p20(f21(c76,c78),f21(c76,c78))
| ~ p60(f25(c75,c79),f21(c76,c78))
| ~ p24(f25(c75,c79),f25(c75,c77))
| p60(f25(c75,c77),f21(c76,c78)) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
( ~ p20(X188,X187)
| ~ p60(X189,X188)
| ~ p24(X189,X186)
| p60(X186,X187) )
| p60(f25(c75,c77),f21(c76,c78))
| ~ p60(f25(c75,c79),f21(c76,c78))
| ~ p24(f25(c75,c79),f25(c75,c77))
| ~ p20(f21(c76,c78),f21(c76,c78)) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
$false,
inference(unit_resolution,[status(thm)],[77,71,68,58,38,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SYN717-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n005.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 06:43:18 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.51 % SZS status Unsatisfiable
% 0.20/0.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------