TSTP Solution File: SYN642-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN642-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 23:56:45 EDT 2022
% Result : Unsatisfiable 5.24s 3.66s
% Output : Proof 5.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 50
% Syntax : Number of formulae : 96 ( 29 unt; 9 typ; 0 def)
% Number of atoms : 411 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 553 ( 256 ~; 252 |; 0 &)
% ( 45 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 27 ( 27 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 221 ( 198 !; 0 ?; 221 :)
% Comments :
%------------------------------------------------------------------------------
tff(p6_type,type,
p6: ( $i * $i ) > $o ).
tff(f8_type,type,
f8: $i > $i ).
tff(f10_type,type,
f10: ( $i * $i ) > $i ).
tff(f3_type,type,
f3: $i > $i ).
tff(c18_type,type,
c18: $i ).
tff(c19_type,type,
c19: $i ).
tff(f9_type,type,
f9: ( $i * $i ) > $i ).
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(p15_type,type,
p15: $i > $o ).
tff(1,plain,
^ [X27: $i] :
refl(
( p2(X27,X27)
<=> p2(X27,X27) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X27: $i] : p2(X27,X27)
<=> ! [X27: $i] : p2(X27,X27) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X27: $i] : p2(X27,X27)
<=> ! [X27: $i] : p2(X27,X27) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X27: $i] : p2(X27,X27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_6) ).
tff(5,plain,
! [X27: $i] : p2(X27,X27),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X27: $i] : p2(X27,X27),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X27: $i] : p2(X27,X27),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X27: $i] : p2(X27,X27)
| p2(f10(f3(c19),f3(c18)),f10(f3(c19),f3(c18))) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p2(f10(f3(c19),f3(c18)),f10(f3(c19),f3(c18))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X51: $i,X50: $i] :
refl(
( ( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) )
<=> ( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X51: $i,X50: $i] :
( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) )
<=> ! [X51: $i,X50: $i] :
( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X51: $i,X50: $i] :
( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) )
<=> ! [X51: $i,X50: $i] :
( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X51: $i,X50: $i] :
rewrite(
( ( p6(f8(X50),f8(X51))
| ~ p2(X50,X51) )
<=> ( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X51: $i,X50: $i] :
( p6(f8(X50),f8(X51))
| ~ p2(X50,X51) )
<=> ! [X51: $i,X50: $i] :
( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X51: $i,X50: $i] :
( p6(f8(X50),f8(X51))
| ~ p2(X50,X51) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_17) ).
tff(16,plain,
! [X51: $i,X50: $i] :
( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X51: $i,X50: $i] :
( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X51: $i,X50: $i] :
( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X51: $i,X50: $i] :
( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [X51: $i,X50: $i] :
( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) )
| ~ p2(f10(f3(c19),f3(c18)),f10(f3(c19),f3(c18)))
| p6(f8(f10(f3(c19),f3(c18))),f8(f10(f3(c19),f3(c18)))) )
<=> ( ~ ! [X51: $i,X50: $i] :
( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) )
| ~ p2(f10(f3(c19),f3(c18)),f10(f3(c19),f3(c18)))
| p6(f8(f10(f3(c19),f3(c18))),f8(f10(f3(c19),f3(c18)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ ! [X51: $i,X50: $i] :
( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) )
| ~ p2(f10(f3(c19),f3(c18)),f10(f3(c19),f3(c18)))
| p6(f8(f10(f3(c19),f3(c18))),f8(f10(f3(c19),f3(c18)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [X51: $i,X50: $i] :
( ~ p2(X50,X51)
| p6(f8(X50),f8(X51)) )
| ~ p2(f10(f3(c19),f3(c18)),f10(f3(c19),f3(c18)))
| p6(f8(f10(f3(c19),f3(c18))),f8(f10(f3(c19),f3(c18)))) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
p6(f8(f10(f3(c19),f3(c18))),f8(f10(f3(c19),f3(c18)))),
inference(unit_resolution,[status(thm)],[22,19,9]) ).
tff(24,plain,
^ [X14: $i,X15: $i] :
refl(
( ( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) )
<=> ( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [X14: $i,X15: $i] :
( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) )
<=> ! [X14: $i,X15: $i] :
( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X14: $i,X15: $i] :
( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) )
<=> ! [X14: $i,X15: $i] :
( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [X14: $i,X15: $i] :
trans(
monotonicity(
rewrite(
( ( p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15)))
| ~ p15(X14) )
<=> ( ~ p15(X14)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) ) )),
( ( p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15)))
| ~ p15(X14)
| ~ p15(X15) )
<=> ( ~ p15(X14)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15)))
| ~ p15(X15) ) )),
rewrite(
( ( ~ p15(X14)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15)))
| ~ p15(X15) )
<=> ( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) ) )),
( ( p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15)))
| ~ p15(X14)
| ~ p15(X15) )
<=> ( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X14: $i,X15: $i] :
( p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15)))
| ~ p15(X14)
| ~ p15(X15) )
<=> ! [X14: $i,X15: $i] :
( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [X14: $i,X15: $i] :
( p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15)))
| ~ p15(X14)
| ~ p15(X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_36) ).
tff(30,plain,
! [X14: $i,X15: $i] :
( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X14: $i,X15: $i] :
( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [X14: $i,X15: $i] :
( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X14: $i,X15: $i] :
( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( p15(f3(c18))
<=> p15(f3(c18)) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
p15(f3(c18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f3_is_p15_2) ).
tff(36,plain,
p15(f3(c18)),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( p15(f3(c19))
<=> p15(f3(c19)) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
p15(f3(c19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f3_is_p15_1) ).
tff(39,plain,
p15(f3(c19)),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( ~ ! [X14: $i,X15: $i] :
( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) )
| ~ p15(f3(c19))
| ~ p15(f3(c18))
| p6(f8(f10(f3(c19),f3(c18))),f9(f8(f3(c19)),f8(f3(c18)))) )
<=> ( ~ ! [X14: $i,X15: $i] :
( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) )
| ~ p15(f3(c19))
| ~ p15(f3(c18))
| p6(f8(f10(f3(c19),f3(c18))),f9(f8(f3(c19)),f8(f3(c18)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ~ ! [X14: $i,X15: $i] :
( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) )
| ~ p15(f3(c19))
| ~ p15(f3(c18))
| p6(f8(f10(f3(c19),f3(c18))),f9(f8(f3(c19)),f8(f3(c18)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( ~ ! [X14: $i,X15: $i] :
( ~ p15(X14)
| ~ p15(X15)
| p6(f8(f10(X14,X15)),f9(f8(X14),f8(X15))) )
| ~ p15(f3(c19))
| ~ p15(f3(c18))
| p6(f8(f10(f3(c19),f3(c18))),f9(f8(f3(c19)),f8(f3(c18)))) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
p6(f8(f10(f3(c19),f3(c18))),f9(f8(f3(c19)),f8(f3(c18)))),
inference(unit_resolution,[status(thm)],[42,39,36,33]) ).
tff(44,plain,
^ [X47: $i,X45: $i,X46: $i] :
refl(
( ( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
<=> ( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
<=> ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
<=> ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
^ [X47: $i,X45: $i,X46: $i] :
trans(
monotonicity(
rewrite(
( ( p6(X46,X47)
| ~ p6(X45,X46) )
<=> ( ~ p6(X45,X46)
| p6(X46,X47) ) )),
( ( p6(X46,X47)
| ~ p6(X45,X46)
| ~ p6(X45,X47) )
<=> ( ~ p6(X45,X46)
| p6(X46,X47)
| ~ p6(X45,X47) ) )),
rewrite(
( ( ~ p6(X45,X46)
| p6(X46,X47)
| ~ p6(X45,X47) )
<=> ( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) ) )),
( ( p6(X46,X47)
| ~ p6(X45,X46)
| ~ p6(X45,X47) )
<=> ( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [X47: $i,X45: $i,X46: $i] :
( p6(X46,X47)
| ~ p6(X45,X46)
| ~ p6(X45,X47) )
<=> ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [X47: $i,X45: $i,X46: $i] :
( p6(X46,X47)
| ~ p6(X45,X46)
| ~ p6(X45,X47) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_23) ).
tff(50,plain,
! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
| ~ p6(f8(f10(f3(c19),f3(c18))),f8(f10(f3(c19),f3(c18))))
| ~ p6(f8(f10(f3(c19),f3(c18))),f9(f8(f3(c19)),f8(f3(c18))))
| p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18)))) )
<=> ( ~ ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
| ~ p6(f8(f10(f3(c19),f3(c18))),f8(f10(f3(c19),f3(c18))))
| ~ p6(f8(f10(f3(c19),f3(c18))),f9(f8(f3(c19)),f8(f3(c18))))
| p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ~ ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
| ~ p6(f8(f10(f3(c19),f3(c18))),f8(f10(f3(c19),f3(c18))))
| ~ p6(f8(f10(f3(c19),f3(c18))),f9(f8(f3(c19)),f8(f3(c18))))
| p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
| ~ p6(f8(f10(f3(c19),f3(c18))),f8(f10(f3(c19),f3(c18))))
| ~ p6(f8(f10(f3(c19),f3(c18))),f9(f8(f3(c19)),f8(f3(c18))))
| p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18)))) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18)))),
inference(unit_resolution,[status(thm)],[56,53,43,23]) ).
tff(58,plain,
^ [X53: $i,X55: $i,X52: $i,X54: $i] :
refl(
( ( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) )
<=> ( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) )
<=> ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) )
<=> ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
^ [X53: $i,X55: $i,X52: $i,X54: $i] :
trans(
monotonicity(
rewrite(
( ( p6(f9(X52,X53),f9(X54,X55))
| ~ p6(X53,X55) )
<=> ( ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) ) )),
( ( p6(f9(X52,X53),f9(X54,X55))
| ~ p6(X53,X55)
| ~ p6(X52,X54) )
<=> ( ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55))
| ~ p6(X52,X54) ) )),
rewrite(
( ( ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55))
| ~ p6(X52,X54) )
<=> ( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) ) )),
( ( p6(f9(X52,X53),f9(X54,X55))
| ~ p6(X53,X55)
| ~ p6(X52,X54) )
<=> ( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( p6(f9(X52,X53),f9(X54,X55))
| ~ p6(X53,X55)
| ~ p6(X52,X54) )
<=> ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( p6(f9(X52,X53),f9(X54,X55))
| ~ p6(X53,X55)
| ~ p6(X52,X54) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_33) ).
tff(64,plain,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( p6(f8(f3(c18)),f8(c18))
<=> p6(f8(f3(c18)),f8(c18)) ),
inference(rewrite,[status(thm)],]) ).
tff(69,axiom,
p6(f8(f3(c18)),f8(c18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_14) ).
tff(70,plain,
p6(f8(f3(c18)),f8(c18)),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
( p6(f8(f3(c19)),f8(c19))
<=> p6(f8(f3(c19)),f8(c19)) ),
inference(rewrite,[status(thm)],]) ).
tff(72,axiom,
p6(f8(f3(c19)),f8(c19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_9) ).
tff(73,plain,
p6(f8(f3(c19)),f8(c19)),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) )
| ~ p6(f8(f3(c19)),f8(c19))
| ~ p6(f8(f3(c18)),f8(c18))
| p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18))) )
<=> ( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) )
| ~ p6(f8(f3(c19)),f8(c19))
| ~ p6(f8(f3(c18)),f8(c18))
| p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) )
| ~ p6(f8(f3(c19)),f8(c19))
| ~ p6(f8(f3(c18)),f8(c18))
| p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18))) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p6(X52,X54)
| ~ p6(X53,X55)
| p6(f9(X52,X53),f9(X54,X55)) )
| ~ p6(f8(f3(c19)),f8(c19))
| ~ p6(f8(f3(c18)),f8(c18))
| p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18))) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18))),
inference(unit_resolution,[status(thm)],[76,73,70,67]) ).
tff(78,plain,
( ~ p6(f8(f10(f3(c19),f3(c18))),f9(f8(c19),f8(c18)))
<=> ~ p6(f8(f10(f3(c19),f3(c18))),f9(f8(c19),f8(c18))) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
~ p6(f8(f10(f3(c19),f3(c18))),f9(f8(c19),f8(c18))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p6_28) ).
tff(80,plain,
~ p6(f8(f10(f3(c19),f3(c18))),f9(f8(c19),f8(c18))),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
( ( ~ ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
| p6(f8(f10(f3(c19),f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18)))) )
<=> ( ~ ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
| p6(f8(f10(f3(c19),f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ( ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18))))
| p6(f8(f10(f3(c19),f3(c18))),f9(f8(c19),f8(c18))) )
<=> ( p6(f8(f10(f3(c19),f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( ~ ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18))))
| p6(f8(f10(f3(c19),f3(c18))),f9(f8(c19),f8(c18))) )
<=> ( ~ ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
| p6(f8(f10(f3(c19),f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18)))) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18))))
| p6(f8(f10(f3(c19),f3(c18))),f9(f8(c19),f8(c18))) )
<=> ( ~ ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
| p6(f8(f10(f3(c19),f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18)))) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18))))
| p6(f8(f10(f3(c19),f3(c18))),f9(f8(c19),f8(c18))) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [X47: $i,X45: $i,X46: $i] :
( ~ p6(X45,X47)
| ~ p6(X45,X46)
| p6(X46,X47) )
| p6(f8(f10(f3(c19),f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f9(f8(c19),f8(c18)))
| ~ p6(f9(f8(f3(c19)),f8(f3(c18))),f8(f10(f3(c19),f3(c18)))) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
$false,
inference(unit_resolution,[status(thm)],[86,53,80,77,57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN642-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 06:37:25 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 5.24/3.66 % SZS status Unsatisfiable
% 5.24/3.66 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------