TSTP Solution File: SYN558-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN558-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 23:56:25 EDT 2022
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 58
% Syntax : Number of formulae : 118 ( 42 unt; 9 typ; 0 def)
% Number of atoms : 710 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 1052 ( 504 ~; 484 |; 0 &)
% ( 64 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 53 ( 53 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 328 ( 297 !; 0 ?; 328 :)
% Comments :
%------------------------------------------------------------------------------
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(f3_type,type,
f3: $i > $i ).
tff(c8_type,type,
c8: $i ).
tff(c9_type,type,
c9: $i ).
tff(p5_type,type,
p5: ( $i * $i * $i ) > $o ).
tff(c7_type,type,
c7: $i ).
tff(p4_type,type,
p4: ( $i * $i ) > $o ).
tff(c10_type,type,
c10: $i ).
tff(p6_type,type,
p6: ( $i * $i ) > $o ).
tff(1,plain,
^ [X21: $i] :
refl(
( p5(c7,X21,f3(X21))
<=> p5(c7,X21,f3(X21)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X21: $i] : p5(c7,X21,f3(X21))
<=> ! [X21: $i] : p5(c7,X21,f3(X21)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X21: $i] : p5(c7,X21,f3(X21))
<=> ! [X21: $i] : p5(c7,X21,f3(X21)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X21: $i] : p5(c7,X21,f3(X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_6) ).
tff(5,plain,
! [X21: $i] : p5(c7,X21,f3(X21)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X21: $i] : p5(c7,X21,f3(X21)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X21: $i] : p5(c7,X21,f3(X21)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X21: $i] : p5(c7,X21,f3(X21))
| p5(c7,c8,f3(c8)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p5(c7,c8,f3(c8)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X26: $i] :
refl(
( ( ~ p5(c7,c8,X26)
| ~ p5(c7,c9,X26) )
<=> ( ~ p5(c7,c8,X26)
| ~ p5(c7,c9,X26) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X26: $i] :
( ~ p5(c7,c8,X26)
| ~ p5(c7,c9,X26) )
<=> ! [X26: $i] :
( ~ p5(c7,c8,X26)
| ~ p5(c7,c9,X26) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X26: $i] :
( ~ p5(c7,c8,X26)
| ~ p5(c7,c9,X26) )
<=> ! [X26: $i] :
( ~ p5(c7,c8,X26)
| ~ p5(c7,c9,X26) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X26: $i] :
( ~ p5(c7,c8,X26)
| ~ p5(c7,c9,X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p5_8) ).
tff(14,plain,
! [X26: $i] :
( ~ p5(c7,c8,X26)
| ~ p5(c7,c9,X26) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X26: $i] :
( ~ p5(c7,c8,X26)
| ~ p5(c7,c9,X26) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X26: $i] :
( ~ p5(c7,c8,X26)
| ~ p5(c7,c9,X26) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [X26: $i] :
( ~ p5(c7,c8,X26)
| ~ p5(c7,c9,X26) )
| ~ p5(c7,c8,f3(c8))
| ~ p5(c7,c9,f3(c8)) )
<=> ( ~ ! [X26: $i] :
( ~ p5(c7,c8,X26)
| ~ p5(c7,c9,X26) )
| ~ p5(c7,c8,f3(c8))
| ~ p5(c7,c9,f3(c8)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [X26: $i] :
( ~ p5(c7,c8,X26)
| ~ p5(c7,c9,X26) )
| ~ p5(c7,c8,f3(c8))
| ~ p5(c7,c9,f3(c8)) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [X26: $i] :
( ~ p5(c7,c8,X26)
| ~ p5(c7,c9,X26) )
| ~ p5(c7,c8,f3(c8))
| ~ p5(c7,c9,f3(c8)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ p5(c7,c9,f3(c8)),
inference(unit_resolution,[status(thm)],[19,16,9]) ).
tff(21,plain,
( ~ ! [X21: $i] : p5(c7,X21,f3(X21))
| p5(c7,c9,f3(c9)) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
p5(c7,c9,f3(c9)),
inference(unit_resolution,[status(thm)],[21,7]) ).
tff(23,plain,
^ [X8: $i] :
refl(
( p4(X8,X8)
<=> p4(X8,X8) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [X8: $i] : p4(X8,X8)
<=> ! [X8: $i] : p4(X8,X8) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [X8: $i] : p4(X8,X8)
<=> ! [X8: $i] : p4(X8,X8) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
! [X8: $i] : p4(X8,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_2) ).
tff(27,plain,
! [X8: $i] : p4(X8,X8),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X8: $i] : p4(X8,X8),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [X8: $i] : p4(X8,X8),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [X8: $i] : p4(X8,X8)
| p4(c7,c7) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
p4(c7,c7),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
^ [X0: $i] :
refl(
( p2(X0,X0)
<=> p2(X0,X0) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X0: $i] : p2(X0,X0)
<=> ! [X0: $i] : p2(X0,X0) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X0: $i] : p2(X0,X0)
<=> ! [X0: $i] : p2(X0,X0) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [X0: $i] : p2(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_1) ).
tff(36,plain,
! [X0: $i] : p2(X0,X0),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X0: $i] : p2(X0,X0),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X0: $i] : p2(X0,X0),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [X0: $i] : p2(X0,X0)
| p2(c9,c9) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
p2(c9,c9),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
^ [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
refl(
( ( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) )
<=> ( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) )
<=> ! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) )
<=> ! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
^ [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p5(X15,X16,X17)
| ~ p2(X18,X16) )
<=> ( ~ p2(X18,X16)
| p5(X15,X16,X17) ) )),
( ( p5(X15,X16,X17)
| ~ p2(X18,X16)
| ~ p2(X19,X17) )
<=> ( ~ p2(X18,X16)
| p5(X15,X16,X17)
| ~ p2(X19,X17) ) )),
rewrite(
( ( ~ p2(X18,X16)
| p5(X15,X16,X17)
| ~ p2(X19,X17) )
<=> ( ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ) )),
( ( p5(X15,X16,X17)
| ~ p2(X18,X16)
| ~ p2(X19,X17) )
<=> ( ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ) )),
( ( p5(X15,X16,X17)
| ~ p2(X18,X16)
| ~ p2(X19,X17)
| ~ p4(X20,X15) )
<=> ( ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17)
| ~ p4(X20,X15) ) )),
rewrite(
( ( ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17)
| ~ p4(X20,X15) )
<=> ( ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ) )),
( ( p5(X15,X16,X17)
| ~ p2(X18,X16)
| ~ p2(X19,X17)
| ~ p4(X20,X15) )
<=> ( ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ) )),
( ( p5(X15,X16,X17)
| ~ p2(X18,X16)
| ~ p2(X19,X17)
| ~ p4(X20,X15)
| ~ p5(X20,X18,X19) )
<=> ( ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17)
| ~ p5(X20,X18,X19) ) )),
rewrite(
( ( ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17)
| ~ p5(X20,X18,X19) )
<=> ( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ) )),
( ( p5(X15,X16,X17)
| ~ p2(X18,X16)
| ~ p2(X19,X17)
| ~ p4(X20,X15)
| ~ p5(X20,X18,X19) )
<=> ( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( p5(X15,X16,X17)
| ~ p2(X18,X16)
| ~ p2(X19,X17)
| ~ p4(X20,X15)
| ~ p5(X20,X18,X19) )
<=> ! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( p5(X15,X16,X17)
| ~ p2(X18,X16)
| ~ p2(X19,X17)
| ~ p4(X20,X15)
| ~ p5(X20,X18,X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_14) ).
tff(47,plain,
! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) )
| ~ p4(c7,c7)
| ~ p5(c7,c9,f3(c9))
| p5(c7,c9,f3(c8))
| ~ p2(f3(c9),f3(c8))
| ~ p2(c9,c9) )
<=> ( ~ ! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) )
| ~ p4(c7,c7)
| ~ p5(c7,c9,f3(c9))
| p5(c7,c9,f3(c8))
| ~ p2(f3(c9),f3(c8))
| ~ p2(c9,c9) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( ~ p5(c7,c9,f3(c9))
| ~ p4(c7,c7)
| ~ p2(f3(c9),f3(c8))
| ~ p2(c9,c9)
| p5(c7,c9,f3(c8)) )
<=> ( ~ p4(c7,c7)
| ~ p5(c7,c9,f3(c9))
| p5(c7,c9,f3(c8))
| ~ p2(f3(c9),f3(c8))
| ~ p2(c9,c9) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( ~ ! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) )
| ~ p5(c7,c9,f3(c9))
| ~ p4(c7,c7)
| ~ p2(f3(c9),f3(c8))
| ~ p2(c9,c9)
| p5(c7,c9,f3(c8)) )
<=> ( ~ ! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) )
| ~ p4(c7,c7)
| ~ p5(c7,c9,f3(c9))
| p5(c7,c9,f3(c8))
| ~ p2(f3(c9),f3(c8))
| ~ p2(c9,c9) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) )
| ~ p5(c7,c9,f3(c9))
| ~ p4(c7,c7)
| ~ p2(f3(c9),f3(c8))
| ~ p2(c9,c9)
| p5(c7,c9,f3(c8)) )
<=> ( ~ ! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) )
| ~ p4(c7,c7)
| ~ p5(c7,c9,f3(c9))
| p5(c7,c9,f3(c8))
| ~ p2(f3(c9),f3(c8))
| ~ p2(c9,c9) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) )
| ~ p5(c7,c9,f3(c9))
| ~ p4(c7,c7)
| ~ p2(f3(c9),f3(c8))
| ~ p2(c9,c9)
| p5(c7,c9,f3(c8)) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [X17: $i,X16: $i,X18: $i,X20: $i,X15: $i,X19: $i] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) )
| ~ p4(c7,c7)
| ~ p5(c7,c9,f3(c9))
| p5(c7,c9,f3(c8))
| ~ p2(f3(c9),f3(c8))
| ~ p2(c9,c9) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
~ p2(f3(c9),f3(c8)),
inference(unit_resolution,[status(thm)],[56,50,40,31,22,20]) ).
tff(58,plain,
^ [X14: $i,X12: $i,X11: $i,X13: $i] :
refl(
( ( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) )
<=> ( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) )
<=> ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) )
<=> ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
^ [X14: $i,X12: $i,X11: $i,X13: $i] :
trans(
monotonicity(
rewrite(
( ( p5(X11,X12,X13)
| ~ p5(X11,X12,X14) )
<=> ( ~ p5(X11,X12,X14)
| p5(X11,X12,X13) ) )),
( ( p5(X11,X12,X13)
| ~ p5(X11,X12,X14)
| ~ p5(X11,X14,X13) )
<=> ( ~ p5(X11,X12,X14)
| p5(X11,X12,X13)
| ~ p5(X11,X14,X13) ) )),
rewrite(
( ( ~ p5(X11,X12,X14)
| p5(X11,X12,X13)
| ~ p5(X11,X14,X13) )
<=> ( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) ) )),
( ( p5(X11,X12,X13)
| ~ p5(X11,X12,X14)
| ~ p5(X11,X14,X13) )
<=> ( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( p5(X11,X12,X13)
| ~ p5(X11,X12,X14)
| ~ p5(X11,X14,X13) )
<=> ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( p5(X11,X12,X13)
| ~ p5(X11,X12,X14)
| ~ p5(X11,X14,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_11) ).
tff(64,plain,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( p5(c7,c10,c8)
<=> p5(c7,c10,c8) ),
inference(rewrite,[status(thm)],]) ).
tff(69,axiom,
p5(c7,c10,c8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_5) ).
tff(70,plain,
p5(c7,c10,c8),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
( ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) )
| ~ p5(c7,c8,f3(c8))
| ~ p5(c7,c10,c8)
| p5(c7,c10,f3(c8)) )
<=> ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) )
| ~ p5(c7,c8,f3(c8))
| ~ p5(c7,c10,c8)
| p5(c7,c10,f3(c8)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) )
| ~ p5(c7,c8,f3(c8))
| ~ p5(c7,c10,c8)
| p5(c7,c10,f3(c8)) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) )
| ~ p5(c7,c8,f3(c8))
| ~ p5(c7,c10,c8)
| p5(c7,c10,f3(c8)) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
p5(c7,c10,f3(c8)),
inference(unit_resolution,[status(thm)],[73,70,67,9]) ).
tff(75,plain,
( p5(c7,c10,c9)
<=> p5(c7,c10,c9) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
p5(c7,c10,c9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_4) ).
tff(77,plain,
p5(c7,c10,c9),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) )
| ~ p5(c7,c9,f3(c9))
| ~ p5(c7,c10,c9)
| p5(c7,c10,f3(c9)) )
<=> ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) )
| ~ p5(c7,c9,f3(c9))
| ~ p5(c7,c10,c9)
| p5(c7,c10,f3(c9)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) )
| ~ p5(c7,c9,f3(c9))
| ~ p5(c7,c10,c9)
| p5(c7,c10,f3(c9)) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) )
| ~ p5(c7,c9,f3(c9))
| ~ p5(c7,c10,c9)
| p5(c7,c10,f3(c9)) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
p5(c7,c10,f3(c9)),
inference(unit_resolution,[status(thm)],[80,77,67,22]) ).
tff(82,plain,
^ [X21: $i] :
refl(
( p6(c7,f3(X21))
<=> p6(c7,f3(X21)) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [X21: $i] : p6(c7,f3(X21))
<=> ! [X21: $i] : p6(c7,f3(X21)) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [X21: $i] : p6(c7,f3(X21))
<=> ! [X21: $i] : p6(c7,f3(X21)) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
! [X21: $i] : p6(c7,f3(X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6_3) ).
tff(86,plain,
! [X21: $i] : p6(c7,f3(X21)),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [X21: $i] : p6(c7,f3(X21)),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [X21: $i] : p6(c7,f3(X21)),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
( ~ ! [X21: $i] : p6(c7,f3(X21))
| p6(c7,f3(c9)) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
p6(c7,f3(c9)),
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
( ~ ! [X21: $i] : p6(c7,f3(X21))
| p6(c7,f3(c8)) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
p6(c7,f3(c8)),
inference(unit_resolution,[status(thm)],[91,88]) ).
tff(93,plain,
^ [X4: $i,X3: $i,X5: $i] :
refl(
( ( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) )
<=> ( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ) )),
inference(bind,[status(th)],]) ).
tff(94,plain,
( ! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) )
<=> ! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) )
<=> ! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
^ [X4: $i,X3: $i,X5: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p2(X3,X4)
| ~ p6(c7,X4) )
<=> ( ~ p6(c7,X4)
| p2(X3,X4) ) )),
( ( p2(X3,X4)
| ~ p6(c7,X4)
| ~ p6(c7,X3) )
<=> ( ~ p6(c7,X4)
| p2(X3,X4)
| ~ p6(c7,X3) ) )),
rewrite(
( ( ~ p6(c7,X4)
| p2(X3,X4)
| ~ p6(c7,X3) )
<=> ( ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ) )),
( ( p2(X3,X4)
| ~ p6(c7,X4)
| ~ p6(c7,X3) )
<=> ( ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ) )),
( ( p2(X3,X4)
| ~ p6(c7,X4)
| ~ p6(c7,X3)
| ~ p5(c7,X5,X4) )
<=> ( ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4)
| ~ p5(c7,X5,X4) ) )),
rewrite(
( ( ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4)
| ~ p5(c7,X5,X4) )
<=> ( ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ) )),
( ( p2(X3,X4)
| ~ p6(c7,X4)
| ~ p6(c7,X3)
| ~ p5(c7,X5,X4) )
<=> ( ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ) )),
( ( p2(X3,X4)
| ~ p6(c7,X4)
| ~ p6(c7,X3)
| ~ p5(c7,X5,X4)
| ~ p5(c7,X5,X3) )
<=> ( ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4)
| ~ p5(c7,X5,X3) ) )),
rewrite(
( ( ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4)
| ~ p5(c7,X5,X3) )
<=> ( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ) )),
( ( p2(X3,X4)
| ~ p6(c7,X4)
| ~ p6(c7,X3)
| ~ p5(c7,X5,X4)
| ~ p5(c7,X5,X3) )
<=> ( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [X4: $i,X3: $i,X5: $i] :
( p2(X3,X4)
| ~ p6(c7,X4)
| ~ p6(c7,X3)
| ~ p5(c7,X5,X4)
| ~ p5(c7,X5,X3) )
<=> ! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,axiom,
! [X4: $i,X3: $i,X5: $i] :
( p2(X3,X4)
| ~ p6(c7,X4)
| ~ p6(c7,X3)
| ~ p5(c7,X5,X4)
| ~ p5(c7,X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_13) ).
tff(99,plain,
! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ),
inference(modus_ponens,[status(thm)],[101,94]) ).
tff(103,plain,
( ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) )
| ~ p5(c7,c10,f3(c9))
| p2(f3(c9),f3(c8))
| ~ p5(c7,c10,f3(c8))
| ~ p6(c7,f3(c9))
| ~ p6(c7,f3(c8)) )
<=> ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) )
| ~ p5(c7,c10,f3(c9))
| p2(f3(c9),f3(c8))
| ~ p5(c7,c10,f3(c8))
| ~ p6(c7,f3(c9))
| ~ p6(c7,f3(c8)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( ~ p5(c7,c10,f3(c9))
| ~ p5(c7,c10,f3(c8))
| ~ p6(c7,f3(c9))
| ~ p6(c7,f3(c8))
| p2(f3(c9),f3(c8)) )
<=> ( ~ p5(c7,c10,f3(c9))
| p2(f3(c9),f3(c8))
| ~ p5(c7,c10,f3(c8))
| ~ p6(c7,f3(c9))
| ~ p6(c7,f3(c8)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) )
| ~ p5(c7,c10,f3(c9))
| ~ p5(c7,c10,f3(c8))
| ~ p6(c7,f3(c9))
| ~ p6(c7,f3(c8))
| p2(f3(c9),f3(c8)) )
<=> ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) )
| ~ p5(c7,c10,f3(c9))
| p2(f3(c9),f3(c8))
| ~ p5(c7,c10,f3(c8))
| ~ p6(c7,f3(c9))
| ~ p6(c7,f3(c8)) ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) )
| ~ p5(c7,c10,f3(c9))
| ~ p5(c7,c10,f3(c8))
| ~ p6(c7,f3(c9))
| ~ p6(c7,f3(c8))
| p2(f3(c9),f3(c8)) )
<=> ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) )
| ~ p5(c7,c10,f3(c9))
| p2(f3(c9),f3(c8))
| ~ p5(c7,c10,f3(c8))
| ~ p6(c7,f3(c9))
| ~ p6(c7,f3(c8)) ) ),
inference(transitivity,[status(thm)],[105,103]) ).
tff(107,plain,
( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) )
| ~ p5(c7,c10,f3(c9))
| ~ p5(c7,c10,f3(c8))
| ~ p6(c7,f3(c9))
| ~ p6(c7,f3(c8))
| p2(f3(c9),f3(c8)) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) )
| ~ p5(c7,c10,f3(c9))
| p2(f3(c9),f3(c8))
| ~ p5(c7,c10,f3(c8))
| ~ p6(c7,f3(c9))
| ~ p6(c7,f3(c8)) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
$false,
inference(unit_resolution,[status(thm)],[108,102,92,90,81,74,57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN558-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 05:44:13 EDT 2022
% 0.12/0.33 % 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.
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------