TSTP Solution File: SYN587-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN587-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 23:56:32 EDT 2022
% Result : Unsatisfiable 9.59s 6.33s
% Output : Proof 9.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 47
% Syntax : Number of formulae : 85 ( 23 unt; 15 typ; 0 def)
% Number of atoms : 423 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 606 ( 284 ~; 280 |; 0 &)
% ( 42 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 31 ( 31 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 9 >; 5 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 227 ( 204 !; 0 ?; 227 :)
% Comments :
%------------------------------------------------------------------------------
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(c20_type,type,
c20: $i ).
tff(f4_type,type,
f4: ( $i * $i ) > $i ).
tff(c21_type,type,
c21: $i ).
tff(f6_type,type,
f6: ( $i * $i ) > $i ).
tff(c18_type,type,
c18: $i ).
tff(f7_type,type,
f7: $i > $i ).
tff(f8_type,type,
f8: $i > $i ).
tff(f9_type,type,
f9: $i > $i ).
tff(c17_type,type,
c17: $i ).
tff(f10_type,type,
f10: $i > $i ).
tff(c16_type,type,
c16: $i ).
tff(c19_type,type,
c19: $i ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(p15_type,type,
p15: ( $i * $i ) > $o ).
tff(1,plain,
^ [X13: $i] :
refl(
( p2(X13,X13)
<=> p2(X13,X13) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X13: $i] : p2(X13,X13)
<=> ! [X13: $i] : p2(X13,X13) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X13: $i] : p2(X13,X13)
<=> ! [X13: $i] : p2(X13,X13) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X13: $i] : p2(X13,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_4) ).
tff(5,plain,
! [X13: $i] : p2(X13,X13),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X13: $i] : p2(X13,X13),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X13: $i] : p2(X13,X13),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X13: $i] : p2(X13,X13)
| p2(c20,c20) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p2(c20,c20),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [X13: $i] : p2(X13,X13)
| p2(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f6(f10(c16),f6(f7(f8(f9(c17))),c18))) ),
inference(quant_inst,[status(thm)],]) ).
tff(11,plain,
p2(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f6(f10(c16),f6(f7(f8(f9(c17))),c18))),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
^ [X17: $i,X16: $i,X18: $i,X19: $i] :
refl(
( ( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) )
<=> ( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [X17: $i,X16: $i,X18: $i,X19: $i] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) )
<=> ! [X17: $i,X16: $i,X18: $i,X19: $i] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [X17: $i,X16: $i,X18: $i,X19: $i] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) )
<=> ! [X17: $i,X16: $i,X18: $i,X19: $i] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
^ [X17: $i,X16: $i,X18: $i,X19: $i] :
trans(
monotonicity(
rewrite(
( ( p2(f4(X16,X17),f4(X18,X19))
| ~ p2(X16,X18) )
<=> ( ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ) )),
( ( p2(f4(X16,X17),f4(X18,X19))
| ~ p2(X16,X18)
| ~ p3(X17,X19) )
<=> ( ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19))
| ~ p3(X17,X19) ) )),
rewrite(
( ( ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19))
| ~ p3(X17,X19) )
<=> ( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ) )),
( ( p2(f4(X16,X17),f4(X18,X19))
| ~ p2(X16,X18)
| ~ p3(X17,X19) )
<=> ( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X17: $i,X16: $i,X18: $i,X19: $i] :
( p2(f4(X16,X17),f4(X18,X19))
| ~ p2(X16,X18)
| ~ p3(X17,X19) )
<=> ! [X17: $i,X16: $i,X18: $i,X19: $i] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,axiom,
! [X17: $i,X16: $i,X18: $i,X19: $i] :
( p2(f4(X16,X17),f4(X18,X19))
| ~ p2(X16,X18)
| ~ p3(X17,X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_20) ).
tff(18,plain,
! [X17: $i,X16: $i,X18: $i,X19: $i] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [X17: $i,X16: $i,X18: $i,X19: $i] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
! [X17: $i,X16: $i,X18: $i,X19: $i] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [X17: $i,X16: $i,X18: $i,X19: $i] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ),
inference(modus_ponens,[status(thm)],[20,13]) ).
tff(22,plain,
( p3(c21,c19)
<=> p3(c21,c19) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
p3(c21,c19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_5) ).
tff(24,plain,
p3(c21,c19),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( ( ~ ! [X17: $i,X16: $i,X18: $i,X19: $i] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) )
| ~ p3(c21,c19)
| ~ p2(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f6(f10(c16),f6(f7(f8(f9(c17))),c18)))
| p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19)) )
<=> ( ~ ! [X17: $i,X16: $i,X18: $i,X19: $i] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) )
| ~ p3(c21,c19)
| ~ p2(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f6(f10(c16),f6(f7(f8(f9(c17))),c18)))
| p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [X17: $i,X16: $i,X18: $i,X19: $i] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) )
| ~ p3(c21,c19)
| ~ p2(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f6(f10(c16),f6(f7(f8(f9(c17))),c18)))
| p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19)) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [X17: $i,X16: $i,X18: $i,X19: $i] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) )
| ~ p3(c21,c19)
| ~ p2(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f6(f10(c16),f6(f7(f8(f9(c17))),c18)))
| p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19)),
inference(unit_resolution,[status(thm)],[27,24,21,11]) ).
tff(29,plain,
( ~ ! [X13: $i] : p2(X13,X13)
| p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21)) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21)),
inference(unit_resolution,[status(thm)],[29,7]) ).
tff(31,plain,
^ [X14: $i,X13: $i,X15: $i] :
refl(
( ( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) )
<=> ( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) )
<=> ! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) )
<=> ! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
^ [X14: $i,X13: $i,X15: $i] :
trans(
monotonicity(
rewrite(
( ( p2(X14,X15)
| ~ p2(X13,X14) )
<=> ( ~ p2(X13,X14)
| p2(X14,X15) ) )),
( ( p2(X14,X15)
| ~ p2(X13,X14)
| ~ p2(X13,X15) )
<=> ( ~ p2(X13,X14)
| p2(X14,X15)
| ~ p2(X13,X15) ) )),
rewrite(
( ( ~ p2(X13,X14)
| p2(X14,X15)
| ~ p2(X13,X15) )
<=> ( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) ) )),
( ( p2(X14,X15)
| ~ p2(X13,X14)
| ~ p2(X13,X15) )
<=> ( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [X14: $i,X13: $i,X15: $i] :
( p2(X14,X15)
| ~ p2(X13,X14)
| ~ p2(X13,X15) )
<=> ! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [X14: $i,X13: $i,X15: $i] :
( p2(X14,X15)
| ~ p2(X13,X14)
| ~ p2(X13,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_16) ).
tff(37,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) )
| p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21)) )
<=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) )
| p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ( ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19))
| p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21)) )
<=> ( p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) )
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19))
| p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21)) )
<=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) )
| p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21)) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) )
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19))
| p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21)) )
<=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) )
| p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21)) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) )
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19))
| p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21)) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) )
| p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19))
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21)) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21)),
inference(unit_resolution,[status(thm)],[46,40,30,28]) ).
tff(48,plain,
( ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
<=> ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p15_19) ).
tff(50,plain,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
<=> p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15_18) ).
tff(53,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
^ [X9: $i,X12: $i,X11: $i,X10: $i] :
refl(
( ( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) )
<=> ( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) )
<=> ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) )
<=> ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
^ [X9: $i,X12: $i,X11: $i,X10: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p15(X9,X10)
| ~ p2(X11,X9) )
<=> ( ~ p2(X11,X9)
| p15(X9,X10) ) )),
( ( p15(X9,X10)
| ~ p2(X11,X9)
| ~ p2(X12,X10) )
<=> ( ~ p2(X11,X9)
| p15(X9,X10)
| ~ p2(X12,X10) ) )),
rewrite(
( ( ~ p2(X11,X9)
| p15(X9,X10)
| ~ p2(X12,X10) )
<=> ( ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ) )),
( ( p15(X9,X10)
| ~ p2(X11,X9)
| ~ p2(X12,X10) )
<=> ( ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ) )),
( ( p15(X9,X10)
| ~ p2(X11,X9)
| ~ p2(X12,X10)
| ~ p15(X11,X12) )
<=> ( ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10)
| ~ p15(X11,X12) ) )),
rewrite(
( ( ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10)
| ~ p15(X11,X12) )
<=> ( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ) )),
( ( p15(X9,X10)
| ~ p2(X11,X9)
| ~ p2(X12,X10)
| ~ p15(X11,X12) )
<=> ( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( p15(X9,X10)
| ~ p2(X11,X9)
| ~ p2(X12,X10)
| ~ p15(X11,X12) )
<=> ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,axiom,
! [X9: $i,X12: $i,X11: $i,X10: $i] :
( p15(X9,X10)
| ~ p2(X11,X9)
| ~ p2(X12,X10)
| ~ p15(X11,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15_17) ).
tff(60,plain,
! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ),
inference(modus_ponens,[status(thm)],[62,55]) ).
tff(64,plain,
( ( ~ ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) )
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(c20,c20) )
<=> ( ~ ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) )
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(c20,c20) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ( ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
| ~ p2(c20,c20)
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20) )
<=> ( p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(c20,c20) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ( ~ ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) )
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
| ~ p2(c20,c20)
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20) )
<=> ( ~ ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) )
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(c20,c20) ) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ( ~ ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) )
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
| ~ p2(c20,c20)
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20) )
<=> ( ~ ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) )
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(c20,c20) ) ),
inference(transitivity,[status(thm)],[66,64]) ).
tff(68,plain,
( ~ ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) )
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
| ~ p2(c20,c20)
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) )
| p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
| ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
| ~ p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21))
| ~ p2(c20,c20) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
$false,
inference(unit_resolution,[status(thm)],[69,63,53,50,47,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN587-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n013.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 05:50:02 EDT 2022
% 0.13/0.34 % 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.
% 9.59/6.33 % SZS status Unsatisfiable
% 9.59/6.33 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------