TSTP Solution File: SYN595-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN595-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 23:56:34 EDT 2022
% Result : Unsatisfiable 0.19s 0.51s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 63
% Syntax : Number of formulae : 116 ( 32 unt; 20 typ; 0 def)
% Number of atoms : 549 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 824 ( 405 ~; 364 |; 0 &)
% ( 55 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of FOOLs : 34 ( 34 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 14 >; 9 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 264 ( 238 !; 0 ?; 264 :)
% Comments :
%------------------------------------------------------------------------------
tff(p7_type,type,
p7: ( $i * $i ) > $o ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(f9_type,type,
f9: ( $i * $i ) > $i ).
tff(f10_type,type,
f10: ( $i * $i ) > $i ).
tff(c22_type,type,
c22: $i ).
tff(f11_type,type,
f11: $i > $i ).
tff(f3_type,type,
f3: $i > $i ).
tff(f4_type,type,
f4: $i > $i ).
tff(f5_type,type,
f5: $i > $i ).
tff(c17_type,type,
c17: $i ).
tff(f6_type,type,
f6: ( $i * $i ) > $i ).
tff(f13_type,type,
f13: ( $i * $i ) > $i ).
tff(c16_type,type,
c16: $i ).
tff(c18_type,type,
c18: $i ).
tff(f12_type,type,
f12: $i > $i ).
tff(p15_type,type,
p15: ( $i * $i ) > $o ).
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(c19_type,type,
c19: $i ).
tff(p14_type,type,
p14: ( $i * $i ) > $o ).
tff(c21_type,type,
c21: $i ).
tff(1,plain,
^ [X10: $i] :
refl(
( p2(X10,X10)
<=> p2(X10,X10) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X10: $i] : p2(X10,X10)
<=> ! [X10: $i] : p2(X10,X10) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X10: $i] : p2(X10,X10)
<=> ! [X10: $i] : p2(X10,X10) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X10: $i] : p2(X10,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_1) ).
tff(5,plain,
! [X10: $i] : p2(X10,X10),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X10: $i] : p2(X10,X10),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X10: $i] : p2(X10,X10),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X10: $i] : p2(X10,X10)
| p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( p14(c19,f6(f3(f4(f5(c17))),c16))
<=> p14(c19,f6(f3(f4(f5(c17))),c16)) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
p14(c19,f6(f3(f4(f5(c17))),c16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14_8) ).
tff(12,plain,
p14(c19,f6(f3(f4(f5(c17))),c16)),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [X4: $i,X5: $i] :
refl(
( ( ~ p14(X4,X5)
| p15(X4,X5) )
<=> ( ~ p14(X4,X5)
| p15(X4,X5) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X4: $i,X5: $i] :
( ~ p14(X4,X5)
| p15(X4,X5) )
<=> ! [X4: $i,X5: $i] :
( ~ p14(X4,X5)
| p15(X4,X5) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [X4: $i,X5: $i] :
( ~ p14(X4,X5)
| p15(X4,X5) )
<=> ! [X4: $i,X5: $i] :
( ~ p14(X4,X5)
| p15(X4,X5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
^ [X4: $i,X5: $i] :
rewrite(
( ( p15(X4,X5)
| ~ p14(X4,X5) )
<=> ( ~ p14(X4,X5)
| p15(X4,X5) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [X4: $i,X5: $i] :
( p15(X4,X5)
| ~ p14(X4,X5) )
<=> ! [X4: $i,X5: $i] :
( ~ p14(X4,X5)
| p15(X4,X5) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [X4: $i,X5: $i] :
( p15(X4,X5)
| ~ p14(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_6) ).
tff(19,plain,
! [X4: $i,X5: $i] :
( ~ p14(X4,X5)
| p15(X4,X5) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X4: $i,X5: $i] :
( ~ p14(X4,X5)
| p15(X4,X5) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [X4: $i,X5: $i] :
( ~ p14(X4,X5)
| p15(X4,X5) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [X4: $i,X5: $i] :
( ~ p14(X4,X5)
| p15(X4,X5) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [X4: $i,X5: $i] :
( ~ p14(X4,X5)
| p15(X4,X5) )
| ~ p14(c19,f6(f3(f4(f5(c17))),c16))
| p15(c19,f6(f3(f4(f5(c17))),c16)) )
<=> ( ~ ! [X4: $i,X5: $i] :
( ~ p14(X4,X5)
| p15(X4,X5) )
| ~ p14(c19,f6(f3(f4(f5(c17))),c16))
| p15(c19,f6(f3(f4(f5(c17))),c16)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [X4: $i,X5: $i] :
( ~ p14(X4,X5)
| p15(X4,X5) )
| ~ p14(c19,f6(f3(f4(f5(c17))),c16))
| p15(c19,f6(f3(f4(f5(c17))),c16)) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [X4: $i,X5: $i] :
( ~ p14(X4,X5)
| p15(X4,X5) )
| ~ p14(c19,f6(f3(f4(f5(c17))),c16))
| p15(c19,f6(f3(f4(f5(c17))),c16)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
p15(c19,f6(f3(f4(f5(c17))),c16)),
inference(unit_resolution,[status(thm)],[25,22,12]) ).
tff(27,plain,
^ [X9: $i,X6: $i,X7: $i,X8: $i] :
refl(
( ( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) )
<=> ( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) )
<=> ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) )
<=> ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [X9: $i,X6: $i,X7: $i,X8: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p15(X6,X7)
| ~ p2(X8,X6) )
<=> ( ~ p2(X8,X6)
| p15(X6,X7) ) )),
( ( p15(X6,X7)
| ~ p2(X8,X6)
| ~ p2(X9,X7) )
<=> ( ~ p2(X8,X6)
| p15(X6,X7)
| ~ p2(X9,X7) ) )),
rewrite(
( ( ~ p2(X8,X6)
| p15(X6,X7)
| ~ p2(X9,X7) )
<=> ( ~ p2(X8,X6)
| ~ p2(X9,X7)
| p15(X6,X7) ) )),
( ( p15(X6,X7)
| ~ p2(X8,X6)
| ~ p2(X9,X7) )
<=> ( ~ p2(X8,X6)
| ~ p2(X9,X7)
| p15(X6,X7) ) )),
( ( p15(X6,X7)
| ~ p2(X8,X6)
| ~ p2(X9,X7)
| ~ p15(X8,X9) )
<=> ( ~ p2(X8,X6)
| ~ p2(X9,X7)
| p15(X6,X7)
| ~ p15(X8,X9) ) )),
rewrite(
( ( ~ p2(X8,X6)
| ~ p2(X9,X7)
| p15(X6,X7)
| ~ p15(X8,X9) )
<=> ( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) ) )),
( ( p15(X6,X7)
| ~ p2(X8,X6)
| ~ p2(X9,X7)
| ~ p15(X8,X9) )
<=> ( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( p15(X6,X7)
| ~ p2(X8,X6)
| ~ p2(X9,X7)
| ~ p15(X8,X9) )
<=> ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [X9: $i,X6: $i,X7: $i,X8: $i] :
( p15(X6,X7)
| ~ p2(X8,X6)
| ~ p2(X9,X7)
| ~ p15(X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_19) ).
tff(33,plain,
! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
<=> p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_17) ).
tff(39,plain,
p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) )
| ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
| ~ p15(c19,f6(f3(f4(f5(c17))),c16))
| p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
| ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)) )
<=> ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) )
| ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
| ~ p15(c19,f6(f3(f4(f5(c17))),c16))
| p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
| ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
| ~ p15(c19,f6(f3(f4(f5(c17))),c16))
| ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16))
| p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) )
<=> ( ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
| ~ p15(c19,f6(f3(f4(f5(c17))),c16))
| p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
| ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) )
| ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
| ~ p15(c19,f6(f3(f4(f5(c17))),c16))
| ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16))
| p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) )
<=> ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) )
| ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
| ~ p15(c19,f6(f3(f4(f5(c17))),c16))
| p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
| ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) )
| ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
| ~ p15(c19,f6(f3(f4(f5(c17))),c16))
| ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16))
| p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) )
<=> ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) )
| ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
| ~ p15(c19,f6(f3(f4(f5(c17))),c16))
| p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
| ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) )
| ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
| ~ p15(c19,f6(f3(f4(f5(c17))),c16))
| ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16))
| p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p2(X8,X6)
| ~ p15(X8,X9)
| ~ p2(X9,X7)
| p15(X6,X7) )
| ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
| ~ p15(c19,f6(f3(f4(f5(c17))),c16))
| p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
| ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)),
inference(unit_resolution,[status(thm)],[45,39,36,26,9]) ).
tff(47,plain,
^ [X12: $i,X11: $i,X10: $i] :
refl(
( ( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) )
<=> ( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) )
<=> ! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) )
<=> ! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
^ [X12: $i,X11: $i,X10: $i] :
trans(
monotonicity(
rewrite(
( ( p2(X11,X12)
| ~ p2(X10,X11) )
<=> ( ~ p2(X10,X11)
| p2(X11,X12) ) )),
( ( p2(X11,X12)
| ~ p2(X10,X11)
| ~ p2(X10,X12) )
<=> ( ~ p2(X10,X11)
| p2(X11,X12)
| ~ p2(X10,X12) ) )),
rewrite(
( ( ~ p2(X10,X11)
| p2(X11,X12)
| ~ p2(X10,X12) )
<=> ( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) ) )),
( ( p2(X11,X12)
| ~ p2(X10,X11)
| ~ p2(X10,X12) )
<=> ( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [X12: $i,X11: $i,X10: $i] :
( p2(X11,X12)
| ~ p2(X10,X11)
| ~ p2(X10,X12) )
<=> ! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [X12: $i,X11: $i,X10: $i] :
( p2(X11,X12)
| ~ p2(X10,X11)
| ~ p2(X10,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_16) ).
tff(53,plain,
! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
( p2(c21,f3(c17))
<=> p2(c21,f3(c17)) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
p2(c21,f3(c17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_3) ).
tff(59,plain,
p2(c21,f3(c17)),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( ( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) )
| ~ p2(c21,f3(c17))
| p2(f3(c17),f3(c17)) )
<=> ( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) )
| ~ p2(c21,f3(c17))
| p2(f3(c17),f3(c17)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ( ~ p2(c21,f3(c17))
| ~ p2(c21,f3(c17))
| p2(f3(c17),f3(c17)) )
<=> ( ~ p2(c21,f3(c17))
| p2(f3(c17),f3(c17)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) )
| ~ p2(c21,f3(c17))
| ~ p2(c21,f3(c17))
| p2(f3(c17),f3(c17)) )
<=> ( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) )
| ~ p2(c21,f3(c17))
| p2(f3(c17),f3(c17)) ) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) )
| ~ p2(c21,f3(c17))
| ~ p2(c21,f3(c17))
| p2(f3(c17),f3(c17)) )
<=> ( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) )
| ~ p2(c21,f3(c17))
| p2(f3(c17),f3(c17)) ) ),
inference(transitivity,[status(thm)],[62,60]) ).
tff(64,plain,
( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) )
| ~ p2(c21,f3(c17))
| ~ p2(c21,f3(c17))
| p2(f3(c17),f3(c17)) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p2(X10,X11)
| ~ p2(X10,X12)
| p2(X11,X12) )
| ~ p2(c21,f3(c17))
| p2(f3(c17),f3(c17)) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
p2(f3(c17),f3(c17)),
inference(unit_resolution,[status(thm)],[65,59,56]) ).
tff(67,plain,
^ [X47: $i,X46: $i,X48: $i] :
refl(
( ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) )
<=> ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) )
<=> ! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) )
<=> ! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
^ [X47: $i,X46: $i,X48: $i] :
trans(
monotonicity(
rewrite(
( ( ~ p2(X48,f3(c17))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16)) )
<=> ( ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) ) )),
( ( ~ p2(X48,f3(c17))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22))))) )
<=> ( ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17))
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22))))) ) )),
rewrite(
( ( ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17))
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22))))) )
<=> ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) ) )),
( ( ~ p2(X48,f3(c17))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22))))) )
<=> ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [X47: $i,X46: $i,X48: $i] :
( ~ p2(X48,f3(c17))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22))))) )
<=> ! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,axiom,
! [X47: $i,X46: $i,X48: $i] :
( ~ p2(X48,f3(c17))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p2_26) ).
tff(73,plain,
! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) ),
inference(modus_ponens,[status(thm)],[75,68]) ).
tff(77,plain,
( p14(c18,f3(f4(f5(c17))))
<=> p14(c18,f3(f4(f5(c17)))) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
p14(c18,f3(f4(f5(c17)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14_5) ).
tff(79,plain,
p14(c18,f3(f4(f5(c17)))),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( ( ~ ! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) )
| ~ p14(c18,f3(f4(f5(c17))))
| ~ p2(f3(c17),f3(c17))
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) )
<=> ( ~ ! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) )
| ~ p14(c18,f3(f4(f5(c17))))
| ~ p2(f3(c17),f3(c17))
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
| ~ p14(c18,f3(f4(f5(c17))))
| ~ p2(f3(c17),f3(c17)) )
<=> ( ~ p14(c18,f3(f4(f5(c17))))
| ~ p2(f3(c17),f3(c17))
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ( ~ ! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) )
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
| ~ p14(c18,f3(f4(f5(c17))))
| ~ p2(f3(c17),f3(c17)) )
<=> ( ~ ! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) )
| ~ p14(c18,f3(f4(f5(c17))))
| ~ p2(f3(c17),f3(c17))
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) ) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( ( ~ ! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) )
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
| ~ p14(c18,f3(f4(f5(c17))))
| ~ p2(f3(c17),f3(c17)) )
<=> ( ~ ! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) )
| ~ p14(c18,f3(f4(f5(c17))))
| ~ p2(f3(c17),f3(c17))
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) ) ),
inference(transitivity,[status(thm)],[82,80]) ).
tff(84,plain,
( ~ ! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) )
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
| ~ p14(c18,f3(f4(f5(c17))))
| ~ p2(f3(c17),f3(c17)) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
( ~ ! [X47: $i,X46: $i,X48: $i] :
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(X47,f6(f3(f4(f5(c17))),c16))
| ~ p14(X46,f3(f4(f5(c17))))
| ~ p2(X48,f3(c17)) )
| ~ p14(c18,f3(f4(f5(c17))))
| ~ p2(f3(c17),f3(c17))
| ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) ),
inference(unit_resolution,[status(thm)],[85,79,76,66]) ).
tff(87,plain,
~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22))))),
inference(unit_resolution,[status(thm)],[86,46]) ).
tff(88,plain,
^ [X27: $i] :
refl(
( p7(X27,X27)
<=> p7(X27,X27) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [X27: $i] : p7(X27,X27)
<=> ! [X27: $i] : p7(X27,X27) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [X27: $i] : p7(X27,X27)
<=> ! [X27: $i] : p7(X27,X27) ),
inference(rewrite,[status(thm)],]) ).
tff(91,axiom,
! [X27: $i] : p7(X27,X27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_2) ).
tff(92,plain,
! [X27: $i] : p7(X27,X27),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [X27: $i] : p7(X27,X27),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [X27: $i] : p7(X27,X27),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
( ~ ! [X27: $i] : p7(X27,X27)
| p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
$false,
inference(unit_resolution,[status(thm)],[95,94,87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN595-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 06:01:16 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.
% 0.19/0.51 % SZS status Unsatisfiable
% 0.19/0.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------