TSTP Solution File: SYN570-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN570-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 23:56:28 EDT 2022
% Result : Unsatisfiable 0.72s 0.70s
% Output : Proof 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 61
% Syntax : Number of formulae : 121 ( 36 unt; 10 typ; 0 def)
% Number of atoms : 542 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 757 ( 354 ~; 350 |; 0 &)
% ( 53 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 28 ( 28 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 284 ( 260 !; 0 ?; 284 :)
% Comments :
%------------------------------------------------------------------------------
tff(p7_type,type,
p7: ( $i * $i ) > $o ).
tff(f8_type,type,
f8: $i > $i ).
tff(c13_type,type,
c13: $i ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(f4_type,type,
f4: $i > $i ).
tff(c12_type,type,
c12: $i ).
tff(c15_type,type,
c15: $i ).
tff(f5_type,type,
f5: $i > $i ).
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(p9_type,type,
p9: ( $i * $i ) > $o ).
tff(1,plain,
^ [X21: $i] :
refl(
( p7(X21,X21)
<=> p7(X21,X21) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X21: $i] : p7(X21,X21)
<=> ! [X21: $i] : p7(X21,X21) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X21: $i] : p7(X21,X21)
<=> ! [X21: $i] : p7(X21,X21) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X21: $i] : p7(X21,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_2) ).
tff(5,plain,
! [X21: $i] : p7(X21,X21),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X21: $i] : p7(X21,X21),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X21: $i] : p7(X21,X21),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X21: $i] : p7(X21,X21)
| p7(f8(c13),f8(c13)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p7(f8(c13),f8(c13)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X17: $i] :
refl(
( p3(f4(f5(X17)),X17)
<=> p3(f4(f5(X17)),X17) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X17: $i] : p3(f4(f5(X17)),X17)
<=> ! [X17: $i] : p3(f4(f5(X17)),X17) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X17: $i] : p3(f4(f5(X17)),X17)
<=> ! [X17: $i] : p3(f4(f5(X17)),X17) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X17: $i] : p3(f4(f5(X17)),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_9) ).
tff(14,plain,
! [X17: $i] : p3(f4(f5(X17)),X17),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X17: $i] : p3(f4(f5(X17)),X17),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X17: $i] : p3(f4(f5(X17)),X17),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X17: $i] : p3(f4(f5(X17)),X17)
| p3(f4(f5(f4(c12))),f4(c12)) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
p3(f4(f5(f4(c12))),f4(c12)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X16: $i,X15: $i] :
refl(
( ( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
<=> ( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
<=> ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
<=> ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [X16: $i,X15: $i] :
rewrite(
( ( p3(f4(X15),f4(X16))
| ~ p2(X15,X16) )
<=> ( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [X16: $i,X15: $i] :
( p3(f4(X15),f4(X16))
| ~ p2(X15,X16) )
<=> ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [X16: $i,X15: $i] :
( p3(f4(X15),f4(X16))
| ~ p2(X15,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_13) ).
tff(25,plain,
! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( p2(c12,f5(c15))
<=> p2(c12,f5(c15)) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
p2(c12,f5(c15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_8) ).
tff(31,plain,
p2(c12,f5(c15)),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(c12,f5(c15))
| p3(f4(c12),f4(f5(c15))) )
<=> ( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(c12,f5(c15))
| p3(f4(c12),f4(f5(c15))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(c12,f5(c15))
| p3(f4(c12),f4(f5(c15))) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(c12,f5(c15))
| p3(f4(c12),f4(f5(c15))) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
p3(f4(c12),f4(f5(c15))),
inference(unit_resolution,[status(thm)],[34,31,28]) ).
tff(36,plain,
^ [X11: $i,X10: $i] :
refl(
( ( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) )
<=> ( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) )
<=> ! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) )
<=> ! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
^ [X11: $i,X10: $i] :
rewrite(
( ( p2(f5(X10),f5(X11))
| ~ p3(X10,X11) )
<=> ( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X11: $i,X10: $i] :
( p2(f5(X10),f5(X11))
| ~ p3(X10,X11) )
<=> ! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X11: $i,X10: $i] :
( p2(f5(X10),f5(X11))
| ~ p3(X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_12) ).
tff(42,plain,
! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) )
| ~ p3(f4(c12),f4(f5(c15)))
| p2(f5(f4(c12)),f5(f4(f5(c15)))) )
<=> ( ~ ! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) )
| ~ p3(f4(c12),f4(f5(c15)))
| p2(f5(f4(c12)),f5(f4(f5(c15)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) )
| ~ p3(f4(c12),f4(f5(c15)))
| p2(f5(f4(c12)),f5(f4(f5(c15)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) )
| ~ p3(f4(c12),f4(f5(c15)))
| p2(f5(f4(c12)),f5(f4(f5(c15)))) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
p2(f5(f4(c12)),f5(f4(f5(c15)))),
inference(unit_resolution,[status(thm)],[48,45,35]) ).
tff(50,plain,
( ( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(f5(f4(c12)),f5(f4(f5(c15))))
| p3(f4(f5(f4(c12))),f4(f5(f4(f5(c15))))) )
<=> ( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(f5(f4(c12)),f5(f4(f5(c15))))
| p3(f4(f5(f4(c12))),f4(f5(f4(f5(c15))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(f5(f4(c12)),f5(f4(f5(c15))))
| p3(f4(f5(f4(c12))),f4(f5(f4(f5(c15))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(f5(f4(c12)),f5(f4(f5(c15))))
| p3(f4(f5(f4(c12))),f4(f5(f4(f5(c15))))) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
p3(f4(f5(f4(c12))),f4(f5(f4(f5(c15))))),
inference(unit_resolution,[status(thm)],[52,28,49]) ).
tff(54,plain,
^ [X14: $i,X12: $i,X13: $i] :
refl(
( ( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
<=> ( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
<=> ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
<=> ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
^ [X14: $i,X12: $i,X13: $i] :
trans(
monotonicity(
rewrite(
( ( p3(X13,X14)
| ~ p3(X12,X13) )
<=> ( ~ p3(X12,X13)
| p3(X13,X14) ) )),
( ( p3(X13,X14)
| ~ p3(X12,X13)
| ~ p3(X12,X14) )
<=> ( ~ p3(X12,X13)
| p3(X13,X14)
| ~ p3(X12,X14) ) )),
rewrite(
( ( ~ p3(X12,X13)
| p3(X13,X14)
| ~ p3(X12,X14) )
<=> ( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) ) )),
( ( p3(X13,X14)
| ~ p3(X12,X13)
| ~ p3(X12,X14) )
<=> ( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [X14: $i,X12: $i,X13: $i] :
( p3(X13,X14)
| ~ p3(X12,X13)
| ~ p3(X12,X14) )
<=> ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,axiom,
! [X14: $i,X12: $i,X13: $i] :
( p3(X13,X14)
| ~ p3(X12,X13)
| ~ p3(X12,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_17) ).
tff(60,plain,
! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) ),
inference(modus_ponens,[status(thm)],[62,55]) ).
tff(64,plain,
( ( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(f4(c12))),f4(c12))
| ~ p3(f4(f5(f4(c12))),f4(f5(f4(f5(c15)))))
| p3(f4(f5(f4(f5(c15)))),f4(c12)) )
<=> ( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(f4(c12))),f4(c12))
| ~ p3(f4(f5(f4(c12))),f4(f5(f4(f5(c15)))))
| p3(f4(f5(f4(f5(c15)))),f4(c12)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(f4(c12))),f4(c12))
| ~ p3(f4(f5(f4(c12))),f4(f5(f4(f5(c15)))))
| p3(f4(f5(f4(f5(c15)))),f4(c12)) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(f4(c12))),f4(c12))
| ~ p3(f4(f5(f4(c12))),f4(f5(f4(f5(c15)))))
| p3(f4(f5(f4(f5(c15)))),f4(c12)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
p3(f4(f5(f4(f5(c15)))),f4(c12)),
inference(unit_resolution,[status(thm)],[66,63,53,18]) ).
tff(68,plain,
( ~ ! [X17: $i] : p3(f4(f5(X17)),X17)
| p3(f4(f5(c15)),c15) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
p3(f4(f5(c15)),c15),
inference(unit_resolution,[status(thm)],[68,16]) ).
tff(70,plain,
( ( ~ ! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) )
| ~ p3(f4(f5(c15)),c15)
| p2(f5(f4(f5(c15))),f5(c15)) )
<=> ( ~ ! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) )
| ~ p3(f4(f5(c15)),c15)
| p2(f5(f4(f5(c15))),f5(c15)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ~ ! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) )
| ~ p3(f4(f5(c15)),c15)
| p2(f5(f4(f5(c15))),f5(c15)) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
( ~ ! [X11: $i,X10: $i] :
( ~ p3(X10,X11)
| p2(f5(X10),f5(X11)) )
| ~ p3(f4(f5(c15)),c15)
| p2(f5(f4(f5(c15))),f5(c15)) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
p2(f5(f4(f5(c15))),f5(c15)),
inference(unit_resolution,[status(thm)],[72,45,69]) ).
tff(74,plain,
( ( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(f5(f4(f5(c15))),f5(c15))
| p3(f4(f5(f4(f5(c15)))),f4(f5(c15))) )
<=> ( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(f5(f4(f5(c15))),f5(c15))
| p3(f4(f5(f4(f5(c15)))),f4(f5(c15))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(f5(f4(f5(c15))),f5(c15))
| p3(f4(f5(f4(f5(c15)))),f4(f5(c15))) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(f5(f4(f5(c15))),f5(c15))
| p3(f4(f5(f4(f5(c15)))),f4(f5(c15))) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
p3(f4(f5(f4(f5(c15)))),f4(f5(c15))),
inference(unit_resolution,[status(thm)],[76,28,73]) ).
tff(78,plain,
( ( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(f4(f5(c15)))),f4(c12))
| ~ p3(f4(f5(f4(f5(c15)))),f4(f5(c15)))
| p3(f4(f5(c15)),f4(c12)) )
<=> ( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(f4(f5(c15)))),f4(c12))
| ~ p3(f4(f5(f4(f5(c15)))),f4(f5(c15)))
| p3(f4(f5(c15)),f4(c12)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(f4(f5(c15)))),f4(c12))
| ~ p3(f4(f5(f4(f5(c15)))),f4(f5(c15)))
| p3(f4(f5(c15)),f4(c12)) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(f4(f5(c15)))),f4(c12))
| ~ p3(f4(f5(f4(f5(c15)))),f4(f5(c15)))
| p3(f4(f5(c15)),f4(c12)) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
p3(f4(f5(c15)),f4(c12)),
inference(unit_resolution,[status(thm)],[80,63,77,67]) ).
tff(82,plain,
( ( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(c15)),c15)
| ~ p3(f4(f5(c15)),f4(c12))
| p3(c15,f4(c12)) )
<=> ( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(c15)),c15)
| ~ p3(f4(f5(c15)),f4(c12))
| p3(c15,f4(c12)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( ~ p3(f4(f5(c15)),f4(c12))
| ~ p3(f4(f5(c15)),c15)
| p3(c15,f4(c12)) )
<=> ( ~ p3(f4(f5(c15)),c15)
| ~ p3(f4(f5(c15)),f4(c12))
| p3(c15,f4(c12)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(c15)),f4(c12))
| ~ p3(f4(f5(c15)),c15)
| p3(c15,f4(c12)) )
<=> ( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(c15)),c15)
| ~ p3(f4(f5(c15)),f4(c12))
| p3(c15,f4(c12)) ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(c15)),f4(c12))
| ~ p3(f4(f5(c15)),c15)
| p3(c15,f4(c12)) )
<=> ( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(c15)),c15)
| ~ p3(f4(f5(c15)),f4(c12))
| p3(c15,f4(c12)) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,plain,
( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(c15)),f4(c12))
| ~ p3(f4(f5(c15)),c15)
| p3(c15,f4(c12)) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
( ~ ! [X14: $i,X12: $i,X13: $i] :
( ~ p3(X12,X14)
| ~ p3(X12,X13)
| p3(X13,X14) )
| ~ p3(f4(f5(c15)),c15)
| ~ p3(f4(f5(c15)),f4(c12))
| p3(c15,f4(c12)) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
p3(c15,f4(c12)),
inference(unit_resolution,[status(thm)],[87,63,69,81]) ).
tff(89,plain,
^ [X27: $i,X29: $i,X28: $i,X26: $i] :
refl(
( ( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) )
<=> ( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) )
<=> ! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) )
<=> ! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [X27: $i,X29: $i,X28: $i,X26: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p9(X26,X27)
| ~ p7(X29,X27) )
<=> ( ~ p7(X29,X27)
| p9(X26,X27) ) )),
( ( p9(X26,X27)
| ~ p7(X29,X27)
| ~ p9(X28,X29) )
<=> ( ~ p7(X29,X27)
| p9(X26,X27)
| ~ p9(X28,X29) ) )),
rewrite(
( ( ~ p7(X29,X27)
| p9(X26,X27)
| ~ p9(X28,X29) )
<=> ( ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) ) )),
( ( p9(X26,X27)
| ~ p7(X29,X27)
| ~ p9(X28,X29) )
<=> ( ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) ) )),
( ( p9(X26,X27)
| ~ p7(X29,X27)
| ~ p9(X28,X29)
| ~ p3(X28,X26) )
<=> ( ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27)
| ~ p3(X28,X26) ) )),
rewrite(
( ( ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27)
| ~ p3(X28,X26) )
<=> ( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) ) )),
( ( p9(X26,X27)
| ~ p7(X29,X27)
| ~ p9(X28,X29)
| ~ p3(X28,X26) )
<=> ( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [X27: $i,X29: $i,X28: $i,X26: $i] :
( p9(X26,X27)
| ~ p7(X29,X27)
| ~ p9(X28,X29)
| ~ p3(X28,X26) )
<=> ! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [X27: $i,X29: $i,X28: $i,X26: $i] :
( p9(X26,X27)
| ~ p7(X29,X27)
| ~ p9(X28,X29)
| ~ p3(X28,X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_19) ).
tff(95,plain,
! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ~ p9(f4(c12),f8(c13))
<=> ~ p9(f4(c12),f8(c13)) ),
inference(rewrite,[status(thm)],]) ).
tff(100,axiom,
~ p9(f4(c12),f8(c13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p9_10) ).
tff(101,plain,
~ p9(f4(c12),f8(c13)),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
( p9(c15,f8(c13))
<=> p9(c15,f8(c13)) ),
inference(rewrite,[status(thm)],]) ).
tff(103,axiom,
p9(c15,f8(c13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_7) ).
tff(104,plain,
p9(c15,f8(c13)),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
( ( ~ ! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) )
| p9(f4(c12),f8(c13))
| ~ p3(c15,f4(c12))
| ~ p9(c15,f8(c13))
| ~ p7(f8(c13),f8(c13)) )
<=> ( ~ ! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) )
| p9(f4(c12),f8(c13))
| ~ p3(c15,f4(c12))
| ~ p9(c15,f8(c13))
| ~ p7(f8(c13),f8(c13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ( ~ p3(c15,f4(c12))
| ~ p9(c15,f8(c13))
| ~ p7(f8(c13),f8(c13))
| p9(f4(c12),f8(c13)) )
<=> ( p9(f4(c12),f8(c13))
| ~ p3(c15,f4(c12))
| ~ p9(c15,f8(c13))
| ~ p7(f8(c13),f8(c13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ( ~ ! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) )
| ~ p3(c15,f4(c12))
| ~ p9(c15,f8(c13))
| ~ p7(f8(c13),f8(c13))
| p9(f4(c12),f8(c13)) )
<=> ( ~ ! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) )
| p9(f4(c12),f8(c13))
| ~ p3(c15,f4(c12))
| ~ p9(c15,f8(c13))
| ~ p7(f8(c13),f8(c13)) ) ),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( ( ~ ! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) )
| ~ p3(c15,f4(c12))
| ~ p9(c15,f8(c13))
| ~ p7(f8(c13),f8(c13))
| p9(f4(c12),f8(c13)) )
<=> ( ~ ! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) )
| p9(f4(c12),f8(c13))
| ~ p3(c15,f4(c12))
| ~ p9(c15,f8(c13))
| ~ p7(f8(c13),f8(c13)) ) ),
inference(transitivity,[status(thm)],[107,105]) ).
tff(109,plain,
( ~ ! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) )
| ~ p3(c15,f4(c12))
| ~ p9(c15,f8(c13))
| ~ p7(f8(c13),f8(c13))
| p9(f4(c12),f8(c13)) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
( ~ ! [X27: $i,X29: $i,X28: $i,X26: $i] :
( ~ p3(X28,X26)
| ~ p9(X28,X29)
| ~ p7(X29,X27)
| p9(X26,X27) )
| p9(f4(c12),f8(c13))
| ~ p3(c15,f4(c12))
| ~ p9(c15,f8(c13))
| ~ p7(f8(c13),f8(c13)) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
$false,
inference(unit_resolution,[status(thm)],[110,104,101,98,88,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN570-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 05:46:53 EDT 2022
% 0.12/0.34 % 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.
% 0.72/0.70 % SZS status Unsatisfiable
% 0.72/0.70 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------