TSTP Solution File: SYN584-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN584-1 : 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 23:56:31 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 45
% Syntax : Number of formulae : 78 ( 24 unt; 17 typ; 0 def)
% Number of atoms : 340 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 478 ( 223 ~; 219 |; 0 &)
% ( 36 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 11 >; 8 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 167 ( 151 !; 0 ?; 167 :)
% Comments :
%------------------------------------------------------------------------------
tff(p12_type,type,
p12: ( $i * $i ) > $o ).
tff(f13_type,type,
f13: ( $i * $i ) > $i ).
tff(f14_type,type,
f14: ( $i * $i ) > $i ).
tff(c17_type,type,
c17: $i ).
tff(f7_type,type,
f7: ( $i * $i ) > $i ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(f9_type,type,
f9: ( $i * $i ) > $i ).
tff(f10_type,type,
f10: $i > $i ).
tff(f11_type,type,
f11: $i > $i ).
tff(c20_type,type,
c20: $i ).
tff(c21_type,type,
c21: $i ).
tff(c19_type,type,
c19: $i ).
tff(c18_type,type,
c18: $i ).
tff(c22_type,type,
c22: $i ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(f4_type,type,
f4: $i > $i ).
tff(p15_type,type,
p15: ( $i * $i ) > $o ).
tff(1,plain,
^ [X0: $i] :
refl(
( p12(X0,X0)
<=> p12(X0,X0) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X0: $i] : p12(X0,X0)
<=> ! [X0: $i] : p12(X0,X0) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X0: $i] : p12(X0,X0)
<=> ! [X0: $i] : p12(X0,X0) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X0: $i] : p12(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_1) ).
tff(5,plain,
! [X0: $i] : p12(X0,X0),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X0: $i] : p12(X0,X0),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X0: $i] : p12(X0,X0),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X0: $i] : p12(X0,X0)
| p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22)
<=> p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_23) ).
tff(12,plain,
p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [X0: $i,X2: $i,X1: $i] :
refl(
( ( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) )
<=> ( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
^ [X0: $i,X2: $i,X1: $i] :
trans(
monotonicity(
rewrite(
( ( p12(X1,X2)
| ~ p12(X0,X1) )
<=> ( ~ p12(X0,X1)
| p12(X1,X2) ) )),
( ( p12(X1,X2)
| ~ p12(X0,X1)
| ~ p12(X0,X2) )
<=> ( ~ p12(X0,X1)
| p12(X1,X2)
| ~ p12(X0,X2) ) )),
rewrite(
( ( ~ p12(X0,X1)
| p12(X1,X2)
| ~ p12(X0,X2) )
<=> ( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) ) )),
( ( p12(X1,X2)
| ~ p12(X0,X1)
| ~ p12(X0,X2) )
<=> ( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( p12(X1,X2)
| ~ p12(X0,X1)
| ~ p12(X0,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [X0: $i,X2: $i,X1: $i] :
( p12(X1,X2)
| ~ p12(X0,X1)
| ~ p12(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_9) ).
tff(19,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) )
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22)
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)))
| p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) )
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22)
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)))
| p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)))
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22)
| p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) )
<=> ( ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22)
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)))
| p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) )
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)))
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22)
| p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) )
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22)
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)))
| p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) )
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)))
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22)
| p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) )
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22)
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)))
| p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) )
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)))
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22)
| p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) )
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22)
| ~ p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)))
| p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))),
inference(unit_resolution,[status(thm)],[28,22,12,9]) ).
tff(30,plain,
^ [X26: $i] :
refl(
( p3(X26,X26)
<=> p3(X26,X26) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X26: $i] : p3(X26,X26)
<=> ! [X26: $i] : p3(X26,X26) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X26: $i] : p3(X26,X26)
<=> ! [X26: $i] : p3(X26,X26) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [X26: $i] : p3(X26,X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_4) ).
tff(34,plain,
! [X26: $i] : p3(X26,X26),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X26: $i] : p3(X26,X26),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X26: $i] : p3(X26,X26),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [X26: $i] : p3(X26,X26)
| p3(f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
p3(f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
( ~ p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
<=> ~ p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
~ p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p15_25) ).
tff(41,plain,
~ p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
<=> p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_21) ).
tff(44,plain,
p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
^ [X14: $i,X12: $i,X11: $i,X13: $i] :
refl(
( ( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) )
<=> ( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) )
<=> ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) )
<=> ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
^ [X14: $i,X12: $i,X11: $i,X13: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p15(X11,X12)
| ~ p15(X13,X14) )
<=> ( ~ p15(X13,X14)
| p15(X11,X12) ) )),
( ( p15(X11,X12)
| ~ p15(X13,X14)
| ~ p3(X14,X12) )
<=> ( ~ p15(X13,X14)
| p15(X11,X12)
| ~ p3(X14,X12) ) )),
rewrite(
( ( ~ p15(X13,X14)
| p15(X11,X12)
| ~ p3(X14,X12) )
<=> ( ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ) )),
( ( p15(X11,X12)
| ~ p15(X13,X14)
| ~ p3(X14,X12) )
<=> ( ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ) )),
( ( p15(X11,X12)
| ~ p15(X13,X14)
| ~ p3(X14,X12)
| ~ p12(X13,X11) )
<=> ( ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12)
| ~ p12(X13,X11) ) )),
rewrite(
( ( ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12)
| ~ p12(X13,X11) )
<=> ( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ) )),
( ( p15(X11,X12)
| ~ p15(X13,X14)
| ~ p3(X14,X12)
| ~ p12(X13,X11) )
<=> ( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( p15(X11,X12)
| ~ p15(X13,X14)
| ~ p3(X14,X12)
| ~ p12(X13,X11) )
<=> ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,axiom,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( p15(X11,X12)
| ~ p15(X13,X14)
| ~ p3(X14,X12)
| ~ p12(X13,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_15) ).
tff(51,plain,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ),
inference(modus_ponens,[status(thm)],[53,46]) ).
tff(55,plain,
( ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) )
| p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p3(f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) )
<=> ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) )
| p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p3(f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ( ~ p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)))
| ~ p3(f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))) )
<=> ( p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p3(f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) )
| ~ p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)))
| ~ p3(f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))) )
<=> ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) )
| p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p3(f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) ) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) )
| ~ p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)))
| ~ p3(f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))) )
<=> ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) )
| p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p3(f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) ) ),
inference(transitivity,[status(thm)],[57,55]) ).
tff(59,plain,
( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) )
| ~ p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)))
| ~ p3(f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) )
| p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p3(f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
$false,
inference(unit_resolution,[status(thm)],[60,54,44,41,38,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN584-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % 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 05:56:46 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.35 Usage: tptp [options] [-file:]file
% 0.19/0.35 -h, -? prints this message.
% 0.19/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.35 -m, -model generate model.
% 0.19/0.35 -p, -proof generate proof.
% 0.19/0.35 -c, -core generate unsat core of named formulas.
% 0.19/0.35 -st, -statistics display statistics.
% 0.19/0.35 -t:timeout set timeout (in second).
% 0.19/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.35 -<param>:<value> configuration parameter and value.
% 0.19/0.35 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------