TSTP Solution File: SYN618-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN618-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 23:56:39 EDT 2022
% Result : Unsatisfiable 1.59s 1.29s
% Output : Proof 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 69
% Syntax : Number of formulae : 131 ( 41 unt; 14 typ; 0 def)
% Number of atoms : 623 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 878 ( 412 ~; 408 |; 0 &)
% ( 58 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 40 ( 40 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 289 ( 265 !; 0 ?; 289 :)
% Comments :
%------------------------------------------------------------------------------
tff(p5_type,type,
p5: ( $i * $i ) > $o ).
tff(f6_type,type,
f6: $i > $i ).
tff(f7_type,type,
f7: $i > $i ).
tff(c22_type,type,
c22: $i ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(c20_type,type,
c20: $i ).
tff(c17_type,type,
c17: $i ).
tff(c23_type,type,
c23: $i ).
tff(f3_type,type,
f3: $i > $i ).
tff(c16_type,type,
c16: $i ).
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(p13_type,type,
p13: ( $i * $i ) > $o ).
tff(c21_type,type,
c21: $i ).
tff(c19_type,type,
c19: $i ).
tff(1,plain,
^ [X24: $i] :
refl(
( p2(X24,X24)
<=> p2(X24,X24) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X24: $i] : p2(X24,X24)
<=> ! [X24: $i] : p2(X24,X24) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X24: $i] : p2(X24,X24)
<=> ! [X24: $i] : p2(X24,X24) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X24: $i] : p2(X24,X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_5) ).
tff(5,plain,
! [X24: $i] : p2(X24,X24),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X24: $i] : p2(X24,X24),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X24: $i] : p2(X24,X24),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X24: $i] : p2(X24,X24)
| p2(c17,c17) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p2(c17,c17),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X25: $i,X24: $i,X26: $i] :
refl(
( ( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) )
<=> ( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X25: $i,X24: $i,X26: $i] :
( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) )
<=> ! [X25: $i,X24: $i,X26: $i] :
( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X25: $i,X24: $i,X26: $i] :
( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) )
<=> ! [X25: $i,X24: $i,X26: $i] :
( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X25: $i,X24: $i,X26: $i] :
trans(
monotonicity(
rewrite(
( ( p2(X25,X26)
| ~ p2(X24,X25) )
<=> ( ~ p2(X24,X25)
| p2(X25,X26) ) )),
( ( p2(X25,X26)
| ~ p2(X24,X25)
| ~ p2(X24,X26) )
<=> ( ~ p2(X24,X25)
| p2(X25,X26)
| ~ p2(X24,X26) ) )),
rewrite(
( ( ~ p2(X24,X25)
| p2(X25,X26)
| ~ p2(X24,X26) )
<=> ( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) ) )),
( ( p2(X25,X26)
| ~ p2(X24,X25)
| ~ p2(X24,X26) )
<=> ( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X25: $i,X24: $i,X26: $i] :
( p2(X25,X26)
| ~ p2(X24,X25)
| ~ p2(X24,X26) )
<=> ! [X25: $i,X24: $i,X26: $i] :
( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X25: $i,X24: $i,X26: $i] :
( p2(X25,X26)
| ~ p2(X24,X25)
| ~ p2(X24,X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_24) ).
tff(16,plain,
! [X25: $i,X24: $i,X26: $i] :
( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X25: $i,X24: $i,X26: $i] :
( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X25: $i,X24: $i,X26: $i] :
( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X25: $i,X24: $i,X26: $i] :
( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( p2(c17,f3(c16))
<=> p2(c17,f3(c16)) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
p2(c17,f3(c16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_12) ).
tff(22,plain,
p2(c17,f3(c16)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [X25: $i,X24: $i,X26: $i] :
( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) )
| ~ p2(c17,c17)
| ~ p2(c17,f3(c16))
| p2(f3(c16),c17) )
<=> ( ~ ! [X25: $i,X24: $i,X26: $i] :
( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) )
| ~ p2(c17,c17)
| ~ p2(c17,f3(c16))
| p2(f3(c16),c17) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [X25: $i,X24: $i,X26: $i] :
( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) )
| ~ p2(c17,c17)
| ~ p2(c17,f3(c16))
| p2(f3(c16),c17) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [X25: $i,X24: $i,X26: $i] :
( ~ p2(X24,X26)
| ~ p2(X24,X25)
| p2(X25,X26) )
| ~ p2(c17,c17)
| ~ p2(c17,f3(c16))
| p2(f3(c16),c17) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
p2(f3(c16),c17),
inference(unit_resolution,[status(thm)],[25,22,19,9]) ).
tff(27,plain,
^ [X34: $i] :
refl(
( p5(X34,X34)
<=> p5(X34,X34) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X34: $i] : p5(X34,X34)
<=> ! [X34: $i] : p5(X34,X34) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X34: $i] : p5(X34,X34)
<=> ! [X34: $i] : p5(X34,X34) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
! [X34: $i] : p5(X34,X34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_3) ).
tff(31,plain,
! [X34: $i] : p5(X34,X34),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [X34: $i] : p5(X34,X34),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X34: $i] : p5(X34,X34),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [X34: $i] : p5(X34,X34)
| p5(c23,c23) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
p5(c23,c23),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
^ [X43: $i,X42: $i,X41: $i,X40: $i] :
refl(
( ( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
<=> ( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
<=> ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
<=> ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
^ [X43: $i,X42: $i,X41: $i,X40: $i] :
trans(
monotonicity(
rewrite(
( ( p5(f8(X40,X41),f8(X42,X43))
| ~ p2(X40,X42) )
<=> ( ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) ) )),
( ( p5(f8(X40,X41),f8(X42,X43))
| ~ p2(X40,X42)
| ~ p5(X41,X43) )
<=> ( ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43))
| ~ p5(X41,X43) ) )),
rewrite(
( ( ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43))
| ~ p5(X41,X43) )
<=> ( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) ) )),
( ( p5(f8(X40,X41),f8(X42,X43))
| ~ p2(X40,X42)
| ~ p5(X41,X43) )
<=> ( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( p5(f8(X40,X41),f8(X42,X43))
| ~ p2(X40,X42)
| ~ p5(X41,X43) )
<=> ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X43: $i,X42: $i,X41: $i,X40: $i] :
( p5(f8(X40,X41),f8(X42,X43))
| ~ p2(X40,X42)
| ~ p5(X41,X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_30) ).
tff(42,plain,
! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
| ~ p5(c23,c23)
| ~ p2(f3(c16),c17)
| p5(f8(f3(c16),c23),f8(c17,c23)) )
<=> ( ~ ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
| ~ p5(c23,c23)
| ~ p2(f3(c16),c17)
| p5(f8(f3(c16),c23),f8(c17,c23)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
| ~ p5(c23,c23)
| ~ p2(f3(c16),c17)
| p5(f8(f3(c16),c23),f8(c17,c23)) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
| ~ p5(c23,c23)
| ~ p2(f3(c16),c17)
| p5(f8(f3(c16),c23),f8(c17,c23)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
p5(f8(f3(c16),c23),f8(c17,c23)),
inference(unit_resolution,[status(thm)],[48,45,26,35]) ).
tff(50,plain,
^ [X35: $i,X34: $i,X36: $i] :
refl(
( ( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
<=> ( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
<=> ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
<=> ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
^ [X35: $i,X34: $i,X36: $i] :
trans(
monotonicity(
rewrite(
( ( p5(X35,X36)
| ~ p5(X34,X35) )
<=> ( ~ p5(X34,X35)
| p5(X35,X36) ) )),
( ( p5(X35,X36)
| ~ p5(X34,X35)
| ~ p5(X34,X36) )
<=> ( ~ p5(X34,X35)
| p5(X35,X36)
| ~ p5(X34,X36) ) )),
rewrite(
( ( ~ p5(X34,X35)
| p5(X35,X36)
| ~ p5(X34,X36) )
<=> ( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) ) )),
( ( p5(X35,X36)
| ~ p5(X34,X35)
| ~ p5(X34,X36) )
<=> ( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [X35: $i,X34: $i,X36: $i] :
( p5(X35,X36)
| ~ p5(X34,X35)
| ~ p5(X34,X36) )
<=> ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,axiom,
! [X35: $i,X34: $i,X36: $i] :
( p5(X35,X36)
| ~ p5(X34,X35)
| ~ p5(X34,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_22) ).
tff(56,plain,
! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( p5(f8(f3(c16),c23),f6(f7(c22)))
<=> p5(f8(f3(c16),c23),f6(f7(c22))) ),
inference(rewrite,[status(thm)],]) ).
tff(61,axiom,
p5(f8(f3(c16),c23),f6(f7(c22))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_16) ).
tff(62,plain,
p5(f8(f3(c16),c23),f6(f7(c22))),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
( ( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(f3(c16),c23),f6(f7(c22)))
| ~ p5(f8(f3(c16),c23),f8(c17,c23))
| p5(f8(c17,c23),f6(f7(c22))) )
<=> ( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(f3(c16),c23),f6(f7(c22)))
| ~ p5(f8(f3(c16),c23),f8(c17,c23))
| p5(f8(c17,c23),f6(f7(c22))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(f3(c16),c23),f6(f7(c22)))
| ~ p5(f8(f3(c16),c23),f8(c17,c23))
| p5(f8(c17,c23),f6(f7(c22))) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(f3(c16),c23),f6(f7(c22)))
| ~ p5(f8(f3(c16),c23),f8(c17,c23))
| p5(f8(c17,c23),f6(f7(c22))) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
p5(f8(c17,c23),f6(f7(c22))),
inference(unit_resolution,[status(thm)],[65,62,59,49]) ).
tff(67,plain,
^ [X37: $i] :
refl(
( ( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) )
<=> ( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [X37: $i] :
( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) )
<=> ! [X37: $i] :
( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [X37: $i] :
( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) )
<=> ! [X37: $i] :
( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
^ [X37: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p5(X37,c20)
| ~ p13(X37,c21) )
<=> ( ~ p13(X37,c21)
| p5(X37,c20) ) )),
( ( p5(X37,c20)
| ~ p13(X37,c21)
| ~ p13(c19,X37) )
<=> ( ~ p13(X37,c21)
| p5(X37,c20)
| ~ p13(c19,X37) ) )),
rewrite(
( ( ~ p13(X37,c21)
| p5(X37,c20)
| ~ p13(c19,X37) )
<=> ( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20) ) )),
( ( p5(X37,c20)
| ~ p13(X37,c21)
| ~ p13(c19,X37) )
<=> ( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20) ) )),
( ( p5(X37,c20)
| ~ p13(X37,c21)
| ~ p13(c19,X37)
| ~ p5(f8(c17,X37),f6(f7(c22))) )
<=> ( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) ) )),
rewrite(
( ( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) )
<=> ( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) ) )),
( ( p5(X37,c20)
| ~ p13(X37,c21)
| ~ p13(c19,X37)
| ~ p5(f8(c17,X37),f6(f7(c22))) )
<=> ( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [X37: $i] :
( p5(X37,c20)
| ~ p13(X37,c21)
| ~ p13(c19,X37)
| ~ p5(f8(c17,X37),f6(f7(c22))) )
<=> ! [X37: $i] :
( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,axiom,
! [X37: $i] :
( p5(X37,c20)
| ~ p13(X37,c21)
| ~ p13(c19,X37)
| ~ p5(f8(c17,X37),f6(f7(c22))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_31) ).
tff(73,plain,
! [X37: $i] :
( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [X37: $i] :
( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
! [X37: $i] :
( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [X37: $i] :
( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) ),
inference(modus_ponens,[status(thm)],[75,68]) ).
tff(77,plain,
( p13(c19,c23)
<=> p13(c19,c23) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
p13(c19,c23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13_9) ).
tff(79,plain,
p13(c19,c23),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( p13(c23,c21)
<=> p13(c23,c21) ),
inference(rewrite,[status(thm)],]) ).
tff(81,axiom,
p13(c23,c21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13_8) ).
tff(82,plain,
p13(c23,c21),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( ( ~ ! [X37: $i] :
( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) )
| ~ p13(c19,c23)
| ~ p13(c23,c21)
| p5(c23,c20)
| ~ p5(f8(c17,c23),f6(f7(c22))) )
<=> ( ~ ! [X37: $i] :
( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) )
| ~ p13(c19,c23)
| ~ p13(c23,c21)
| p5(c23,c20)
| ~ p5(f8(c17,c23),f6(f7(c22))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ~ ! [X37: $i] :
( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) )
| ~ p13(c19,c23)
| ~ p13(c23,c21)
| p5(c23,c20)
| ~ p5(f8(c17,c23),f6(f7(c22))) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
( ~ ! [X37: $i] :
( ~ p13(c19,X37)
| ~ p13(X37,c21)
| p5(X37,c20)
| ~ p5(f8(c17,X37),f6(f7(c22))) )
| ~ p13(c19,c23)
| ~ p13(c23,c21)
| p5(c23,c20)
| ~ p5(f8(c17,c23),f6(f7(c22))) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( p5(c23,c20)
| ~ p5(f8(c17,c23),f6(f7(c22))) ),
inference(unit_resolution,[status(thm)],[85,82,79,76]) ).
tff(87,plain,
p5(c23,c20),
inference(unit_resolution,[status(thm)],[86,66]) ).
tff(88,plain,
( ( ~ ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
| ~ p5(c23,c20)
| ~ p2(f3(c16),c17)
| p5(f8(f3(c16),c23),f8(c17,c20)) )
<=> ( ~ ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
| ~ p5(c23,c20)
| ~ p2(f3(c16),c17)
| p5(f8(f3(c16),c23),f8(c17,c20)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ~ ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
| ~ p5(c23,c20)
| ~ p2(f3(c16),c17)
| p5(f8(f3(c16),c23),f8(c17,c20)) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
| ~ p5(c23,c20)
| ~ p2(f3(c16),c17)
| p5(f8(f3(c16),c23),f8(c17,c20)) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
p5(f8(f3(c16),c23),f8(c17,c20)),
inference(unit_resolution,[status(thm)],[90,45,87,26]) ).
tff(92,plain,
( ( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(f3(c16),c23),f6(f7(c22)))
| ~ p5(f8(f3(c16),c23),f8(c17,c20))
| p5(f8(c17,c20),f6(f7(c22))) )
<=> ( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(f3(c16),c23),f6(f7(c22)))
| ~ p5(f8(f3(c16),c23),f8(c17,c20))
| p5(f8(c17,c20),f6(f7(c22))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(f3(c16),c23),f6(f7(c22)))
| ~ p5(f8(f3(c16),c23),f8(c17,c20))
| p5(f8(c17,c20),f6(f7(c22))) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(f3(c16),c23),f6(f7(c22)))
| ~ p5(f8(f3(c16),c23),f8(c17,c20))
| p5(f8(c17,c20),f6(f7(c22))) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
p5(f8(c17,c20),f6(f7(c22))),
inference(unit_resolution,[status(thm)],[94,62,59,91]) ).
tff(96,plain,
( ~ ! [X34: $i] : p5(X34,X34)
| p5(c20,c20) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
p5(c20,c20),
inference(unit_resolution,[status(thm)],[96,33]) ).
tff(98,plain,
( ( ~ ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
| ~ p5(c20,c20)
| ~ p2(f3(c16),c17)
| p5(f8(f3(c16),c20),f8(c17,c20)) )
<=> ( ~ ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
| ~ p5(c20,c20)
| ~ p2(f3(c16),c17)
| p5(f8(f3(c16),c20),f8(c17,c20)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ~ ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
| ~ p5(c20,c20)
| ~ p2(f3(c16),c17)
| p5(f8(f3(c16),c20),f8(c17,c20)) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
( ~ ! [X43: $i,X42: $i,X41: $i,X40: $i] :
( ~ p5(X41,X43)
| ~ p2(X40,X42)
| p5(f8(X40,X41),f8(X42,X43)) )
| ~ p5(c20,c20)
| ~ p2(f3(c16),c17)
| p5(f8(f3(c16),c20),f8(c17,c20)) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
p5(f8(f3(c16),c20),f8(c17,c20)),
inference(unit_resolution,[status(thm)],[100,45,97,26]) ).
tff(102,plain,
( ~ ! [X34: $i] : p5(X34,X34)
| p5(f8(f3(c16),c20),f8(f3(c16),c20)) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
p5(f8(f3(c16),c20),f8(f3(c16),c20)),
inference(unit_resolution,[status(thm)],[102,33]) ).
tff(104,plain,
( ( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| p5(f8(c17,c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(c17,c20)) )
<=> ( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| p5(f8(c17,c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(c17,c20)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( ~ p5(f8(f3(c16),c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(c17,c20))
| p5(f8(c17,c20),f8(f3(c16),c20)) )
<=> ( p5(f8(c17,c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(c17,c20)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(f3(c16),c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(c17,c20))
| p5(f8(c17,c20),f8(f3(c16),c20)) )
<=> ( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| p5(f8(c17,c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(c17,c20)) ) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(f3(c16),c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(c17,c20))
| p5(f8(c17,c20),f8(f3(c16),c20)) )
<=> ( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| p5(f8(c17,c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(c17,c20)) ) ),
inference(transitivity,[status(thm)],[106,104]) ).
tff(108,plain,
( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(f3(c16),c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(c17,c20))
| p5(f8(c17,c20),f8(f3(c16),c20)) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| p5(f8(c17,c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(f3(c16),c20))
| ~ p5(f8(f3(c16),c20),f8(c17,c20)) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
p5(f8(c17,c20),f8(f3(c16),c20)),
inference(unit_resolution,[status(thm)],[109,59,103,101]) ).
tff(111,plain,
( ~ p5(f8(f3(c16),c20),f6(f7(c22)))
<=> ~ p5(f8(f3(c16),c20),f6(f7(c22))) ),
inference(rewrite,[status(thm)],]) ).
tff(112,axiom,
~ p5(f8(f3(c16),c20),f6(f7(c22))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p5_17) ).
tff(113,plain,
~ p5(f8(f3(c16),c20),f6(f7(c22))),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
( ( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(c17,c20),f6(f7(c22)))
| ~ p5(f8(c17,c20),f8(f3(c16),c20))
| p5(f8(f3(c16),c20),f6(f7(c22))) )
<=> ( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(c17,c20),f6(f7(c22)))
| ~ p5(f8(c17,c20),f8(f3(c16),c20))
| p5(f8(f3(c16),c20),f6(f7(c22))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(c17,c20),f6(f7(c22)))
| ~ p5(f8(c17,c20),f8(f3(c16),c20))
| p5(f8(f3(c16),c20),f6(f7(c22))) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
( ~ ! [X35: $i,X34: $i,X36: $i] :
( ~ p5(X34,X36)
| ~ p5(X34,X35)
| p5(X35,X36) )
| ~ p5(f8(c17,c20),f6(f7(c22)))
| ~ p5(f8(c17,c20),f8(f3(c16),c20))
| p5(f8(f3(c16),c20),f6(f7(c22))) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
$false,
inference(unit_resolution,[status(thm)],[116,113,59,110,95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN618-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 06:05:04 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 1.59/1.29 % SZS status Unsatisfiable
% 1.59/1.29 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------