TSTP Solution File: SYN669-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN669-1 : 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 23:56:52 EDT 2022
% Result : Unsatisfiable 244.81s 158.40s
% Output : Proof 244.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 58
% Syntax : Number of formulae : 108 ( 33 unt; 15 typ; 0 def)
% Number of atoms : 457 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 623 ( 293 ~; 280 |; 0 &)
% ( 50 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 34 ( 34 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 9 >; 6 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 231 ( 207 !; 0 ?; 231 :)
% Comments :
%------------------------------------------------------------------------------
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(f11_type,type,
f11: ( $i * $i ) > $i ).
tff(c34_type,type,
c34: $i ).
tff(f4_type,type,
f4: $i > $i ).
tff(c36_type,type,
c36: $i ).
tff(c32_type,type,
c32: $i ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(p10_type,type,
p10: ( $i * $i ) > $o ).
tff(c37_type,type,
c37: $i ).
tff(p25_type,type,
p25: ( $i * $i ) > $o ).
tff(c33_type,type,
c33: $i ).
tff(f18_type,type,
f18: ( $i * $i ) > $i ).
tff(f9_type,type,
f9: $i > $i ).
tff(f17_type,type,
f17: $i > $i ).
tff(c31_type,type,
c31: $i ).
tff(1,plain,
^ [X83: $i] :
refl(
( p3(X83,X83)
<=> p3(X83,X83) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X83: $i] : p3(X83,X83)
<=> ! [X83: $i] : p3(X83,X83) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X83: $i] : p3(X83,X83)
<=> ! [X83: $i] : p3(X83,X83) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X83: $i] : p3(X83,X83),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_5) ).
tff(5,plain,
! [X83: $i] : p3(X83,X83),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X83: $i] : p3(X83,X83),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X83: $i] : p3(X83,X83),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X83: $i] : p3(X83,X83)
| p3(f4(c36),f4(c36)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p3(f4(c36),f4(c36)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X0: $i,X2: $i,X1: $i] :
refl(
( ( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) )
<=> ( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X0: $i,X2: $i,X1: $i] :
trans(
monotonicity(
rewrite(
( ( p10(X1,X2)
| ~ p10(X0,X1) )
<=> ( ~ p10(X0,X1)
| p10(X1,X2) ) )),
( ( p10(X1,X2)
| ~ p10(X0,X1)
| ~ p10(X0,X2) )
<=> ( ~ p10(X0,X1)
| p10(X1,X2)
| ~ p10(X0,X2) ) )),
rewrite(
( ( ~ p10(X0,X1)
| p10(X1,X2)
| ~ p10(X0,X2) )
<=> ( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) ) )),
( ( p10(X1,X2)
| ~ p10(X0,X1)
| ~ p10(X0,X2) )
<=> ( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( p10(X1,X2)
| ~ p10(X0,X1)
| ~ p10(X0,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X0: $i,X2: $i,X1: $i] :
( p10(X1,X2)
| ~ p10(X0,X1)
| ~ p10(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10_25) ).
tff(16,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( p10(c37,c34)
<=> p10(c37,c34) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
p10(c37,c34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10_11) ).
tff(22,plain,
p10(c37,c34),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) )
| ~ p10(c37,c34)
| p10(c34,c34) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) )
| ~ p10(c37,c34)
| p10(c34,c34) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ p10(c37,c34)
| ~ p10(c37,c34)
| p10(c34,c34) )
<=> ( ~ p10(c37,c34)
| p10(c34,c34) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) )
| ~ p10(c37,c34)
| ~ p10(c37,c34)
| p10(c34,c34) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) )
| ~ p10(c37,c34)
| p10(c34,c34) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) )
| ~ p10(c37,c34)
| ~ p10(c37,c34)
| p10(c34,c34) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) )
| ~ p10(c37,c34)
| p10(c34,c34) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) )
| ~ p10(c37,c34)
| ~ p10(c37,c34)
| p10(c34,c34) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p10(X0,X2)
| ~ p10(X0,X1)
| p10(X1,X2) )
| ~ p10(c37,c34)
| p10(c34,c34) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
p10(c34,c34),
inference(unit_resolution,[status(thm)],[28,22,19]) ).
tff(30,plain,
^ [X31: $i,X32: $i,X34: $i,X33: $i] :
refl(
( ( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) )
<=> ( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) )
<=> ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) )
<=> ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
^ [X31: $i,X32: $i,X34: $i,X33: $i] :
trans(
monotonicity(
rewrite(
( ( p2(f11(X31,X32),f11(X33,X34))
| ~ p10(X32,X34) )
<=> ( ~ p10(X32,X34)
| p2(f11(X31,X32),f11(X33,X34)) ) )),
( ( p2(f11(X31,X32),f11(X33,X34))
| ~ p10(X32,X34)
| ~ p3(X31,X33) )
<=> ( ~ p10(X32,X34)
| p2(f11(X31,X32),f11(X33,X34))
| ~ p3(X31,X33) ) )),
rewrite(
( ( ~ p10(X32,X34)
| p2(f11(X31,X32),f11(X33,X34))
| ~ p3(X31,X33) )
<=> ( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) ) )),
( ( p2(f11(X31,X32),f11(X33,X34))
| ~ p10(X32,X34)
| ~ p3(X31,X33) )
<=> ( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( p2(f11(X31,X32),f11(X33,X34))
| ~ p10(X32,X34)
| ~ p3(X31,X33) )
<=> ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [X31: $i,X32: $i,X34: $i,X33: $i] :
( p2(f11(X31,X32),f11(X33,X34))
| ~ p10(X32,X34)
| ~ p3(X31,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_46) ).
tff(36,plain,
! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) )
| ~ p10(c34,c34)
| ~ p3(f4(c36),f4(c36))
| p2(f11(f4(c36),c34),f11(f4(c36),c34)) )
<=> ( ~ ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) )
| ~ p10(c34,c34)
| ~ p3(f4(c36),f4(c36))
| p2(f11(f4(c36),c34),f11(f4(c36),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ~ ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) )
| ~ p10(c34,c34)
| ~ p3(f4(c36),f4(c36))
| p2(f11(f4(c36),c34),f11(f4(c36),c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( ~ ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p10(X32,X34)
| ~ p3(X31,X33)
| p2(f11(X31,X32),f11(X33,X34)) )
| ~ p10(c34,c34)
| ~ p3(f4(c36),f4(c36))
| p2(f11(f4(c36),c34),f11(f4(c36),c34)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
p2(f11(f4(c36),c34),f11(f4(c36),c34)),
inference(unit_resolution,[status(thm)],[42,39,29,9]) ).
tff(44,plain,
^ [X35: $i] :
refl(
( ( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) )
<=> ( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [X35: $i] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) )
<=> ! [X35: $i] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [X35: $i] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) )
<=> ! [X35: $i] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
^ [X35: $i] :
trans(
monotonicity(
rewrite(
( ( p2(f11(f4(X35),c34),f11(f4(c32),c34))
| ~ p25(X35,c33) )
<=> ( ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ) )),
( ( p2(f11(f4(X35),c34),f11(f4(c32),c34))
| ~ p25(X35,c33)
| ~ p25(c32,X35) )
<=> ( ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34))
| ~ p25(c32,X35) ) )),
rewrite(
( ( ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34))
| ~ p25(c32,X35) )
<=> ( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ) )),
( ( p2(f11(f4(X35),c34),f11(f4(c32),c34))
| ~ p25(X35,c33)
| ~ p25(c32,X35) )
<=> ( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [X35: $i] :
( p2(f11(f4(X35),c34),f11(f4(c32),c34))
| ~ p25(X35,c33)
| ~ p25(c32,X35) )
<=> ! [X35: $i] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [X35: $i] :
( p2(f11(f4(X35),c34),f11(f4(c32),c34))
| ~ p25(X35,c33)
| ~ p25(c32,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_49) ).
tff(50,plain,
! [X35: $i] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [X35: $i] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [X35: $i] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [X35: $i] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( p25(c32,c36)
<=> p25(c32,c36) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
p25(c32,c36),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25_13) ).
tff(56,plain,
p25(c32,c36),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( p25(c36,c33)
<=> p25(c36,c33) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
p25(c36,c33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25_12) ).
tff(59,plain,
p25(c36,c33),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( ( ~ ! [X35: $i] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) )
| ~ p25(c32,c36)
| ~ p25(c36,c33)
| p2(f11(f4(c36),c34),f11(f4(c32),c34)) )
<=> ( ~ ! [X35: $i] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) )
| ~ p25(c32,c36)
| ~ p25(c36,c33)
| p2(f11(f4(c36),c34),f11(f4(c32),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ! [X35: $i] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) )
| ~ p25(c32,c36)
| ~ p25(c36,c33)
| p2(f11(f4(c36),c34),f11(f4(c32),c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [X35: $i] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) )
| ~ p25(c32,c36)
| ~ p25(c36,c33)
| p2(f11(f4(c36),c34),f11(f4(c32),c34)) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
p2(f11(f4(c36),c34),f11(f4(c32),c34)),
inference(unit_resolution,[status(thm)],[62,59,56,53]) ).
tff(64,plain,
^ [X30: $i,X29: $i,X28: $i] :
refl(
( ( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) )
<=> ( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) )
<=> ! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) )
<=> ! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
^ [X30: $i,X29: $i,X28: $i] :
trans(
monotonicity(
rewrite(
( ( p2(X29,X30)
| ~ p2(X28,X29) )
<=> ( ~ p2(X28,X29)
| p2(X29,X30) ) )),
( ( p2(X29,X30)
| ~ p2(X28,X29)
| ~ p2(X28,X30) )
<=> ( ~ p2(X28,X29)
| p2(X29,X30)
| ~ p2(X28,X30) ) )),
rewrite(
( ( ~ p2(X28,X29)
| p2(X29,X30)
| ~ p2(X28,X30) )
<=> ( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) ) )),
( ( p2(X29,X30)
| ~ p2(X28,X29)
| ~ p2(X28,X30) )
<=> ( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [X30: $i,X29: $i,X28: $i] :
( p2(X29,X30)
| ~ p2(X28,X29)
| ~ p2(X28,X30) )
<=> ! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,axiom,
! [X30: $i,X29: $i,X28: $i] :
( p2(X29,X30)
| ~ p2(X28,X29)
| ~ p2(X28,X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_30) ).
tff(70,plain,
! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
( ( ~ ! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) )
| ~ p2(f11(f4(c36),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c36),c34),f11(f4(c36),c34))
| p2(f11(f4(c32),c34),f11(f4(c36),c34)) )
<=> ( ~ ! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) )
| ~ p2(f11(f4(c36),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c36),c34),f11(f4(c36),c34))
| p2(f11(f4(c32),c34),f11(f4(c36),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ~ ! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) )
| ~ p2(f11(f4(c36),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c36),c34),f11(f4(c36),c34))
| p2(f11(f4(c32),c34),f11(f4(c36),c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) )
| ~ p2(f11(f4(c36),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c36),c34),f11(f4(c36),c34))
| p2(f11(f4(c32),c34),f11(f4(c36),c34)) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
p2(f11(f4(c32),c34),f11(f4(c36),c34)),
inference(unit_resolution,[status(thm)],[76,73,63,43]) ).
tff(78,plain,
^ [X96: $i] :
refl(
( ~ p2(X96,f18(X96,f9(f17(c31))))
<=> ~ p2(X96,f18(X96,f9(f17(c31)))) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [X96: $i] : ~ p2(X96,f18(X96,f9(f17(c31))))
<=> ! [X96: $i] : ~ p2(X96,f18(X96,f9(f17(c31)))) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [X96: $i] : ~ p2(X96,f18(X96,f9(f17(c31))))
<=> ! [X96: $i] : ~ p2(X96,f18(X96,f9(f17(c31)))) ),
inference(rewrite,[status(thm)],]) ).
tff(81,axiom,
! [X96: $i] : ~ p2(X96,f18(X96,f9(f17(c31)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p2_18) ).
tff(82,plain,
! [X96: $i] : ~ p2(X96,f18(X96,f9(f17(c31)))),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [X96: $i] : ~ p2(X96,f18(X96,f9(f17(c31)))),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [X96: $i] : ~ p2(X96,f18(X96,f9(f17(c31)))),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
( ~ ! [X96: $i] : ~ p2(X96,f18(X96,f9(f17(c31))))
| ~ p2(f11(f4(c36),c34),f18(f11(f4(c36),c34),f9(f17(c31)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
~ p2(f11(f4(c36),c34),f18(f11(f4(c36),c34),f9(f17(c31)))),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
( p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31))))
<=> p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31)))) ),
inference(rewrite,[status(thm)],]) ).
tff(88,axiom,
p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_39) ).
tff(89,plain,
p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31)))),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
( ( ~ ! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) )
| ~ p2(f11(f4(c32),c34),f11(f4(c36),c34))
| ~ p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31))))
| p2(f11(f4(c36),c34),f18(f11(f4(c36),c34),f9(f17(c31)))) )
<=> ( ~ ! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) )
| ~ p2(f11(f4(c32),c34),f11(f4(c36),c34))
| ~ p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31))))
| p2(f11(f4(c36),c34),f18(f11(f4(c36),c34),f9(f17(c31)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ~ ! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) )
| ~ p2(f11(f4(c32),c34),f11(f4(c36),c34))
| ~ p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31))))
| p2(f11(f4(c36),c34),f18(f11(f4(c36),c34),f9(f17(c31)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [X30: $i,X29: $i,X28: $i] :
( ~ p2(X28,X29)
| ~ p2(X28,X30)
| p2(X29,X30) )
| ~ p2(f11(f4(c32),c34),f11(f4(c36),c34))
| ~ p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31))))
| p2(f11(f4(c36),c34),f18(f11(f4(c36),c34),f9(f17(c31)))) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
$false,
inference(unit_resolution,[status(thm)],[92,73,89,86,77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN669-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.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 06:24:49 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.
% 244.81/158.40 % SZS status Unsatisfiable
% 244.81/158.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------