TSTP Solution File: SYN662-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN662-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 23:56:50 EDT 2022
% Result : Unsatisfiable 174.19s 111.72s
% Output : Proof 174.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 55
% Syntax : Number of formulae : 105 ( 34 unt; 14 typ; 0 def)
% Number of atoms : 442 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 612 ( 288 ~; 275 |; 0 &)
% ( 49 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 27 ( 27 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 218 ( 199 !; 0 ?; 218 :)
% 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(c33_type,type,
c33: $i ).
tff(c32_type,type,
c32: $i ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(p10_type,type,
p10: ( $i * $i ) > $o ).
tff(p25_type,type,
p25: ( $i * $i ) > $o ).
tff(c36_type,type,
c36: $i ).
tff(f16_type,type,
f16: ( $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/sandbox/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(c33),f4(c33)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p3(f4(c33),f4(c33)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X0: $i] :
refl(
( p10(X0,X0)
<=> p10(X0,X0) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X0: $i] : p10(X0,X0)
<=> ! [X0: $i] : p10(X0,X0) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X0: $i] : p10(X0,X0)
<=> ! [X0: $i] : p10(X0,X0) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X0: $i] : p10(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_2) ).
tff(14,plain,
! [X0: $i] : p10(X0,X0),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X0: $i] : p10(X0,X0),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X0: $i] : p10(X0,X0),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X0: $i] : p10(X0,X0)
| p10(c34,c34) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
p10(c34,c34),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X39: $i,X38: $i,X41: $i,X40: $i] :
refl(
( ( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) )
<=> ( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) )
<=> ! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) )
<=> ! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [X39: $i,X38: $i,X41: $i,X40: $i] :
trans(
monotonicity(
rewrite(
( ( p2(f11(X38,X39),f11(X40,X41))
| ~ p10(X39,X41) )
<=> ( ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) ) )),
( ( p2(f11(X38,X39),f11(X40,X41))
| ~ p10(X39,X41)
| ~ p3(X38,X40) )
<=> ( ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41))
| ~ p3(X38,X40) ) )),
rewrite(
( ( ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41))
| ~ p3(X38,X40) )
<=> ( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) ) )),
( ( p2(f11(X38,X39),f11(X40,X41))
| ~ p10(X39,X41)
| ~ p3(X38,X40) )
<=> ( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [X39: $i,X38: $i,X41: $i,X40: $i] :
( p2(f11(X38,X39),f11(X40,X41))
| ~ p10(X39,X41)
| ~ p3(X38,X40) )
<=> ! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [X39: $i,X38: $i,X41: $i,X40: $i] :
( p2(f11(X38,X39),f11(X40,X41))
| ~ p10(X39,X41)
| ~ p3(X38,X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_47) ).
tff(25,plain,
! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( ~ ! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) )
| ~ p10(c34,c34)
| ~ p3(f4(c33),f4(c33))
| p2(f11(f4(c33),c34),f11(f4(c33),c34)) )
<=> ( ~ ! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) )
| ~ p10(c34,c34)
| ~ p3(f4(c33),f4(c33))
| p2(f11(f4(c33),c34),f11(f4(c33),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ p3(f4(c33),f4(c33))
| ~ p10(c34,c34)
| p2(f11(f4(c33),c34),f11(f4(c33),c34)) )
<=> ( ~ p10(c34,c34)
| ~ p3(f4(c33),f4(c33))
| p2(f11(f4(c33),c34),f11(f4(c33),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) )
| ~ p3(f4(c33),f4(c33))
| ~ p10(c34,c34)
| p2(f11(f4(c33),c34),f11(f4(c33),c34)) )
<=> ( ~ ! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) )
| ~ p10(c34,c34)
| ~ p3(f4(c33),f4(c33))
| p2(f11(f4(c33),c34),f11(f4(c33),c34)) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) )
| ~ p3(f4(c33),f4(c33))
| ~ p10(c34,c34)
| p2(f11(f4(c33),c34),f11(f4(c33),c34)) )
<=> ( ~ ! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) )
| ~ p10(c34,c34)
| ~ p3(f4(c33),f4(c33))
| p2(f11(f4(c33),c34),f11(f4(c33),c34)) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) )
| ~ p3(f4(c33),f4(c33))
| ~ p10(c34,c34)
| p2(f11(f4(c33),c34),f11(f4(c33),c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [X39: $i,X38: $i,X41: $i,X40: $i] :
( ~ p3(X38,X40)
| ~ p10(X39,X41)
| p2(f11(X38,X39),f11(X40,X41)) )
| ~ p10(c34,c34)
| ~ p3(f4(c33),f4(c33))
| p2(f11(f4(c33),c34),f11(f4(c33),c34)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
p2(f11(f4(c33),c34),f11(f4(c33),c34)),
inference(unit_resolution,[status(thm)],[34,28,18,9]) ).
tff(36,plain,
^ [X43: $i] :
refl(
( ( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
<=> ( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
<=> ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
<=> ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
^ [X43: $i] :
trans(
monotonicity(
rewrite(
( ( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
<=> ( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ) )),
( ( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36)
| ~ p25(c32,X43) )
<=> ( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36)
| ~ p25(c32,X43) ) )),
rewrite(
( ( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36)
| ~ p25(c32,X43) )
<=> ( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ) )),
( ( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36)
| ~ p25(c32,X43) )
<=> ( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X43: $i] :
( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36)
| ~ p25(c32,X43) )
<=> ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X43: $i] :
( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36)
| ~ p25(c32,X43) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_50) ).
tff(42,plain,
! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( p25(c32,c33)
<=> p25(c32,c33) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
p25(c32,c33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25_12) ).
tff(48,plain,
p25(c32,c33),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( p25(c33,c36)
<=> p25(c33,c36) ),
inference(rewrite,[status(thm)],]) ).
tff(50,axiom,
p25(c33,c36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25_11) ).
tff(51,plain,
p25(c33,c36),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ( ~ ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
| ~ p25(c32,c33)
| p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p25(c33,c36) )
<=> ( ~ ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
| ~ p25(c32,c33)
| p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p25(c33,c36) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ~ ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
| ~ p25(c32,c33)
| p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p25(c33,c36) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
| ~ p25(c32,c33)
| p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p25(c33,c36) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
p2(f11(f4(c33),c34),f11(f4(c32),c34)),
inference(unit_resolution,[status(thm)],[54,51,48,45]) ).
tff(56,plain,
^ [X37: $i,X35: $i,X36: $i] :
refl(
( ( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
<=> ( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
<=> ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
<=> ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
^ [X37: $i,X35: $i,X36: $i] :
trans(
monotonicity(
rewrite(
( ( p2(X36,X37)
| ~ p2(X35,X36) )
<=> ( ~ p2(X35,X36)
| p2(X36,X37) ) )),
( ( p2(X36,X37)
| ~ p2(X35,X36)
| ~ p2(X35,X37) )
<=> ( ~ p2(X35,X36)
| p2(X36,X37)
| ~ p2(X35,X37) ) )),
rewrite(
( ( ~ p2(X35,X36)
| p2(X36,X37)
| ~ p2(X35,X37) )
<=> ( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ) )),
( ( p2(X36,X37)
| ~ p2(X35,X36)
| ~ p2(X35,X37) )
<=> ( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [X37: $i,X35: $i,X36: $i] :
( p2(X36,X37)
| ~ p2(X35,X36)
| ~ p2(X35,X37) )
<=> ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,axiom,
! [X37: $i,X35: $i,X36: $i] :
( p2(X36,X37)
| ~ p2(X35,X36)
| ~ p2(X35,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_30) ).
tff(62,plain,
! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) )
<=> ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) )
<=> ( ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) )
<=> ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) )
<=> ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,plain,
( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
p2(f11(f4(c32),c34),f11(f4(c33),c34)),
inference(unit_resolution,[status(thm)],[71,65,55,35]) ).
tff(73,plain,
^ [X96: $i] :
refl(
( ~ p2(X96,f16(X96,f9(f17(c31))))
<=> ~ p2(X96,f16(X96,f9(f17(c31)))) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31))))
<=> ! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31)))) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31))))
<=> ! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31)))) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_19) ).
tff(77,plain,
! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31)))),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31)))),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31)))),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
( ~ ! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31))))
| ~ p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
~ p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31)))),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
( p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
<=> p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31)))) ),
inference(rewrite,[status(thm)],]) ).
tff(83,axiom,
p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_39) ).
tff(84,plain,
p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31)))),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
( ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34)) )
<=> ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ( ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31)))) )
<=> ( ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31)))) )
<=> ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31)))) )
<=> ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(transitivity,[status(thm)],[87,85]) ).
tff(89,plain,
( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34)) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
$false,
inference(unit_resolution,[status(thm)],[90,65,84,81,72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN662-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 06:39:03 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.
% 174.19/111.72 % SZS status Unsatisfiable
% 174.19/111.72 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------