TSTP Solution File: SYN597-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN597-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 23:56:35 EDT 2022
% Result : Unsatisfiable 1.38s 1.12s
% Output : Proof 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 93
% Syntax : Number of formulae : 191 ( 60 unt; 16 typ; 0 def)
% Number of atoms : 922 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1261 ( 583 ~; 579 |; 0 &)
% ( 99 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 69 ( 69 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 11 >; 10 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 570 ( 509 !; 0 ?; 570 :)
% Comments :
%------------------------------------------------------------------------------
tff(p10_type,type,
p10: ( $i * $i ) > $o ).
tff(f11_type,type,
f11: ( $i * $i * $i ) > $i ).
tff(c24_type,type,
c24: $i ).
tff(c23_type,type,
c23: $i ).
tff(f13_type,type,
f13: ( $i * $i ) > $i ).
tff(f14_type,type,
f14: ( $i * $i ) > $i ).
tff(c22_type,type,
c22: $i ).
tff(f4_type,type,
f4: $i > $i ).
tff(c20_type,type,
c20: $i ).
tff(f15_type,type,
f15: $i > $i ).
tff(c21_type,type,
c21: $i ).
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(p12_type,type,
p12: ( $i * $i ) > $o ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(p9_type,type,
p9: ( $i * $i ) > $o ).
tff(p18_type,type,
p18: ( $i * $i ) > $o ).
tff(1,plain,
^ [X35: $i] :
refl(
( p3(X35,X35)
<=> p3(X35,X35) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X35: $i] : p3(X35,X35)
<=> ! [X35: $i] : p3(X35,X35) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X35: $i] : p3(X35,X35)
<=> ! [X35: $i] : p3(X35,X35) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X35: $i] : p3(X35,X35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_3) ).
tff(5,plain,
! [X35: $i] : p3(X35,X35),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X35: $i] : p3(X35,X35),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X35: $i] : p3(X35,X35),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X35: $i] : p3(X35,X35)
| p3(c21,c21) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p3(c21,c21),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X37: $i,X35: $i,X36: $i] :
refl(
( ( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) )
<=> ( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X37: $i,X35: $i,X36: $i] :
( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) )
<=> ! [X37: $i,X35: $i,X36: $i] :
( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X37: $i,X35: $i,X36: $i] :
( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) )
<=> ! [X37: $i,X35: $i,X36: $i] :
( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X37: $i,X35: $i,X36: $i] :
trans(
monotonicity(
rewrite(
( ( p3(X36,X37)
| ~ p3(X35,X36) )
<=> ( ~ p3(X35,X36)
| p3(X36,X37) ) )),
( ( p3(X36,X37)
| ~ p3(X35,X36)
| ~ p3(X35,X37) )
<=> ( ~ p3(X35,X36)
| p3(X36,X37)
| ~ p3(X35,X37) ) )),
rewrite(
( ( ~ p3(X35,X36)
| p3(X36,X37)
| ~ p3(X35,X37) )
<=> ( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) ) )),
( ( p3(X36,X37)
| ~ p3(X35,X36)
| ~ p3(X35,X37) )
<=> ( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X37: $i,X35: $i,X36: $i] :
( p3(X36,X37)
| ~ p3(X35,X36)
| ~ p3(X35,X37) )
<=> ! [X37: $i,X35: $i,X36: $i] :
( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X37: $i,X35: $i,X36: $i] :
( p3(X36,X37)
| ~ p3(X35,X36)
| ~ p3(X35,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_18) ).
tff(16,plain,
! [X37: $i,X35: $i,X36: $i] :
( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X37: $i,X35: $i,X36: $i] :
( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X37: $i,X35: $i,X36: $i] :
( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X37: $i,X35: $i,X36: $i] :
( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( p3(c21,c22)
<=> p3(c21,c22) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
p3(c21,c22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_7) ).
tff(22,plain,
p3(c21,c22),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) )
| ~ p3(c21,c21)
| ~ p3(c21,c22)
| p3(c22,c21) )
<=> ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) )
| ~ p3(c21,c21)
| ~ p3(c21,c22)
| p3(c22,c21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) )
| ~ p3(c21,c21)
| ~ p3(c21,c22)
| p3(c22,c21) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p3(X35,X37)
| ~ p3(X35,X36)
| p3(X36,X37) )
| ~ p3(c21,c21)
| ~ p3(c21,c22)
| p3(c22,c21) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
p3(c22,c21),
inference(unit_resolution,[status(thm)],[25,22,19,9]) ).
tff(27,plain,
^ [X28: $i] :
refl(
( p2(X28,X28)
<=> p2(X28,X28) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X28: $i] : p2(X28,X28)
<=> ! [X28: $i] : p2(X28,X28) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X28: $i] : p2(X28,X28)
<=> ! [X28: $i] : p2(X28,X28) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
! [X28: $i] : p2(X28,X28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_4) ).
tff(31,plain,
! [X28: $i] : p2(X28,X28),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [X28: $i] : p2(X28,X28),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X28: $i] : p2(X28,X28),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [X28: $i] : p2(X28,X28)
| p2(c20,c20) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
p2(c20,c20),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
^ [X41: $i,X40: $i] :
refl(
( ( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) )
<=> ( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X41: $i,X40: $i] :
( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) )
<=> ! [X41: $i,X40: $i] :
( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X41: $i,X40: $i] :
( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) )
<=> ! [X41: $i,X40: $i] :
( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
^ [X41: $i,X40: $i] :
rewrite(
( ( p3(f4(X40),f4(X41))
| ~ p2(X40,X41) )
<=> ( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X41: $i,X40: $i] :
( p3(f4(X40),f4(X41))
| ~ p2(X40,X41) )
<=> ! [X41: $i,X40: $i] :
( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X41: $i,X40: $i] :
( p3(f4(X40),f4(X41))
| ~ p2(X40,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_12) ).
tff(42,plain,
! [X41: $i,X40: $i] :
( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X41: $i,X40: $i] :
( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X41: $i,X40: $i] :
( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X41: $i,X40: $i] :
( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [X41: $i,X40: $i] :
( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) )
| ~ p2(c20,c20)
| p3(f4(c20),f4(c20)) )
<=> ( ~ ! [X41: $i,X40: $i] :
( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) )
| ~ p2(c20,c20)
| p3(f4(c20),f4(c20)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ! [X41: $i,X40: $i] :
( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) )
| ~ p2(c20,c20)
| p3(f4(c20),f4(c20)) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X41: $i,X40: $i] :
( ~ p2(X40,X41)
| p3(f4(X40),f4(X41)) )
| ~ p2(c20,c20)
| p3(f4(c20),f4(c20)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
p3(f4(c20),f4(c20)),
inference(unit_resolution,[status(thm)],[48,45,35]) ).
tff(50,plain,
^ [X14: $i,X12: $i,X13: $i,X15: $i] :
refl(
( ( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) )
<=> ( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) )
<=> ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) )
<=> ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
^ [X14: $i,X12: $i,X13: $i,X15: $i] :
trans(
monotonicity(
rewrite(
( ( p12(f14(X12,X13),f14(X14,X15))
| ~ p3(X12,X14) )
<=> ( ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) ) )),
( ( p12(f14(X12,X13),f14(X14,X15))
| ~ p3(X12,X14)
| ~ p3(X13,X15) )
<=> ( ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15))
| ~ p3(X13,X15) ) )),
rewrite(
( ( ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15))
| ~ p3(X13,X15) )
<=> ( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) ) )),
( ( p12(f14(X12,X13),f14(X14,X15))
| ~ p3(X12,X14)
| ~ p3(X13,X15) )
<=> ( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( p12(f14(X12,X13),f14(X14,X15))
| ~ p3(X12,X14)
| ~ p3(X13,X15) )
<=> ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,axiom,
! [X14: $i,X12: $i,X13: $i,X15: $i] :
( p12(f14(X12,X13),f14(X14,X15))
| ~ p3(X12,X14)
| ~ p3(X13,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_27) ).
tff(56,plain,
! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ( ~ ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) )
| ~ p3(c22,c21)
| ~ p3(f4(c20),f4(c20))
| p12(f14(f4(c20),c22),f14(f4(c20),c21)) )
<=> ( ~ ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) )
| ~ p3(c22,c21)
| ~ p3(f4(c20),f4(c20))
| p12(f14(f4(c20),c22),f14(f4(c20),c21)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) )
| ~ p3(c22,c21)
| ~ p3(f4(c20),f4(c20))
| p12(f14(f4(c20),c22),f14(f4(c20),c21)) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p3(X13,X15)
| ~ p3(X12,X14)
| p12(f14(X12,X13),f14(X14,X15)) )
| ~ p3(c22,c21)
| ~ p3(f4(c20),f4(c20))
| p12(f14(f4(c20),c22),f14(f4(c20),c21)) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
p12(f14(f4(c20),c22),f14(f4(c20),c21)),
inference(unit_resolution,[status(thm)],[62,59,49,26]) ).
tff(64,plain,
^ [X9: $i] :
refl(
( p12(X9,X9)
<=> p12(X9,X9) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [X9: $i] : p12(X9,X9)
<=> ! [X9: $i] : p12(X9,X9) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [X9: $i] : p12(X9,X9)
<=> ! [X9: $i] : p12(X9,X9) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
! [X9: $i] : p12(X9,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_5) ).
tff(68,plain,
! [X9: $i] : p12(X9,X9),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [X9: $i] : p12(X9,X9),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [X9: $i] : p12(X9,X9),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [X9: $i] : p12(X9,X9)
| p12(f14(f4(c20),c22),f14(f4(c20),c22)) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
p12(f14(f4(c20),c22),f14(f4(c20),c22)),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
^ [X9: $i,X11: $i,X10: $i] :
refl(
( ( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) )
<=> ( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) )
<=> ! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) )
<=> ! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
^ [X9: $i,X11: $i,X10: $i] :
trans(
monotonicity(
rewrite(
( ( p12(X10,X11)
| ~ p12(X9,X10) )
<=> ( ~ p12(X9,X10)
| p12(X10,X11) ) )),
( ( p12(X10,X11)
| ~ p12(X9,X10)
| ~ p12(X9,X11) )
<=> ( ~ p12(X9,X10)
| p12(X10,X11)
| ~ p12(X9,X11) ) )),
rewrite(
( ( ~ p12(X9,X10)
| p12(X10,X11)
| ~ p12(X9,X11) )
<=> ( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) ) )),
( ( p12(X10,X11)
| ~ p12(X9,X10)
| ~ p12(X9,X11) )
<=> ( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) ) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [X9: $i,X11: $i,X10: $i] :
( p12(X10,X11)
| ~ p12(X9,X10)
| ~ p12(X9,X11) )
<=> ! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,axiom,
! [X9: $i,X11: $i,X10: $i] :
( p12(X10,X11)
| ~ p12(X9,X10)
| ~ p12(X9,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_20) ).
tff(79,plain,
! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) ),
inference(modus_ponens,[status(thm)],[81,74]) ).
tff(83,plain,
( ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) )
| p12(f14(f4(c20),c21),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c21)) )
<=> ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) )
| p12(f14(f4(c20),c21),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c21)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ( ~ p12(f14(f4(c20),c22),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c21))
| p12(f14(f4(c20),c21),f14(f4(c20),c22)) )
<=> ( p12(f14(f4(c20),c21),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c21)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
( ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) )
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c21))
| p12(f14(f4(c20),c21),f14(f4(c20),c22)) )
<=> ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) )
| p12(f14(f4(c20),c21),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c21)) ) ),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) )
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c21))
| p12(f14(f4(c20),c21),f14(f4(c20),c22)) )
<=> ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) )
| p12(f14(f4(c20),c21),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c21)) ) ),
inference(transitivity,[status(thm)],[85,83]) ).
tff(87,plain,
( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) )
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c21))
| p12(f14(f4(c20),c21),f14(f4(c20),c22)) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p12(X9,X11)
| ~ p12(X9,X10)
| p12(X10,X11) )
| p12(f14(f4(c20),c21),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c22))
| ~ p12(f14(f4(c20),c22),f14(f4(c20),c21)) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
p12(f14(f4(c20),c21),f14(f4(c20),c22)),
inference(unit_resolution,[status(thm)],[88,82,72,63]) ).
tff(90,plain,
^ [X39: $i,X38: $i] :
refl(
( ( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) )
<=> ( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) ) )),
inference(bind,[status(th)],]) ).
tff(91,plain,
( ! [X39: $i,X38: $i] :
( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) )
<=> ! [X39: $i,X38: $i] :
( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,plain,
( ! [X39: $i,X38: $i] :
( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) )
<=> ! [X39: $i,X38: $i] :
( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
^ [X39: $i,X38: $i] :
rewrite(
( ( p3(f15(X38),f15(X39))
| ~ p2(X38,X39) )
<=> ( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) ) )),
inference(bind,[status(th)],]) ).
tff(94,plain,
( ! [X39: $i,X38: $i] :
( p3(f15(X38),f15(X39))
| ~ p2(X38,X39) )
<=> ! [X39: $i,X38: $i] :
( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,axiom,
! [X39: $i,X38: $i] :
( p3(f15(X38),f15(X39))
| ~ p2(X38,X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_11) ).
tff(96,plain,
! [X39: $i,X38: $i] :
( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [X39: $i,X38: $i] :
( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
! [X39: $i,X38: $i] :
( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) ),
inference(skolemize,[status(sab)],[97]) ).
tff(99,plain,
! [X39: $i,X38: $i] :
( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) ),
inference(modus_ponens,[status(thm)],[98,91]) ).
tff(100,plain,
( ( ~ ! [X39: $i,X38: $i] :
( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) )
| ~ p2(c20,c20)
| p3(f15(c20),f15(c20)) )
<=> ( ~ ! [X39: $i,X38: $i] :
( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) )
| ~ p2(c20,c20)
| p3(f15(c20),f15(c20)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ~ ! [X39: $i,X38: $i] :
( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) )
| ~ p2(c20,c20)
| p3(f15(c20),f15(c20)) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
( ~ ! [X39: $i,X38: $i] :
( ~ p2(X38,X39)
| p3(f15(X38),f15(X39)) )
| ~ p2(c20,c20)
| p3(f15(c20),f15(c20)) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
p3(f15(c20),f15(c20)),
inference(unit_resolution,[status(thm)],[102,99,35]) ).
tff(104,plain,
^ [X31: $i,X32: $i,X34: $i,X33: $i] :
refl(
( ( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) )
<=> ( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) ) )),
inference(bind,[status(th)],]) ).
tff(105,plain,
( ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) )
<=> ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) )
<=> ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
^ [X31: $i,X32: $i,X34: $i,X33: $i] :
trans(
monotonicity(
rewrite(
( ( p2(f13(X31,X32),f13(X33,X34))
| ~ p12(X32,X34) )
<=> ( ~ p12(X32,X34)
| p2(f13(X31,X32),f13(X33,X34)) ) )),
( ( p2(f13(X31,X32),f13(X33,X34))
| ~ p12(X32,X34)
| ~ p3(X31,X33) )
<=> ( ~ p12(X32,X34)
| p2(f13(X31,X32),f13(X33,X34))
| ~ p3(X31,X33) ) )),
rewrite(
( ( ~ p12(X32,X34)
| p2(f13(X31,X32),f13(X33,X34))
| ~ p3(X31,X33) )
<=> ( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) ) )),
( ( p2(f13(X31,X32),f13(X33,X34))
| ~ p12(X32,X34)
| ~ p3(X31,X33) )
<=> ( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) ) )),
inference(bind,[status(th)],]) ).
tff(108,plain,
( ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( p2(f13(X31,X32),f13(X33,X34))
| ~ p12(X32,X34)
| ~ p3(X31,X33) )
<=> ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,axiom,
! [X31: $i,X32: $i,X34: $i,X33: $i] :
( p2(f13(X31,X32),f13(X33,X34))
| ~ p12(X32,X34)
| ~ p3(X31,X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_26) ).
tff(110,plain,
! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) ),
inference(modus_ponens,[status(thm)],[110,106]) ).
tff(112,plain,
! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) ),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) ),
inference(modus_ponens,[status(thm)],[112,105]) ).
tff(114,plain,
( ( ~ ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) )
| ~ p3(f15(c20),f15(c20))
| p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22)))
| ~ p12(f14(f4(c20),c21),f14(f4(c20),c22)) )
<=> ( ~ ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) )
| ~ p3(f15(c20),f15(c20))
| p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22)))
| ~ p12(f14(f4(c20),c21),f14(f4(c20),c22)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
( ( ~ p12(f14(f4(c20),c21),f14(f4(c20),c22))
| ~ p3(f15(c20),f15(c20))
| p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22))) )
<=> ( ~ p3(f15(c20),f15(c20))
| p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22)))
| ~ p12(f14(f4(c20),c21),f14(f4(c20),c22)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,plain,
( ( ~ ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) )
| ~ p12(f14(f4(c20),c21),f14(f4(c20),c22))
| ~ p3(f15(c20),f15(c20))
| p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22))) )
<=> ( ~ ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) )
| ~ p3(f15(c20),f15(c20))
| p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22)))
| ~ p12(f14(f4(c20),c21),f14(f4(c20),c22)) ) ),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
( ( ~ ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) )
| ~ p12(f14(f4(c20),c21),f14(f4(c20),c22))
| ~ p3(f15(c20),f15(c20))
| p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22))) )
<=> ( ~ ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) )
| ~ p3(f15(c20),f15(c20))
| p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22)))
| ~ p12(f14(f4(c20),c21),f14(f4(c20),c22)) ) ),
inference(transitivity,[status(thm)],[116,114]) ).
tff(118,plain,
( ~ ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) )
| ~ p12(f14(f4(c20),c21),f14(f4(c20),c22))
| ~ p3(f15(c20),f15(c20))
| p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22))) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
( ~ ! [X31: $i,X32: $i,X34: $i,X33: $i] :
( ~ p12(X32,X34)
| ~ p3(X31,X33)
| p2(f13(X31,X32),f13(X33,X34)) )
| ~ p3(f15(c20),f15(c20))
| p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22)))
| ~ p12(f14(f4(c20),c21),f14(f4(c20),c22)) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22))),
inference(unit_resolution,[status(thm)],[119,113,103,89]) ).
tff(121,plain,
^ [X50: $i] :
refl(
( p9(X50,X50)
<=> p9(X50,X50) )),
inference(bind,[status(th)],]) ).
tff(122,plain,
( ! [X50: $i] : p9(X50,X50)
<=> ! [X50: $i] : p9(X50,X50) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [X50: $i] : p9(X50,X50)
<=> ! [X50: $i] : p9(X50,X50) ),
inference(rewrite,[status(thm)],]) ).
tff(124,axiom,
! [X50: $i] : p9(X50,X50),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_2) ).
tff(125,plain,
! [X50: $i] : p9(X50,X50),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [X50: $i] : p9(X50,X50),
inference(skolemize,[status(sab)],[125]) ).
tff(127,plain,
! [X50: $i] : p9(X50,X50),
inference(modus_ponens,[status(thm)],[126,122]) ).
tff(128,plain,
( ~ ! [X50: $i] : p9(X50,X50)
| p9(c23,c23) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
p9(c23,c23),
inference(unit_resolution,[status(thm)],[128,127]) ).
tff(130,plain,
^ [X0: $i] :
refl(
( p10(X0,X0)
<=> p10(X0,X0) )),
inference(bind,[status(th)],]) ).
tff(131,plain,
( ! [X0: $i] : p10(X0,X0)
<=> ! [X0: $i] : p10(X0,X0) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
( ! [X0: $i] : p10(X0,X0)
<=> ! [X0: $i] : p10(X0,X0) ),
inference(rewrite,[status(thm)],]) ).
tff(133,axiom,
! [X0: $i] : p10(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_1) ).
tff(134,plain,
! [X0: $i] : p10(X0,X0),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [X0: $i] : p10(X0,X0),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [X0: $i] : p10(X0,X0),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
( ~ ! [X0: $i] : p10(X0,X0)
| p10(c24,c24) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
p10(c24,c24),
inference(unit_resolution,[status(thm)],[137,136]) ).
tff(139,plain,
^ [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
refl(
( ( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) )
<=> ( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) ) )),
inference(bind,[status(th)],]) ).
tff(140,plain,
( ! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) )
<=> ! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,plain,
( ! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) )
<=> ! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(142,plain,
^ [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p10(f11(X3,X4,X5),f11(X6,X7,X8))
| ~ p2(X3,X6) )
<=> ( ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) ) )),
( ( p10(f11(X3,X4,X5),f11(X6,X7,X8))
| ~ p2(X3,X6)
| ~ p9(X4,X7) )
<=> ( ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8))
| ~ p9(X4,X7) ) )),
rewrite(
( ( ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8))
| ~ p9(X4,X7) )
<=> ( ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) ) )),
( ( p10(f11(X3,X4,X5),f11(X6,X7,X8))
| ~ p2(X3,X6)
| ~ p9(X4,X7) )
<=> ( ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) ) )),
( ( p10(f11(X3,X4,X5),f11(X6,X7,X8))
| ~ p2(X3,X6)
| ~ p9(X4,X7)
| ~ p10(X5,X8) )
<=> ( ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8))
| ~ p10(X5,X8) ) )),
rewrite(
( ( ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8))
| ~ p10(X5,X8) )
<=> ( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) ) )),
( ( p10(f11(X3,X4,X5),f11(X6,X7,X8))
| ~ p2(X3,X6)
| ~ p9(X4,X7)
| ~ p10(X5,X8) )
<=> ( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) ) )),
inference(bind,[status(th)],]) ).
tff(143,plain,
( ! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( p10(f11(X3,X4,X5),f11(X6,X7,X8))
| ~ p2(X3,X6)
| ~ p9(X4,X7)
| ~ p10(X5,X8) )
<=> ! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,axiom,
! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( p10(f11(X3,X4,X5),f11(X6,X7,X8))
| ~ p2(X3,X6)
| ~ p9(X4,X7)
| ~ p10(X5,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_28) ).
tff(145,plain,
! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) ),
inference(modus_ponens,[status(thm)],[145,141]) ).
tff(147,plain,
! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) ),
inference(skolemize,[status(sab)],[146]) ).
tff(148,plain,
! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) ),
inference(modus_ponens,[status(thm)],[147,140]) ).
tff(149,plain,
( ( ~ ! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) )
| ~ p10(c24,c24)
| ~ p9(c23,c23)
| ~ p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22)))
| p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24)) )
<=> ( ~ ! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) )
| ~ p10(c24,c24)
| ~ p9(c23,c23)
| ~ p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22)))
| p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(150,plain,
( ~ ! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) )
| ~ p10(c24,c24)
| ~ p9(c23,c23)
| ~ p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22)))
| p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24)) ),
inference(quant_inst,[status(thm)],]) ).
tff(151,plain,
( ~ ! [X6: $i,X4: $i,X3: $i,X7: $i,X5: $i,X8: $i] :
( ~ p10(X5,X8)
| ~ p9(X4,X7)
| ~ p2(X3,X6)
| p10(f11(X3,X4,X5),f11(X6,X7,X8)) )
| ~ p10(c24,c24)
| ~ p9(c23,c23)
| ~ p2(f13(f15(c20),f14(f4(c20),c21)),f13(f15(c20),f14(f4(c20),c22)))
| p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24)) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24)),
inference(unit_resolution,[status(thm)],[151,148,138,129,120]) ).
tff(153,plain,
^ [X25: $i,X27: $i,X26: $i,X24: $i] :
refl(
( ( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) )
<=> ( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) ) )),
inference(bind,[status(th)],]) ).
tff(154,plain,
( ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) )
<=> ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) ) ),
inference(quant_intro,[status(thm)],[153]) ).
tff(155,plain,
( ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) )
<=> ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
^ [X25: $i,X27: $i,X26: $i,X24: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p18(X24,X25)
| ~ p18(X27,X26) )
<=> ( ~ p18(X27,X26)
| p18(X24,X25) ) )),
( ( p18(X24,X25)
| ~ p18(X27,X26)
| ~ p2(X27,X24) )
<=> ( ~ p18(X27,X26)
| p18(X24,X25)
| ~ p2(X27,X24) ) )),
rewrite(
( ( ~ p18(X27,X26)
| p18(X24,X25)
| ~ p2(X27,X24) )
<=> ( ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) ) )),
( ( p18(X24,X25)
| ~ p18(X27,X26)
| ~ p2(X27,X24) )
<=> ( ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) ) )),
( ( p18(X24,X25)
| ~ p18(X27,X26)
| ~ p2(X27,X24)
| ~ p10(X26,X25) )
<=> ( ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25)
| ~ p10(X26,X25) ) )),
rewrite(
( ( ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25)
| ~ p10(X26,X25) )
<=> ( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) ) )),
( ( p18(X24,X25)
| ~ p18(X27,X26)
| ~ p2(X27,X24)
| ~ p10(X26,X25) )
<=> ( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) ) )),
inference(bind,[status(th)],]) ).
tff(157,plain,
( ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( p18(X24,X25)
| ~ p18(X27,X26)
| ~ p2(X27,X24)
| ~ p10(X26,X25) )
<=> ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) ) ),
inference(quant_intro,[status(thm)],[156]) ).
tff(158,axiom,
! [X25: $i,X27: $i,X26: $i,X24: $i] :
( p18(X24,X25)
| ~ p18(X27,X26)
| ~ p2(X27,X24)
| ~ p10(X26,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18_24) ).
tff(159,plain,
! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) ),
inference(modus_ponens,[status(thm)],[159,155]) ).
tff(161,plain,
! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) ),
inference(skolemize,[status(sab)],[160]) ).
tff(162,plain,
! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) ),
inference(modus_ponens,[status(thm)],[161,154]) ).
tff(163,plain,
( ~ p18(c20,f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
<=> ~ p18(c20,f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24)) ),
inference(rewrite,[status(thm)],]) ).
tff(164,axiom,
~ p18(c20,f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p18_22) ).
tff(165,plain,
~ p18(c20,f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24)),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
( p18(c20,f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24))
<=> p18(c20,f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24)) ),
inference(rewrite,[status(thm)],]) ).
tff(167,axiom,
p18(c20,f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18_21) ).
tff(168,plain,
p18(c20,f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24)),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
( ( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) )
| p18(c20,f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p2(c20,c20)
| ~ p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p18(c20,f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24)) )
<=> ( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) )
| p18(c20,f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p2(c20,c20)
| ~ p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p18(c20,f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(170,plain,
( ( ~ p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p2(c20,c20)
| ~ p18(c20,f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24))
| p18(c20,f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24)) )
<=> ( p18(c20,f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p2(c20,c20)
| ~ p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p18(c20,f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(171,plain,
( ( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) )
| ~ p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p2(c20,c20)
| ~ p18(c20,f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24))
| p18(c20,f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24)) )
<=> ( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) )
| p18(c20,f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p2(c20,c20)
| ~ p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p18(c20,f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24)) ) ),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
( ( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) )
| ~ p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p2(c20,c20)
| ~ p18(c20,f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24))
| p18(c20,f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24)) )
<=> ( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) )
| p18(c20,f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p2(c20,c20)
| ~ p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p18(c20,f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24)) ) ),
inference(transitivity,[status(thm)],[171,169]) ).
tff(173,plain,
( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) )
| ~ p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p2(c20,c20)
| ~ p18(c20,f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24))
| p18(c20,f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24)) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p10(X26,X25)
| ~ p2(X27,X24)
| ~ p18(X27,X26)
| p18(X24,X25) )
| p18(c20,f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p2(c20,c20)
| ~ p10(f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24),f11(f13(f15(c20),f14(f4(c20),c22)),c23,c24))
| ~ p18(c20,f11(f13(f15(c20),f14(f4(c20),c21)),c23,c24)) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
$false,
inference(unit_resolution,[status(thm)],[174,168,165,162,35,152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN597-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n014.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 05:58:29 EDT 2022
% 0.12/0.33 % 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.
% 1.38/1.12 % SZS status Unsatisfiable
% 1.38/1.12 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------