TSTP Solution File: SYN628-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN628-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:56:41 EDT 2022
% Result : Unsatisfiable 69.29s 44.87s
% Output : Proof 69.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 66
% Syntax : Number of formulae : 122 ( 34 unt; 20 typ; 0 def)
% Number of atoms : 534 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 727 ( 337 ~; 333 |; 0 &)
% ( 57 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 42 ( 42 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 13 >; 8 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 343 ( 305 !; 0 ?; 343 :)
% Comments :
%------------------------------------------------------------------------------
tff(p9_type,type,
p9: ( $i * $i ) > $o ).
tff(f16_type,type,
f16: $i > $i ).
tff(f17_type,type,
f17: ( $i * $i ) > $i ).
tff(c27_type,type,
c27: $i ).
tff(c22_type,type,
c22: $i ).
tff(c28_type,type,
c28: $i ).
tff(f10_type,type,
f10: ( $i * $i ) > $i ).
tff(f11_type,type,
f11: $i > $i ).
tff(f12_type,type,
f12: $i > $i ).
tff(f13_type,type,
f13: $i > $i ).
tff(f14_type,type,
f14: $i > $i ).
tff(c29_type,type,
c29: $i ).
tff(f15_type,type,
f15: ( $i * $i ) > $i ).
tff(f7_type,type,
f7: ( $i * $i ) > $i ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(c25_type,type,
c25: $i ).
tff(c24_type,type,
c24: $i ).
tff(c23_type,type,
c23: $i ).
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(p20_type,type,
p20: ( $i * $i ) > $o ).
tff(1,plain,
^ [X40: $i] :
refl(
( p9(X40,X40)
<=> p9(X40,X40) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X40: $i] : p9(X40,X40)
<=> ! [X40: $i] : p9(X40,X40) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X40: $i] : p9(X40,X40)
<=> ! [X40: $i] : p9(X40,X40) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X40: $i] : p9(X40,X40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_2) ).
tff(5,plain,
! [X40: $i] : p9(X40,X40),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X40: $i] : p9(X40,X40),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X40: $i] : p9(X40,X40),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X40: $i] : p9(X40,X40)
| p9(c27,c27) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p9(c27,c27),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X57: $i,X56: $i,X55: $i,X58: $i] :
refl(
( ( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) )
<=> ( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X57: $i,X56: $i,X55: $i,X58: $i] :
( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) )
<=> ! [X57: $i,X56: $i,X55: $i,X58: $i] :
( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X57: $i,X56: $i,X55: $i,X58: $i] :
( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) )
<=> ! [X57: $i,X56: $i,X55: $i,X58: $i] :
( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X57: $i,X56: $i,X55: $i,X58: $i] :
trans(
monotonicity(
rewrite(
( ( p9(f17(X55,X56),f17(X57,X58))
| ~ p9(X55,X57) )
<=> ( ~ p9(X55,X57)
| p9(f17(X55,X56),f17(X57,X58)) ) )),
( ( p9(f17(X55,X56),f17(X57,X58))
| ~ p9(X55,X57)
| ~ p9(X56,X58) )
<=> ( ~ p9(X55,X57)
| p9(f17(X55,X56),f17(X57,X58))
| ~ p9(X56,X58) ) )),
rewrite(
( ( ~ p9(X55,X57)
| p9(f17(X55,X56),f17(X57,X58))
| ~ p9(X56,X58) )
<=> ( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) ) )),
( ( p9(f17(X55,X56),f17(X57,X58))
| ~ p9(X55,X57)
| ~ p9(X56,X58) )
<=> ( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X57: $i,X56: $i,X55: $i,X58: $i] :
( p9(f17(X55,X56),f17(X57,X58))
| ~ p9(X55,X57)
| ~ p9(X56,X58) )
<=> ! [X57: $i,X56: $i,X55: $i,X58: $i] :
( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X57: $i,X56: $i,X55: $i,X58: $i] :
( p9(f17(X55,X56),f17(X57,X58))
| ~ p9(X55,X57)
| ~ p9(X56,X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_29) ).
tff(16,plain,
! [X57: $i,X56: $i,X55: $i,X58: $i] :
( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X57: $i,X56: $i,X55: $i,X58: $i] :
( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X57: $i,X56: $i,X55: $i,X58: $i] :
( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X57: $i,X56: $i,X55: $i,X58: $i] :
( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( p9(c28,c22)
<=> p9(c28,c22) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
p9(c28,c22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_6) ).
tff(22,plain,
p9(c28,c22),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [X57: $i,X56: $i,X55: $i,X58: $i] :
( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) )
| ~ p9(c28,c22)
| ~ p9(c27,c27)
| p9(f17(c28,c27),f17(c22,c27)) )
<=> ( ~ ! [X57: $i,X56: $i,X55: $i,X58: $i] :
( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) )
| ~ p9(c28,c22)
| ~ p9(c27,c27)
| p9(f17(c28,c27),f17(c22,c27)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [X57: $i,X56: $i,X55: $i,X58: $i] :
( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) )
| ~ p9(c28,c22)
| ~ p9(c27,c27)
| p9(f17(c28,c27),f17(c22,c27)) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [X57: $i,X56: $i,X55: $i,X58: $i] :
( ~ p9(X55,X57)
| ~ p9(X56,X58)
| p9(f17(X55,X56),f17(X57,X58)) )
| ~ p9(c28,c22)
| ~ p9(c27,c27)
| p9(f17(c28,c27),f17(c22,c27)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
p9(f17(c28,c27),f17(c22,c27)),
inference(unit_resolution,[status(thm)],[25,22,19,9]) ).
tff(27,plain,
^ [X53: $i,X54: $i] :
refl(
( ( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) )
<=> ( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X53: $i,X54: $i] :
( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) )
<=> ! [X53: $i,X54: $i] :
( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X53: $i,X54: $i] :
( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) )
<=> ! [X53: $i,X54: $i] :
( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [X53: $i,X54: $i] :
rewrite(
( ( p9(f16(X53),f16(X54))
| ~ p9(X53,X54) )
<=> ( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X53: $i,X54: $i] :
( p9(f16(X53),f16(X54))
| ~ p9(X53,X54) )
<=> ! [X53: $i,X54: $i] :
( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [X53: $i,X54: $i] :
( p9(f16(X53),f16(X54))
| ~ p9(X53,X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_13) ).
tff(33,plain,
! [X53: $i,X54: $i] :
( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [X53: $i,X54: $i] :
( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [X53: $i,X54: $i] :
( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X53: $i,X54: $i] :
( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [X53: $i,X54: $i] :
( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) )
| ~ p9(f17(c28,c27),f17(c22,c27))
| p9(f16(f17(c28,c27)),f16(f17(c22,c27))) )
<=> ( ~ ! [X53: $i,X54: $i] :
( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) )
| ~ p9(f17(c28,c27),f17(c22,c27))
| p9(f16(f17(c28,c27)),f16(f17(c22,c27))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [X53: $i,X54: $i] :
( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) )
| ~ p9(f17(c28,c27),f17(c22,c27))
| p9(f16(f17(c28,c27)),f16(f17(c22,c27))) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [X53: $i,X54: $i] :
( ~ p9(X53,X54)
| p9(f16(X53),f16(X54)) )
| ~ p9(f17(c28,c27),f17(c22,c27))
| p9(f16(f17(c28,c27)),f16(f17(c22,c27))) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
p9(f16(f17(c28,c27)),f16(f17(c22,c27))),
inference(unit_resolution,[status(thm)],[39,36,26]) ).
tff(41,plain,
( ~ ! [X40: $i] : p9(X40,X40)
| p9(f11(f12(f13(f14(c29)))),f11(f12(f13(f14(c29))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
p9(f11(f12(f13(f14(c29)))),f11(f12(f13(f14(c29))))),
inference(unit_resolution,[status(thm)],[41,7]) ).
tff(43,plain,
^ [X4: $i] :
refl(
( p2(X4,X4)
<=> p2(X4,X4) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [X4: $i] : p2(X4,X4)
<=> ! [X4: $i] : p2(X4,X4) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [X4: $i] : p2(X4,X4)
<=> ! [X4: $i] : p2(X4,X4) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
! [X4: $i] : p2(X4,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_1) ).
tff(47,plain,
! [X4: $i] : p2(X4,X4),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [X4: $i] : p2(X4,X4),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [X4: $i] : p2(X4,X4),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ~ ! [X4: $i] : p2(X4,X4)
| p2(f7(c23,f8(c24,c25)),f7(c23,f8(c24,c25))) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
p2(f7(c23,f8(c24,c25)),f7(c23,f8(c24,c25))),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
^ [X49: $i,X52: $i,X51: $i,X50: $i] :
refl(
( ( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) )
<=> ( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [X49: $i,X52: $i,X51: $i,X50: $i] :
( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) )
<=> ! [X49: $i,X52: $i,X51: $i,X50: $i] :
( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [X49: $i,X52: $i,X51: $i,X50: $i] :
( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) )
<=> ! [X49: $i,X52: $i,X51: $i,X50: $i] :
( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
^ [X49: $i,X52: $i,X51: $i,X50: $i] :
trans(
monotonicity(
rewrite(
( ( p9(f15(X49,X50),f15(X51,X52))
| ~ p2(X49,X51) )
<=> ( ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) ) )),
( ( p9(f15(X49,X50),f15(X51,X52))
| ~ p2(X49,X51)
| ~ p9(X50,X52) )
<=> ( ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52))
| ~ p9(X50,X52) ) )),
rewrite(
( ( ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52))
| ~ p9(X50,X52) )
<=> ( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) ) )),
( ( p9(f15(X49,X50),f15(X51,X52))
| ~ p2(X49,X51)
| ~ p9(X50,X52) )
<=> ( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [X49: $i,X52: $i,X51: $i,X50: $i] :
( p9(f15(X49,X50),f15(X51,X52))
| ~ p2(X49,X51)
| ~ p9(X50,X52) )
<=> ! [X49: $i,X52: $i,X51: $i,X50: $i] :
( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [X49: $i,X52: $i,X51: $i,X50: $i] :
( p9(f15(X49,X50),f15(X51,X52))
| ~ p2(X49,X51)
| ~ p9(X50,X52) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_30) ).
tff(58,plain,
! [X49: $i,X52: $i,X51: $i,X50: $i] :
( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [X49: $i,X52: $i,X51: $i,X50: $i] :
( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [X49: $i,X52: $i,X51: $i,X50: $i] :
( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [X49: $i,X52: $i,X51: $i,X50: $i] :
( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [X49: $i,X52: $i,X51: $i,X50: $i] :
( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) )
| ~ p9(c28,c22)
| ~ p2(f7(c23,f8(c24,c25)),f7(c23,f8(c24,c25)))
| p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22)) )
<=> ( ~ ! [X49: $i,X52: $i,X51: $i,X50: $i] :
( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) )
| ~ p9(c28,c22)
| ~ p2(f7(c23,f8(c24,c25)),f7(c23,f8(c24,c25)))
| p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ~ ! [X49: $i,X52: $i,X51: $i,X50: $i] :
( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) )
| ~ p9(c28,c22)
| ~ p2(f7(c23,f8(c24,c25)),f7(c23,f8(c24,c25)))
| p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22)) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
( ~ ! [X49: $i,X52: $i,X51: $i,X50: $i] :
( ~ p9(X50,X52)
| ~ p2(X49,X51)
| p9(f15(X49,X50),f15(X51,X52)) )
| ~ p9(c28,c22)
| ~ p2(f7(c23,f8(c24,c25)),f7(c23,f8(c24,c25)))
| p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22)) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22)),
inference(unit_resolution,[status(thm)],[64,22,61,51]) ).
tff(66,plain,
^ [X43: $i,X45: $i,X46: $i,X44: $i] :
refl(
( ( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) )
<=> ( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) )
<=> ! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) )
<=> ! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
^ [X43: $i,X45: $i,X46: $i,X44: $i] :
trans(
monotonicity(
rewrite(
( ( p9(f10(X43,X44),f10(X45,X46))
| ~ p9(X43,X45) )
<=> ( ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) ) )),
( ( p9(f10(X43,X44),f10(X45,X46))
| ~ p9(X43,X45)
| ~ p9(X44,X46) )
<=> ( ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46))
| ~ p9(X44,X46) ) )),
rewrite(
( ( ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46))
| ~ p9(X44,X46) )
<=> ( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) ) )),
( ( p9(f10(X43,X44),f10(X45,X46))
| ~ p9(X43,X45)
| ~ p9(X44,X46) )
<=> ( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [X43: $i,X45: $i,X46: $i,X44: $i] :
( p9(f10(X43,X44),f10(X45,X46))
| ~ p9(X43,X45)
| ~ p9(X44,X46) )
<=> ! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [X43: $i,X45: $i,X46: $i,X44: $i] :
( p9(f10(X43,X44),f10(X45,X46))
| ~ p9(X43,X45)
| ~ p9(X44,X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_31) ).
tff(72,plain,
! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ( ~ ! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) )
| ~ p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22))
| p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29))))))
| ~ p9(f11(f12(f13(f14(c29)))),f11(f12(f13(f14(c29))))) )
<=> ( ~ ! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) )
| ~ p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22))
| p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29))))))
| ~ p9(f11(f12(f13(f14(c29)))),f11(f12(f13(f14(c29))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ( ~ p9(f11(f12(f13(f14(c29)))),f11(f12(f13(f14(c29)))))
| ~ p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22))
| p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29)))))) )
<=> ( ~ p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22))
| p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29))))))
| ~ p9(f11(f12(f13(f14(c29)))),f11(f12(f13(f14(c29))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ( ~ ! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) )
| ~ p9(f11(f12(f13(f14(c29)))),f11(f12(f13(f14(c29)))))
| ~ p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22))
| p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29)))))) )
<=> ( ~ ! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) )
| ~ p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22))
| p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29))))))
| ~ p9(f11(f12(f13(f14(c29)))),f11(f12(f13(f14(c29))))) ) ),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( ( ~ ! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) )
| ~ p9(f11(f12(f13(f14(c29)))),f11(f12(f13(f14(c29)))))
| ~ p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22))
| p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29)))))) )
<=> ( ~ ! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) )
| ~ p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22))
| p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29))))))
| ~ p9(f11(f12(f13(f14(c29)))),f11(f12(f13(f14(c29))))) ) ),
inference(transitivity,[status(thm)],[78,76]) ).
tff(80,plain,
( ~ ! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) )
| ~ p9(f11(f12(f13(f14(c29)))),f11(f12(f13(f14(c29)))))
| ~ p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22))
| p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29)))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [X43: $i,X45: $i,X46: $i,X44: $i] :
( ~ p9(X44,X46)
| ~ p9(X43,X45)
| p9(f10(X43,X44),f10(X45,X46)) )
| ~ p9(f15(f7(c23,f8(c24,c25)),c28),f15(f7(c23,f8(c24,c25)),c22))
| p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29))))))
| ~ p9(f11(f12(f13(f14(c29)))),f11(f12(f13(f14(c29))))) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29)))))),
inference(unit_resolution,[status(thm)],[81,75,65,42]) ).
tff(83,plain,
( ~ p20(f16(f17(c22,c27)),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29))))))
<=> ~ p20(f16(f17(c22,c27)),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29)))))) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
~ p20(f16(f17(c22,c27)),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p20_35) ).
tff(85,plain,
~ p20(f16(f17(c22,c27)),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29)))))),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( p20(f16(f17(c28,c27)),f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))))
<=> p20(f16(f17(c28,c27)),f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29)))))) ),
inference(rewrite,[status(thm)],]) ).
tff(87,axiom,
p20(f16(f17(c28,c27)),f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20_34) ).
tff(88,plain,
p20(f16(f17(c28,c27)),f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29)))))),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
^ [X14: $i,X12: $i,X11: $i,X13: $i] :
refl(
( ( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) )
<=> ( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) )
<=> ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) )
<=> ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [X14: $i,X12: $i,X11: $i,X13: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p20(X11,X12)
| ~ p9(X13,X11) )
<=> ( ~ p9(X13,X11)
| p20(X11,X12) ) )),
( ( p20(X11,X12)
| ~ p9(X13,X11)
| ~ p9(X14,X12) )
<=> ( ~ p9(X13,X11)
| p20(X11,X12)
| ~ p9(X14,X12) ) )),
rewrite(
( ( ~ p9(X13,X11)
| p20(X11,X12)
| ~ p9(X14,X12) )
<=> ( ~ p9(X13,X11)
| ~ p9(X14,X12)
| p20(X11,X12) ) )),
( ( p20(X11,X12)
| ~ p9(X13,X11)
| ~ p9(X14,X12) )
<=> ( ~ p9(X13,X11)
| ~ p9(X14,X12)
| p20(X11,X12) ) )),
( ( p20(X11,X12)
| ~ p9(X13,X11)
| ~ p9(X14,X12)
| ~ p20(X13,X14) )
<=> ( ~ p9(X13,X11)
| ~ p9(X14,X12)
| p20(X11,X12)
| ~ p20(X13,X14) ) )),
rewrite(
( ( ~ p9(X13,X11)
| ~ p9(X14,X12)
| p20(X11,X12)
| ~ p20(X13,X14) )
<=> ( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) ) )),
( ( p20(X11,X12)
| ~ p9(X13,X11)
| ~ p9(X14,X12)
| ~ p20(X13,X14) )
<=> ( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( p20(X11,X12)
| ~ p9(X13,X11)
| ~ p9(X14,X12)
| ~ p20(X13,X14) )
<=> ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( p20(X11,X12)
| ~ p9(X13,X11)
| ~ p9(X14,X12)
| ~ p20(X13,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20_26) ).
tff(95,plain,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) )
| ~ p9(f16(f17(c28,c27)),f16(f17(c22,c27)))
| ~ p20(f16(f17(c28,c27)),f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))))
| ~ p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29))))))
| p20(f16(f17(c22,c27)),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29)))))) )
<=> ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) )
| ~ p9(f16(f17(c28,c27)),f16(f17(c22,c27)))
| ~ p20(f16(f17(c28,c27)),f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))))
| ~ p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29))))))
| p20(f16(f17(c22,c27)),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) )
| ~ p9(f16(f17(c28,c27)),f16(f17(c22,c27)))
| ~ p20(f16(f17(c28,c27)),f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))))
| ~ p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29))))))
| p20(f16(f17(c22,c27)),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29)))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
( ~ p9(X13,X11)
| ~ p20(X13,X14)
| ~ p9(X14,X12)
| p20(X11,X12) )
| ~ p9(f16(f17(c28,c27)),f16(f17(c22,c27)))
| ~ p20(f16(f17(c28,c27)),f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))))
| ~ p9(f10(f15(f7(c23,f8(c24,c25)),c28),f11(f12(f13(f14(c29))))),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29))))))
| p20(f16(f17(c22,c27)),f10(f15(f7(c23,f8(c24,c25)),c22),f11(f12(f13(f14(c29)))))) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
$false,
inference(unit_resolution,[status(thm)],[101,98,88,85,82,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN628-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 06:17:31 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.
% 69.29/44.87 % SZS status Unsatisfiable
% 69.29/44.87 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------