TSTP Solution File: SYN576-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN576-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 23:56:29 EDT 2022
% Result : Unsatisfiable 0.76s 0.74s
% Output : Proof 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 73
% Syntax : Number of formulae : 146 ( 46 unt; 15 typ; 0 def)
% Number of atoms : 808 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 1145 ( 524 ~; 542 |; 0 &)
% ( 79 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 56 ( 56 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 : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 453 ( 410 !; 0 ?; 453 :)
% Comments :
%------------------------------------------------------------------------------
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(f7_type,type,
f7: ( $i * $i ) > $i ).
tff(f3_type,type,
f3: ( $i * $i ) > $i ).
tff(c16_type,type,
c16: $i ).
tff(c15_type,type,
c15: $i ).
tff(f9_type,type,
f9: ( $i * $i * $i ) > $i ).
tff(c14_type,type,
c14: $i ).
tff(c13_type,type,
c13: $i ).
tff(p4_type,type,
p4: ( $i * $i ) > $o ).
tff(p8_type,type,
p8: ( $i * $i ) > $o ).
tff(p12_type,type,
p12: ( $i * $i ) > $o ).
tff(f6_type,type,
f6: $i > $i ).
tff(p11_type,type,
p11: ( $i * $i ) > $o ).
tff(f10_type,type,
f10: $i > $i ).
tff(p5_type,type,
p5: ( $i * $i ) > $o ).
tff(1,plain,
^ [X34: $i] :
refl(
( p4(X34,X34)
<=> p4(X34,X34) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X34: $i] : p4(X34,X34)
<=> ! [X34: $i] : p4(X34,X34) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X34: $i] : p4(X34,X34)
<=> ! [X34: $i] : p4(X34,X34) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X34: $i] : p4(X34,X34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_3) ).
tff(5,plain,
! [X34: $i] : p4(X34,X34),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X34: $i] : p4(X34,X34),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X34: $i] : p4(X34,X34),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X34: $i] : p4(X34,X34)
| p4(c13,c13) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p4(c13,c13),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X42: $i] :
refl(
( p8(X42,X42)
<=> p8(X42,X42) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X42: $i] : p8(X42,X42)
<=> ! [X42: $i] : p8(X42,X42) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X42: $i] : p8(X42,X42)
<=> ! [X42: $i] : p8(X42,X42) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X42: $i] : p8(X42,X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_1) ).
tff(14,plain,
! [X42: $i] : p8(X42,X42),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X42: $i] : p8(X42,X42),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X42: $i] : p8(X42,X42),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X42: $i] : p8(X42,X42)
| p8(c14,c14) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
p8(c14,c14),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X22: $i,X23: $i] :
refl(
( p2(f3(X22,X23),f3(X23,X22))
<=> p2(f3(X22,X23),f3(X23,X22)) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X22: $i,X23: $i] : p2(f3(X22,X23),f3(X23,X22))
<=> ! [X22: $i,X23: $i] : p2(f3(X22,X23),f3(X23,X22)) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X22: $i,X23: $i] : p2(f3(X22,X23),f3(X23,X22))
<=> ! [X22: $i,X23: $i] : p2(f3(X22,X23),f3(X23,X22)) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [X22: $i,X23: $i] : p2(f3(X22,X23),f3(X23,X22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_8) ).
tff(23,plain,
! [X22: $i,X23: $i] : p2(f3(X22,X23),f3(X23,X22)),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X22: $i,X23: $i] : p2(f3(X22,X23),f3(X23,X22)),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X22: $i,X23: $i] : p2(f3(X22,X23),f3(X23,X22)),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [X22: $i,X23: $i] : p2(f3(X22,X23),f3(X23,X22))
| p2(f3(c16,c15),f3(c15,c16)) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
p2(f3(c16,c15),f3(c15,c16)),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
^ [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
refl(
( ( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) )
<=> ( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) )
<=> ! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) )
<=> ! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
^ [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p2(f9(X28,X29,X30),f9(X31,X32,X33))
| ~ p4(X28,X31) )
<=> ( ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) ) )),
( ( p2(f9(X28,X29,X30),f9(X31,X32,X33))
| ~ p4(X28,X31)
| ~ p8(X29,X32) )
<=> ( ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33))
| ~ p8(X29,X32) ) )),
rewrite(
( ( ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33))
| ~ p8(X29,X32) )
<=> ( ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) ) )),
( ( p2(f9(X28,X29,X30),f9(X31,X32,X33))
| ~ p4(X28,X31)
| ~ p8(X29,X32) )
<=> ( ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) ) )),
( ( p2(f9(X28,X29,X30),f9(X31,X32,X33))
| ~ p4(X28,X31)
| ~ p8(X29,X32)
| ~ p2(X30,X33) )
<=> ( ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33))
| ~ p2(X30,X33) ) )),
rewrite(
( ( ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33))
| ~ p2(X30,X33) )
<=> ( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) ) )),
( ( p2(f9(X28,X29,X30),f9(X31,X32,X33))
| ~ p4(X28,X31)
| ~ p8(X29,X32)
| ~ p2(X30,X33) )
<=> ( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( p2(f9(X28,X29,X30),f9(X31,X32,X33))
| ~ p4(X28,X31)
| ~ p8(X29,X32)
| ~ p2(X30,X33) )
<=> ! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( p2(f9(X28,X29,X30),f9(X31,X32,X33))
| ~ p4(X28,X31)
| ~ p8(X29,X32)
| ~ p2(X30,X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_20) ).
tff(34,plain,
! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ( ~ ! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) )
| ~ p2(f3(c16,c15),f3(c15,c16))
| p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| ~ p4(c13,c13)
| ~ p8(c14,c14) )
<=> ( ~ ! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) )
| ~ p2(f3(c16,c15),f3(c15,c16))
| p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| ~ p4(c13,c13)
| ~ p8(c14,c14) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ( ~ p2(f3(c16,c15),f3(c15,c16))
| ~ p8(c14,c14)
| ~ p4(c13,c13)
| p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16))) )
<=> ( ~ p2(f3(c16,c15),f3(c15,c16))
| p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| ~ p4(c13,c13)
| ~ p8(c14,c14) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( ~ ! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) )
| ~ p2(f3(c16,c15),f3(c15,c16))
| ~ p8(c14,c14)
| ~ p4(c13,c13)
| p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16))) )
<=> ( ~ ! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) )
| ~ p2(f3(c16,c15),f3(c15,c16))
| p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| ~ p4(c13,c13)
| ~ p8(c14,c14) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( ~ ! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) )
| ~ p2(f3(c16,c15),f3(c15,c16))
| ~ p8(c14,c14)
| ~ p4(c13,c13)
| p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16))) )
<=> ( ~ ! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) )
| ~ p2(f3(c16,c15),f3(c15,c16))
| p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| ~ p4(c13,c13)
| ~ p8(c14,c14) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
( ~ ! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) )
| ~ p2(f3(c16,c15),f3(c15,c16))
| ~ p8(c14,c14)
| ~ p4(c13,c13)
| p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16))) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [X31: $i,X32: $i,X30: $i,X29: $i,X28: $i,X33: $i] :
( ~ p2(X30,X33)
| ~ p8(X29,X32)
| ~ p4(X28,X31)
| p2(f9(X28,X29,X30),f9(X31,X32,X33)) )
| ~ p2(f3(c16,c15),f3(c15,c16))
| p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| ~ p4(c13,c13)
| ~ p8(c14,c14) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16))),
inference(unit_resolution,[status(thm)],[43,37,27,18,9]) ).
tff(45,plain,
^ [X25: $i,X27: $i,X26: $i,X24: $i] :
refl(
( ( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) )
<=> ( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) )
<=> ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) )
<=> ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
^ [X25: $i,X27: $i,X26: $i,X24: $i] :
trans(
monotonicity(
rewrite(
( ( p2(f7(X24,X25),f7(X26,X27))
| ~ p2(X24,X26) )
<=> ( ~ p2(X24,X26)
| p2(f7(X24,X25),f7(X26,X27)) ) )),
( ( p2(f7(X24,X25),f7(X26,X27))
| ~ p2(X24,X26)
| ~ p2(X25,X27) )
<=> ( ~ p2(X24,X26)
| p2(f7(X24,X25),f7(X26,X27))
| ~ p2(X25,X27) ) )),
rewrite(
( ( ~ p2(X24,X26)
| p2(f7(X24,X25),f7(X26,X27))
| ~ p2(X25,X27) )
<=> ( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) ) )),
( ( p2(f7(X24,X25),f7(X26,X27))
| ~ p2(X24,X26)
| ~ p2(X25,X27) )
<=> ( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( p2(f7(X24,X25),f7(X26,X27))
| ~ p2(X24,X26)
| ~ p2(X25,X27) )
<=> ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,axiom,
! [X25: $i,X27: $i,X26: $i,X24: $i] :
( p2(f7(X24,X25),f7(X26,X27))
| ~ p2(X24,X26)
| ~ p2(X25,X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_19) ).
tff(51,plain,
! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) ),
inference(modus_ponens,[status(thm)],[53,46]) ).
tff(55,plain,
( ( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) )
| ~ p2(f3(c16,c15),f3(c15,c16))
| ~ p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16))) )
<=> ( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) )
| ~ p2(f3(c16,c15),f3(c15,c16))
| ~ p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ( ~ p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| ~ p2(f3(c16,c15),f3(c15,c16))
| p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16))) )
<=> ( ~ p2(f3(c16,c15),f3(c15,c16))
| ~ p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) )
| ~ p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| ~ p2(f3(c16,c15),f3(c15,c16))
| p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16))) )
<=> ( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) )
| ~ p2(f3(c16,c15),f3(c15,c16))
| ~ p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16))) ) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) )
| ~ p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| ~ p2(f3(c16,c15),f3(c15,c16))
| p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16))) )
<=> ( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) )
| ~ p2(f3(c16,c15),f3(c15,c16))
| ~ p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16))) ) ),
inference(transitivity,[status(thm)],[57,55]) ).
tff(59,plain,
( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) )
| ~ p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| ~ p2(f3(c16,c15),f3(c15,c16))
| p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16))) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( ~ ! [X25: $i,X27: $i,X26: $i,X24: $i] :
( ~ p2(X24,X26)
| ~ p2(X25,X27)
| p2(f7(X24,X25),f7(X26,X27)) )
| ~ p2(f3(c16,c15),f3(c15,c16))
| ~ p2(f9(c13,c14,f3(c16,c15)),f9(c13,c14,f3(c15,c16)))
| p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16))) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16))),
inference(unit_resolution,[status(thm)],[60,54,27,44]) ).
tff(62,plain,
^ [X12: $i,X11: $i,X10: $i] :
refl(
( ( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
<=> ( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
<=> ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
<=> ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
^ [X12: $i,X11: $i,X10: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10))
| ~ p12(X12,f6(X10)) )
<=> ( ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) ) )),
( ( p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10))
| ~ p12(X12,f6(X10))
| ~ p12(X11,f6(X10)) )
<=> ( ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10))
| ~ p12(X11,f6(X10)) ) )),
rewrite(
( ( ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10))
| ~ p12(X11,f6(X10)) )
<=> ( ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) ) )),
( ( p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10))
| ~ p12(X12,f6(X10))
| ~ p12(X11,f6(X10)) )
<=> ( ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) ) )),
( ( p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10))
| ~ p12(X12,f6(X10))
| ~ p12(X11,f6(X10))
| ~ p11(f10(X11),f10(X12)) )
<=> ( ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10))
| ~ p11(f10(X11),f10(X12)) ) )),
rewrite(
( ( ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10))
| ~ p11(f10(X11),f10(X12)) )
<=> ( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) ) )),
( ( p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10))
| ~ p12(X12,f6(X10))
| ~ p12(X11,f6(X10))
| ~ p11(f10(X11),f10(X12)) )
<=> ( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [X12: $i,X11: $i,X10: $i] :
( p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10))
| ~ p12(X12,f6(X10))
| ~ p12(X11,f6(X10))
| ~ p11(f10(X11),f10(X12)) )
<=> ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,axiom,
! [X12: $i,X11: $i,X10: $i] :
( p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10))
| ~ p12(X12,f6(X10))
| ~ p12(X11,f6(X10))
| ~ p11(f10(X11),f10(X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_22) ).
tff(68,plain,
! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,plain,
( ~ p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13))
<=> ~ p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13)) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
~ p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p12_17) ).
tff(74,plain,
~ p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13)),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
( p12(c16,f6(c13))
<=> p12(c16,f6(c13)) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
p12(c16,f6(c13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_6) ).
tff(77,plain,
p12(c16,f6(c13)),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( p12(c15,f6(c13))
<=> p12(c15,f6(c13)) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
p12(c15,f6(c13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_5) ).
tff(80,plain,
p12(c15,f6(c13)),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
( ( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
| ~ p11(f10(c15),f10(c16))
| ~ p12(c15,f6(c13))
| ~ p12(c16,f6(c13))
| p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13)) )
<=> ( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
| ~ p11(f10(c15),f10(c16))
| ~ p12(c15,f6(c13))
| ~ p12(c16,f6(c13))
| p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
| ~ p11(f10(c15),f10(c16))
| ~ p12(c15,f6(c13))
| ~ p12(c16,f6(c13))
| p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13)) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
| ~ p11(f10(c15),f10(c16))
| ~ p12(c15,f6(c13))
| ~ p12(c16,f6(c13))
| p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13)) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
~ p11(f10(c15),f10(c16)),
inference(unit_resolution,[status(thm)],[83,80,77,74,71]) ).
tff(85,plain,
^ [X4: $i,X5: $i] :
refl(
( ( p11(X5,X4)
| p11(X4,X5) )
<=> ( p11(X5,X4)
| p11(X4,X5) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [X4: $i,X5: $i] :
( p11(X5,X4)
| p11(X4,X5) )
<=> ! [X4: $i,X5: $i] :
( p11(X5,X4)
| p11(X4,X5) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [X4: $i,X5: $i] :
( p11(X5,X4)
| p11(X4,X5) )
<=> ! [X4: $i,X5: $i] :
( p11(X5,X4)
| p11(X4,X5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
^ [X4: $i,X5: $i] :
rewrite(
( ( p11(X4,X5)
| p11(X5,X4) )
<=> ( p11(X5,X4)
| p11(X4,X5) ) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [X4: $i,X5: $i] :
( p11(X4,X5)
| p11(X5,X4) )
<=> ! [X4: $i,X5: $i] :
( p11(X5,X4)
| p11(X4,X5) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,axiom,
! [X4: $i,X5: $i] :
( p11(X4,X5)
| p11(X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_7) ).
tff(91,plain,
! [X4: $i,X5: $i] :
( p11(X5,X4)
| p11(X4,X5) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [X4: $i,X5: $i] :
( p11(X5,X4)
| p11(X4,X5) ),
inference(modus_ponens,[status(thm)],[91,87]) ).
tff(93,plain,
! [X4: $i,X5: $i] :
( p11(X5,X4)
| p11(X4,X5) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [X4: $i,X5: $i] :
( p11(X5,X4)
| p11(X4,X5) ),
inference(modus_ponens,[status(thm)],[93,86]) ).
tff(95,plain,
( ( ~ ! [X4: $i,X5: $i] :
( p11(X5,X4)
| p11(X4,X5) )
| p11(f10(c15),f10(c16))
| p11(f10(c16),f10(c15)) )
<=> ( ~ ! [X4: $i,X5: $i] :
( p11(X5,X4)
| p11(X4,X5) )
| p11(f10(c15),f10(c16))
| p11(f10(c16),f10(c15)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ~ ! [X4: $i,X5: $i] :
( p11(X5,X4)
| p11(X4,X5) )
| p11(f10(c15),f10(c16))
| p11(f10(c16),f10(c15)) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
( ~ ! [X4: $i,X5: $i] :
( p11(X5,X4)
| p11(X4,X5) )
| p11(f10(c15),f10(c16))
| p11(f10(c16),f10(c15)) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
p11(f10(c16),f10(c15)),
inference(unit_resolution,[status(thm)],[97,94,84]) ).
tff(99,plain,
( ( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
| ~ p12(c15,f6(c13))
| ~ p12(c16,f6(c13))
| ~ p11(f10(c16),f10(c15))
| p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) )
<=> ( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
| ~ p12(c15,f6(c13))
| ~ p12(c16,f6(c13))
| ~ p11(f10(c16),f10(c15))
| p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ( ~ p11(f10(c16),f10(c15))
| ~ p12(c16,f6(c13))
| ~ p12(c15,f6(c13))
| p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) )
<=> ( ~ p12(c15,f6(c13))
| ~ p12(c16,f6(c13))
| ~ p11(f10(c16),f10(c15))
| p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
| ~ p11(f10(c16),f10(c15))
| ~ p12(c16,f6(c13))
| ~ p12(c15,f6(c13))
| p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) )
<=> ( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
| ~ p12(c15,f6(c13))
| ~ p12(c16,f6(c13))
| ~ p11(f10(c16),f10(c15))
| p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) ) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
| ~ p11(f10(c16),f10(c15))
| ~ p12(c16,f6(c13))
| ~ p12(c15,f6(c13))
| p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) )
<=> ( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
| ~ p12(c15,f6(c13))
| ~ p12(c16,f6(c13))
| ~ p11(f10(c16),f10(c15))
| p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) ) ),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,plain,
( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
| ~ p11(f10(c16),f10(c15))
| ~ p12(c16,f6(c13))
| ~ p12(c15,f6(c13))
| p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
( ~ ! [X12: $i,X11: $i,X10: $i] :
( ~ p11(f10(X11),f10(X12))
| ~ p12(X11,f6(X10))
| ~ p12(X12,f6(X10))
| p12(f7(f9(X10,c14,f3(X11,X12)),f3(X11,X12)),f6(X10)) )
| ~ p12(c15,f6(c13))
| ~ p12(c16,f6(c13))
| ~ p11(f10(c16),f10(c15))
| p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)),
inference(unit_resolution,[status(thm)],[104,80,77,71,98]) ).
tff(106,plain,
^ [X37: $i] :
refl(
( p5(X37,X37)
<=> p5(X37,X37) )),
inference(bind,[status(th)],]) ).
tff(107,plain,
( ! [X37: $i] : p5(X37,X37)
<=> ! [X37: $i] : p5(X37,X37) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [X37: $i] : p5(X37,X37)
<=> ! [X37: $i] : p5(X37,X37) ),
inference(rewrite,[status(thm)],]) ).
tff(109,axiom,
! [X37: $i] : p5(X37,X37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_4) ).
tff(110,plain,
! [X37: $i] : p5(X37,X37),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [X37: $i] : p5(X37,X37),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [X37: $i] : p5(X37,X37),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
( ~ ! [X37: $i] : p5(X37,X37)
| p5(f6(c13),f6(c13)) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
p5(f6(c13),f6(c13)),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
^ [X9: $i,X6: $i,X7: $i,X8: $i] :
refl(
( ( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) )
<=> ( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) ) )),
inference(bind,[status(th)],]) ).
tff(116,plain,
( ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) )
<=> ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) )
<=> ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
^ [X9: $i,X6: $i,X7: $i,X8: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p12(X6,X7)
| ~ p2(X8,X6) )
<=> ( ~ p2(X8,X6)
| p12(X6,X7) ) )),
( ( p12(X6,X7)
| ~ p2(X8,X6)
| ~ p5(X9,X7) )
<=> ( ~ p2(X8,X6)
| p12(X6,X7)
| ~ p5(X9,X7) ) )),
rewrite(
( ( ~ p2(X8,X6)
| p12(X6,X7)
| ~ p5(X9,X7) )
<=> ( ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) ) )),
( ( p12(X6,X7)
| ~ p2(X8,X6)
| ~ p5(X9,X7) )
<=> ( ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) ) )),
( ( p12(X6,X7)
| ~ p2(X8,X6)
| ~ p5(X9,X7)
| ~ p12(X8,X9) )
<=> ( ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7)
| ~ p12(X8,X9) ) )),
rewrite(
( ( ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7)
| ~ p12(X8,X9) )
<=> ( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) ) )),
( ( p12(X6,X7)
| ~ p2(X8,X6)
| ~ p5(X9,X7)
| ~ p12(X8,X9) )
<=> ( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) ) )),
inference(bind,[status(th)],]) ).
tff(119,plain,
( ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( p12(X6,X7)
| ~ p2(X8,X6)
| ~ p5(X9,X7)
| ~ p12(X8,X9) )
<=> ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,axiom,
! [X9: $i,X6: $i,X7: $i,X8: $i] :
( p12(X6,X7)
| ~ p2(X8,X6)
| ~ p5(X9,X7)
| ~ p12(X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_16) ).
tff(121,plain,
! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) ),
inference(modus_ponens,[status(thm)],[121,117]) ).
tff(123,plain,
! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) ),
inference(modus_ponens,[status(thm)],[123,116]) ).
tff(125,plain,
( ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) )
| p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13))
| ~ p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)))
| ~ p5(f6(c13),f6(c13))
| ~ p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) )
<=> ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) )
| p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13))
| ~ p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)))
| ~ p5(f6(c13),f6(c13))
| ~ p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ( ~ p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13))
| ~ p5(f6(c13),f6(c13))
| ~ p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)))
| p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13)) )
<=> ( p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13))
| ~ p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)))
| ~ p5(f6(c13),f6(c13))
| ~ p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
( ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) )
| ~ p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13))
| ~ p5(f6(c13),f6(c13))
| ~ p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)))
| p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13)) )
<=> ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) )
| p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13))
| ~ p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)))
| ~ p5(f6(c13),f6(c13))
| ~ p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) ) ),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
( ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) )
| ~ p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13))
| ~ p5(f6(c13),f6(c13))
| ~ p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)))
| p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13)) )
<=> ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) )
| p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13))
| ~ p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)))
| ~ p5(f6(c13),f6(c13))
| ~ p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) ) ),
inference(transitivity,[status(thm)],[127,125]) ).
tff(129,plain,
( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) )
| ~ p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13))
| ~ p5(f6(c13),f6(c13))
| ~ p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)))
| p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13)) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
( ~ p12(X8,X9)
| ~ p5(X9,X7)
| ~ p2(X8,X6)
| p12(X6,X7) )
| p12(f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)),f6(c13))
| ~ p2(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f7(f9(c13,c14,f3(c15,c16)),f3(c15,c16)))
| ~ p5(f6(c13),f6(c13))
| ~ p12(f7(f9(c13,c14,f3(c16,c15)),f3(c16,c15)),f6(c13)) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
$false,
inference(unit_resolution,[status(thm)],[130,124,74,114,105,61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN576-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.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 05:59:25 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.
% 0.76/0.74 % SZS status Unsatisfiable
% 0.76/0.74 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------