TSTP Solution File: SYN687-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN687-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 23:56:56 EDT 2022
% Result : Unsatisfiable 0.68s 0.67s
% Output : Proof 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 52
% Syntax : Number of formulae : 90 ( 18 unt; 22 typ; 0 def)
% Number of atoms : 365 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 478 ( 200 ~; 242 |; 0 &)
% ( 36 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 14 >; 14 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-2 aty)
% Number of variables : 235 ( 214 !; 0 ?; 235 :)
% Comments :
%------------------------------------------------------------------------------
tff(p4_type,type,
p4: ( $i * $i ) > $o ).
tff(f5_type,type,
f5: ( $i * $i ) > $i ).
tff(f14_type,type,
f14: ( $i * $i ) > $i ).
tff(f30_type,type,
f30: ( $i * $i ) > $i ).
tff(c39_type,type,
c39: $i ).
tff(f32_type,type,
f32: ( $i * $i ) > $i ).
tff(c37_type,type,
c37: $i ).
tff(c45_type,type,
c45: $i ).
tff(f16_type,type,
f16: ( $i * $i ) > $i ).
tff(f26_type,type,
f26: ( $i * $i ) > $i ).
tff(f28_type,type,
f28: ( $i * $i ) > $i ).
tff(c47_type,type,
c47: $i ).
tff(f18_type,type,
f18: ( $i * $i ) > $i ).
tff(c46_type,type,
c46: $i ).
tff(c40_type,type,
c40: $i ).
tff(f9_type,type,
f9: ( $i * $i ) > $i ).
tff(f7_type,type,
f7: ( $i * $i ) > $i ).
tff(c38_type,type,
c38: $i ).
tff(p34_type,type,
p34: ( $i * $i ) > $o ).
tff(c36_type,type,
c36: $i ).
tff(p35_type,type,
p35: ( $i * $i ) > $o ).
tff(f12_type,type,
f12: ( $i * $i ) > $i ).
tff(1,plain,
^ [X130: $i] :
refl(
( ~ p4(f5(X130,f7(c38,X130)),f5(f9(c39,X130),f7(c38,X130)))
<=> ~ p4(f5(X130,f7(c38,X130)),f5(f9(c39,X130),f7(c38,X130))) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X130: $i] : ~ p4(f5(X130,f7(c38,X130)),f5(f9(c39,X130),f7(c38,X130)))
<=> ! [X130: $i] : ~ p4(f5(X130,f7(c38,X130)),f5(f9(c39,X130),f7(c38,X130))) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X130: $i] : ~ p4(f5(X130,f7(c38,X130)),f5(f9(c39,X130),f7(c38,X130)))
<=> ! [X130: $i] : ~ p4(f5(X130,f7(c38,X130)),f5(f9(c39,X130),f7(c38,X130))) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X130: $i] : ~ p4(f5(X130,f7(c38,X130)),f5(f9(c39,X130),f7(c38,X130))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p4_40) ).
tff(5,plain,
! [X130: $i] : ~ p4(f5(X130,f7(c38,X130)),f5(f9(c39,X130),f7(c38,X130))),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X130: $i] : ~ p4(f5(X130,f7(c38,X130)),f5(f9(c39,X130),f7(c38,X130))),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X130: $i] : ~ p4(f5(X130,f7(c38,X130)),f5(f9(c39,X130),f7(c38,X130))),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X130: $i] : ~ p4(f5(X130,f7(c38,X130)),f5(f9(c39,X130),f7(c38,X130)))
| ~ p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
~ p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39)))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X119: $i,X116: $i,X117: $i] :
refl(
( ( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) )
<=> ( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X119: $i,X116: $i,X117: $i] :
( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) )
<=> ! [X119: $i,X116: $i,X117: $i] :
( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X119: $i,X116: $i,X117: $i] :
( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) )
<=> ! [X119: $i,X116: $i,X117: $i] :
( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X119: $i,X116: $i,X117: $i] :
trans(
monotonicity(
rewrite(
( ( p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p34(c36,X116) )
<=> ( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119)) ) )),
( ( p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p34(c36,X116)
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) )
<=> ( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) ) )),
rewrite(
( ( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) )
<=> ( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) ) )),
( ( p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p34(c36,X116)
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) )
<=> ( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X119: $i,X116: $i,X117: $i] :
( p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p34(c36,X116)
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) )
<=> ! [X119: $i,X116: $i,X117: $i] :
( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X119: $i,X116: $i,X117: $i] :
( p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p34(c36,X116)
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_58) ).
tff(16,plain,
! [X119: $i,X116: $i,X117: $i] :
( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X119: $i,X116: $i,X117: $i] :
( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X119: $i,X116: $i,X117: $i] :
( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X119: $i,X116: $i,X117: $i] :
( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( p34(c36,c37)
<=> p34(c36,c37) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
p34(c36,c37),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p34_19) ).
tff(22,plain,
p34(c36,c37),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [X119: $i,X116: $i,X117: $i] :
( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) )
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39))))
| ~ p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))) )
<=> ( ~ ! [X119: $i,X116: $i,X117: $i] :
( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) )
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39))))
| ~ p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [X119: $i,X116: $i,X117: $i] :
( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) )
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39))))
| ~ p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [X119: $i,X116: $i,X117: $i] :
( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p4(f5(f9(X117,f26(f28(c46,X116),X117)),f30(f32(c45,X116),X117)),f5(f9(X117,f26(f28(c47,X116),X117)),f30(f32(c45,X116),X117))) )
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39))))
| ~ p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),
inference(unit_resolution,[status(thm)],[25,22,19,9]) ).
tff(27,plain,
^ [X107: $i,X106: $i,X108: $i] :
refl(
( ( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) )
<=> ( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) )
<=> ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) )
<=> ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_56) ).
tff(31,plain,
! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ( ~ ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) )
| ~ p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))))
| p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))) )
<=> ( ~ ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) )
| ~ p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))))
| p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))
| ~ p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))) )
<=> ( ~ p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))))
| p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ~ ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) )
| p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))
| ~ p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))) )
<=> ( ~ ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) )
| ~ p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))))
| p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) )
| p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))
| ~ p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))) )
<=> ( ~ ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) )
| ~ p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))))
| p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) )
| p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))
| ~ p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| ~ p4(f5(X106,f14(f16(f18(c40,X106),X107),X108)),f5(X107,f14(f16(f18(c40,X106),X107),X108))) )
| ~ p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))))
| p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
~ p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))),
inference(unit_resolution,[status(thm)],[39,33,26]) ).
tff(41,plain,
^ [X107: $i,X106: $i,X108: $i] :
refl(
( ( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| p35(f12(c37,f14(f16(f18(c40,X106),X107),X108)),X108) )
<=> ( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| p35(f12(c37,f14(f16(f18(c40,X106),X107),X108)),X108) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| p35(f12(c37,f14(f16(f18(c40,X106),X107),X108)),X108) )
<=> ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| p35(f12(c37,f14(f16(f18(c40,X106),X107),X108)),X108) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| p35(f12(c37,f14(f16(f18(c40,X106),X107),X108)),X108) )
<=> ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| p35(f12(c37,f14(f16(f18(c40,X106),X107),X108)),X108) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| p35(f12(c37,f14(f16(f18(c40,X106),X107),X108)),X108) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_55) ).
tff(45,plain,
! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| p35(f12(c37,f14(f16(f18(c40,X106),X107),X108)),X108) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| p35(f12(c37,f14(f16(f18(c40,X106),X107),X108)),X108) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| p35(f12(c37,f14(f16(f18(c40,X106),X107),X108)),X108) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ( ~ ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| p35(f12(c37,f14(f16(f18(c40,X106),X107),X108)),X108) )
| p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))
| p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39)) )
<=> ( ~ ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| p35(f12(c37,f14(f16(f18(c40,X106),X107),X108)),X108) )
| p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))
| p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ~ ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| p35(f12(c37,f14(f16(f18(c40,X106),X107),X108)),X108) )
| p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))
| p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39)) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
( ~ ! [X107: $i,X106: $i,X108: $i] :
( p4(f5(f9(c39,X106),X108),f5(f9(c39,X107),X108))
| p35(f12(c37,f14(f16(f18(c40,X106),X107),X108)),X108) )
| p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))
| p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39)) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39)),
inference(unit_resolution,[status(thm)],[50,47,26]) ).
tff(52,plain,
^ [X118: $i,X119: $i,X116: $i,X117: $i] :
refl(
( ( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) )
<=> ( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) )
<=> ! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) )
<=> ! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
^ [X118: $i,X119: $i,X116: $i,X117: $i] :
trans(
monotonicity(
rewrite(
( ( p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118))
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p34(c36,X116) )
<=> ( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) ) )),
( ( p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118))
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p34(c36,X116)
| ~ p35(f12(X116,X118),f30(f32(c45,X116),X117)) )
<=> ( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118))
| ~ p35(f12(X116,X118),f30(f32(c45,X116),X117)) ) )),
rewrite(
( ( ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118))
| ~ p35(f12(X116,X118),f30(f32(c45,X116),X117)) )
<=> ( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) ) )),
( ( p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118))
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p34(c36,X116)
| ~ p35(f12(X116,X118),f30(f32(c45,X116),X117)) )
<=> ( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [X118: $i,X119: $i,X116: $i,X117: $i] :
( p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118))
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p34(c36,X116)
| ~ p35(f12(X116,X118),f30(f32(c45,X116),X117)) )
<=> ! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [X118: $i,X119: $i,X116: $i,X117: $i] :
( p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118))
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| ~ p34(c36,X116)
| ~ p35(f12(X116,X118),f30(f32(c45,X116),X117)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_57) ).
tff(58,plain,
! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) )
| p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))))
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39))))
| ~ p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39)) )
<=> ( ~ ! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) )
| p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))))
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39))))
| ~ p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ( ~ p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39))
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39))))
| p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))) )
<=> ( p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))))
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39))))
| ~ p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ( ~ ! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) )
| ~ p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39))
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39))))
| p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))) )
<=> ( ~ ! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) )
| p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))))
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39))))
| ~ p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39)) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) )
| ~ p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39))
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39))))
| p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))) )
<=> ( ~ ! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) )
| p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))))
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39))))
| ~ p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39)) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) )
| ~ p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39))
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39))))
| p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
( ~ ! [X118: $i,X119: $i,X116: $i,X117: $i] :
( ~ p35(f12(X116,X118),f30(f32(c45,X116),X117))
| ~ p34(c36,X116)
| p4(f5(f26(f28(c46,X116),X117),X119),f5(f9(X117,f26(f28(c46,X116),X117)),X119))
| p4(f5(f26(f28(c46,X116),X117),X118),f5(f26(f28(c47,X116),X117),X118)) )
| p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))))
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),f7(c38,f26(f28(c46,c37),c39))),f5(f9(c39,f26(f28(c46,c37),c39)),f7(c38,f26(f28(c46,c37),c39))))
| ~ p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39)) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
$false,
inference(unit_resolution,[status(thm)],[67,22,61,9,51,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN687-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 06:32:33 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.
% 0.68/0.67 % SZS status Unsatisfiable
% 0.68/0.67 % SZS output start Proof
% See solution above
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