TSTP Solution File: SYN648-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN648-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 23:56:46 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 52
% Syntax : Number of formulae : 88 ( 21 unt; 22 typ; 0 def)
% Number of atoms : 670 ( 0 equ)
% Maximal formula atoms : 23 ( 10 avg)
% Number of connectives : 1012 ( 457 ~; 504 |; 0 &)
% ( 51 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 49 ( 49 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 14 >; 14 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-2 aty)
% Number of variables : 212 ( 191 !; 0 ?; 212 :)
% Comments :
%------------------------------------------------------------------------------
tff(p24_type,type,
p24: ( $i * $i ) > $o ).
tff(f9_type,type,
f9: ( $i * $i ) > $i ).
tff(c30_type,type,
c30: $i ).
tff(f11_type,type,
f11: ( $i * $i ) > $i ).
tff(c27_type,type,
c27: $i ).
tff(f13_type,type,
f13: ( $i * $i ) > $i ).
tff(f4_type,type,
f4: ( $i * $i ) > $i ).
tff(c28_type,type,
c28: $i ).
tff(f15_type,type,
f15: ( $i * $i ) > $i ).
tff(c34_type,type,
c34: $i ).
tff(f17_type,type,
f17: ( $i * $i ) > $i ).
tff(f19_type,type,
f19: ( $i * $i ) > $i ).
tff(f21_type,type,
f21: ( $i * $i ) > $i ).
tff(f23_type,type,
f23: ( $i * $i ) > $i ).
tff(c33_type,type,
c33: $i ).
tff(f6_type,type,
f6: ( $i * $i ) > $i ).
tff(c32_type,type,
c32: $i ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(c29_type,type,
c29: $i ).
tff(p26_type,type,
p26: ( $i * $i ) > $o ).
tff(c31_type,type,
c31: $i ).
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(1,plain,
^ [X65: $i] :
refl(
( p3(X65,X65)
<=> p3(X65,X65) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X65: $i] : p3(X65,X65)
<=> ! [X65: $i] : p3(X65,X65) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X65: $i] : p3(X65,X65)
<=> ! [X65: $i] : p3(X65,X65) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X65: $i] : p3(X65,X65),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_5) ).
tff(5,plain,
! [X65: $i] : p3(X65,X65),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X65: $i] : p3(X65,X65),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X65: $i] : p3(X65,X65),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X65: $i] : p3(X65,X65)
| p3(f4(c27,c28),f4(c27,c28)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p3(f4(c27,c28),f4(c27,c28)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X53: $i,X55: $i,X52: $i,X54: $i] :
refl(
( ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
<=> ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
<=> ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X53: $i,X55: $i,X52: $i,X54: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X52,X54) )
<=> ( ~ p3(X52,X54)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ) )),
( ( p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X52,X54)
| ~ p2(X55,X53) )
<=> ( ~ p3(X52,X54)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p2(X55,X53) ) )),
rewrite(
( ( ~ p3(X52,X54)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p2(X55,X53) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ) )),
( ( p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X52,X54)
| ~ p2(X55,X53) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ) )),
( ( p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p26(c31,X53) ) )),
rewrite(
( ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p26(c31,X53) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ) )),
( ( p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ) )),
( ( p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| ~ p3(X54,f4(X55,c28)) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28)) ) )),
rewrite(
( ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28)) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ) )),
( ( p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| ~ p3(X54,f4(X55,c28)) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| ~ p3(X54,f4(X55,c28)) )
<=> ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| ~ p3(X54,f4(X55,c28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24_44) ).
tff(16,plain,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ~ p24(f4(c27,c28),c29)
<=> ~ p24(f4(c27,c28),c29) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
~ p24(f4(c27,c28),c29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p24_16) ).
tff(22,plain,
~ p24(f4(c27,c28),c29),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( p26(c31,c30)
<=> p26(c31,c30) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
p26(c31,c30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26_15) ).
tff(25,plain,
p26(c31,c30),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( p2(c27,c30)
<=> p2(c27,c30) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
p2(c27,c30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_14) ).
tff(28,plain,
p2(c27,c30),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
| p24(f4(c27,c28),c29)
| ~ p2(c27,c30)
| ~ p26(c31,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) )
<=> ( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
| p24(f4(c27,c28),c29)
| ~ p2(c27,c30)
| ~ p26(c31,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p2(c27,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p26(c31,c30)
| p24(f4(c27,c28),c29)
| p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) )
<=> ( p24(f4(c27,c28),c29)
| ~ p2(c27,c30)
| ~ p26(c31,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p2(c27,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p26(c31,c30)
| p24(f4(c27,c28),c29)
| p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) )
<=> ( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
| p24(f4(c27,c28),c29)
| ~ p2(c27,c30)
| ~ p26(c31,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p2(c27,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p26(c31,c30)
| p24(f4(c27,c28),c29)
| p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) )
<=> ( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
| p24(f4(c27,c28),c29)
| ~ p2(c27,c30)
| ~ p26(c31,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p2(c27,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p26(c31,c30)
| p24(f4(c27,c28),c29)
| p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| p24(f4(f6(c32,X53),f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
| p24(f4(c27,c28),c29)
| ~ p2(c27,c30)
| ~ p26(c31,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)),
inference(unit_resolution,[status(thm)],[34,28,25,22,19,9]) ).
tff(36,plain,
^ [X57: $i,X56: $i] :
refl(
( ( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) )
<=> ( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X57: $i,X56: $i] :
( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) )
<=> ! [X57: $i,X56: $i] :
( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X57: $i,X56: $i] :
( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) )
<=> ! [X57: $i,X56: $i] :
( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
^ [X57: $i,X56: $i] :
rewrite(
( ( p24(f4(c30,X56),X57)
| ~ p24(f4(f6(c32,c30),X56),X57) )
<=> ( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X57: $i,X56: $i] :
( p24(f4(c30,X56),X57)
| ~ p24(f4(f6(c32,c30),X56),X57) )
<=> ! [X57: $i,X56: $i] :
( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X57: $i,X56: $i] :
( p24(f4(c30,X56),X57)
| ~ p24(f4(f6(c32,c30),X56),X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24_30) ).
tff(42,plain,
! [X57: $i,X56: $i] :
( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X57: $i,X56: $i] :
( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X57: $i,X56: $i] :
( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X57: $i,X56: $i] :
( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [X57: $i,X56: $i] :
( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) )
| ~ p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30))
| p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) )
<=> ( ~ ! [X57: $i,X56: $i] :
( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) )
| ~ p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30))
| p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ! [X57: $i,X56: $i] :
( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) )
| ~ p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30))
| p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X57: $i,X56: $i] :
( ~ p24(f4(f6(c32,c30),X56),X57)
| p24(f4(c30,X56),X57) )
| ~ p24(f4(f6(c32,c30),f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30))
| p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)),
inference(unit_resolution,[status(thm)],[48,45,35]) ).
tff(50,plain,
^ [X53: $i,X55: $i,X52: $i,X54: $i] :
refl(
( ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) )
<=> ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) )
<=> ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
^ [X53: $i,X55: $i,X52: $i,X54: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p24(X52,c29)
| ~ p3(X52,X54) )
<=> ( ~ p3(X52,X54)
| p24(X52,c29) ) )),
( ( p24(X52,c29)
| ~ p3(X52,X54)
| ~ p2(X55,X53) )
<=> ( ~ p3(X52,X54)
| p24(X52,c29)
| ~ p2(X55,X53) ) )),
rewrite(
( ( ~ p3(X52,X54)
| p24(X52,c29)
| ~ p2(X55,X53) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| p24(X52,c29) ) )),
( ( p24(X52,c29)
| ~ p3(X52,X54)
| ~ p2(X55,X53) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| p24(X52,c29) ) )),
( ( p24(X52,c29)
| ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| p24(X52,c29)
| ~ p26(c31,X53) ) )),
rewrite(
( ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| p24(X52,c29)
| ~ p26(c31,X53) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| p24(X52,c29) ) )),
( ( p24(X52,c29)
| ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| p24(X52,c29) ) )),
( ( p24(X52,c29)
| ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| ~ p3(X54,f4(X55,c28)) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| p24(X52,c29)
| ~ p3(X54,f4(X55,c28)) ) )),
rewrite(
( ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| p24(X52,c29)
| ~ p3(X54,f4(X55,c28)) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) ) )),
( ( p24(X52,c29)
| ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| ~ p3(X54,f4(X55,c28)) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) ) )),
( ( p24(X52,c29)
| ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ) )),
rewrite(
( ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) ) )),
( ( p24(X52,c29)
| ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
<=> ( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( p24(X52,c29)
| ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) )
<=> ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,axiom,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( p24(X52,c29)
| ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p26(c31,X53)
| ~ p3(X54,f4(X55,c28))
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24_43) ).
tff(56,plain,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) )
| p24(f4(c27,c28),c29)
| ~ p2(c27,c30)
| ~ p26(c31,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) )
<=> ( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) )
| p24(f4(c27,c28),c29)
| ~ p2(c27,c30)
| ~ p26(c31,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ( ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p2(c27,c30)
| ~ p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30))
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p26(c31,c30)
| p24(f4(c27,c28),c29) )
<=> ( p24(f4(c27,c28),c29)
| ~ p2(c27,c30)
| ~ p26(c31,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) )
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p2(c27,c30)
| ~ p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30))
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p26(c31,c30)
| p24(f4(c27,c28),c29) )
<=> ( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) )
| p24(f4(c27,c28),c29)
| ~ p2(c27,c30)
| ~ p26(c31,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) ) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) )
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p2(c27,c30)
| ~ p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30))
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p26(c31,c30)
| p24(f4(c27,c28),c29) )
<=> ( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) )
| p24(f4(c27,c28),c29)
| ~ p2(c27,c30)
| ~ p26(c31,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) ) ),
inference(transitivity,[status(thm)],[62,60]) ).
tff(64,plain,
( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) )
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p2(c27,c30)
| ~ p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30))
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p26(c31,c30)
| p24(f4(c27,c28),c29) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
( ~ ! [X53: $i,X55: $i,X52: $i,X54: $i] :
( ~ p3(X52,X54)
| ~ p2(X55,X53)
| ~ p24(f4(X53,f17(f19(f21(f23(c33,X52),X54),X55),X53)),f9(f11(f13(f15(c34,X52),X54),X55),X53))
| ~ p3(X54,f4(X55,c28))
| ~ p26(c31,X53)
| p24(X52,c29) )
| p24(f4(c27,c28),c29)
| ~ p2(c27,c30)
| ~ p26(c31,c30)
| ~ p3(f4(c27,c28),f4(c27,c28))
| ~ p24(f4(c30,f17(f19(f21(f23(c33,f4(c27,c28)),f4(c27,c28)),c27),c30)),f9(f11(f13(f15(c34,f4(c27,c28)),f4(c27,c28)),c27),c30)) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
$false,
inference(unit_resolution,[status(thm)],[65,28,25,22,59,9,49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN648-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.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 06:30:34 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------