TSTP Solution File: SYN600-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN600-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 23:56:36 EDT 2022
% Result : Unsatisfiable 3.10s 2.22s
% Output : Proof 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 79
% Syntax : Number of formulae : 155 ( 37 unt; 19 typ; 0 def)
% Number of atoms : 843 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 1223 ( 573 ~; 568 |; 0 &)
% ( 82 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 12 ( 4 avg)
% Number of FOOLs : 57 ( 57 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 16 >; 7 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 353 ( 318 !; 0 ?; 353 :)
% Comments :
%------------------------------------------------------------------------------
tff(p18_type,type,
p18: ( $i * $i ) > $o ).
tff(f15_type,type,
f15: $i > $i ).
tff(f16_type,type,
f16: $i > $i ).
tff(c21_type,type,
c21: $i ).
tff(f9_type,type,
f9: ( $i * $i ) > $i ).
tff(f10_type,type,
f10: ( $i * $i ) > $i ).
tff(f11_type,type,
f11: $i > $i ).
tff(f12_type,type,
f12: $i > $i ).
tff(c20_type,type,
c20: $i ).
tff(f13_type,type,
f13: $i > $i ).
tff(f14_type,type,
f14: $i > $i ).
tff(f4_type,type,
f4: $i > $i ).
tff(f6_type,type,
f6: $i > $i ).
tff(c22_type,type,
c22: $i ).
tff(p7_type,type,
p7: ( $i * $i ) > $o ).
tff(p19_type,type,
p19: $i > $o ).
tff(p17_type,type,
p17: ( $i * $i ) > $o ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(1,plain,
^ [X32: $i] :
refl(
( p7(X32,X32)
<=> p7(X32,X32) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X32: $i] : p7(X32,X32)
<=> ! [X32: $i] : p7(X32,X32) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X32: $i] : p7(X32,X32)
<=> ! [X32: $i] : p7(X32,X32) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X32: $i] : p7(X32,X32),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_4) ).
tff(5,plain,
! [X32: $i] : p7(X32,X32),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X32: $i] : p7(X32,X32),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X32: $i] : p7(X32,X32),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X32: $i] : p7(X32,X32)
| p7(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p7(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [X32: $i] : p7(X32,X32)
| p7(f16(c21),f16(c21)) ),
inference(quant_inst,[status(thm)],]) ).
tff(11,plain,
p7(f16(c21),f16(c21)),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
^ [X32: $i,X34: $i,X33: $i] :
refl(
( ( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) )
<=> ( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) )
<=> ! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) )
<=> ! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
^ [X32: $i,X34: $i,X33: $i] :
trans(
monotonicity(
rewrite(
( ( p7(X33,X34)
| ~ p7(X32,X33) )
<=> ( p7(X33,X34)
| ~ p7(X32,X33) ) )),
( ( p7(X33,X34)
| ~ p7(X32,X33)
| ~ p7(X32,X34) )
<=> ( p7(X33,X34)
| ~ p7(X32,X33)
| ~ p7(X32,X34) ) )),
rewrite(
( ( p7(X33,X34)
| ~ p7(X32,X33)
| ~ p7(X32,X34) )
<=> ( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) ) )),
( ( p7(X33,X34)
| ~ p7(X32,X33)
| ~ p7(X32,X34) )
<=> ( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X33)
| ~ p7(X32,X34) )
<=> ! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,axiom,
! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X33)
| ~ p7(X32,X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_19) ).
tff(18,plain,
! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) ),
inference(modus_ponens,[status(thm)],[20,13]) ).
tff(22,plain,
( p7(f16(c21),f16(c22))
<=> p7(f16(c21),f16(c22)) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
p7(f16(c21),f16(c22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_7) ).
tff(24,plain,
p7(f16(c21),f16(c22)),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( ( ~ ! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) )
| ~ p7(f16(c21),f16(c22))
| ~ p7(f16(c21),f16(c21))
| p7(f16(c22),f16(c21)) )
<=> ( ~ ! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) )
| ~ p7(f16(c21),f16(c22))
| ~ p7(f16(c21),f16(c21))
| p7(f16(c22),f16(c21)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ( p7(f16(c22),f16(c21))
| ~ p7(f16(c21),f16(c21))
| ~ p7(f16(c21),f16(c22)) )
<=> ( ~ p7(f16(c21),f16(c22))
| ~ p7(f16(c21),f16(c21))
| p7(f16(c22),f16(c21)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( ~ ! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) )
| p7(f16(c22),f16(c21))
| ~ p7(f16(c21),f16(c21))
| ~ p7(f16(c21),f16(c22)) )
<=> ( ~ ! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) )
| ~ p7(f16(c21),f16(c22))
| ~ p7(f16(c21),f16(c21))
| p7(f16(c22),f16(c21)) ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ( ~ ! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) )
| p7(f16(c22),f16(c21))
| ~ p7(f16(c21),f16(c21))
| ~ p7(f16(c21),f16(c22)) )
<=> ( ~ ! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) )
| ~ p7(f16(c21),f16(c22))
| ~ p7(f16(c21),f16(c21))
| p7(f16(c22),f16(c21)) ) ),
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,plain,
( ~ ! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) )
| p7(f16(c22),f16(c21))
| ~ p7(f16(c21),f16(c21))
| ~ p7(f16(c21),f16(c22)) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [X32: $i,X34: $i,X33: $i] :
( p7(X33,X34)
| ~ p7(X32,X34)
| ~ p7(X32,X33) )
| ~ p7(f16(c21),f16(c22))
| ~ p7(f16(c21),f16(c21))
| p7(f16(c22),f16(c21)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
p7(f16(c22),f16(c21)),
inference(unit_resolution,[status(thm)],[30,24,21,11]) ).
tff(32,plain,
^ [X42: $i,X41: $i] :
refl(
( ( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) )
<=> ( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X42: $i,X41: $i] :
( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) )
<=> ! [X42: $i,X41: $i] :
( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X42: $i,X41: $i] :
( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) )
<=> ! [X42: $i,X41: $i] :
( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
^ [X42: $i,X41: $i] :
rewrite(
( ( p7(f15(X41),f15(X42))
| ~ p7(X41,X42) )
<=> ( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [X42: $i,X41: $i] :
( p7(f15(X41),f15(X42))
| ~ p7(X41,X42) )
<=> ! [X42: $i,X41: $i] :
( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [X42: $i,X41: $i] :
( p7(f15(X41),f15(X42))
| ~ p7(X41,X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_17) ).
tff(38,plain,
! [X42: $i,X41: $i] :
( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [X42: $i,X41: $i] :
( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [X42: $i,X41: $i] :
( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X42: $i,X41: $i] :
( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [X42: $i,X41: $i] :
( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) )
| ~ p7(f16(c22),f16(c21))
| p7(f15(f16(c22)),f15(f16(c21))) )
<=> ( ~ ! [X42: $i,X41: $i] :
( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) )
| ~ p7(f16(c22),f16(c21))
| p7(f15(f16(c22)),f15(f16(c21))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [X42: $i,X41: $i] :
( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) )
| ~ p7(f16(c22),f16(c21))
| p7(f15(f16(c22)),f15(f16(c21))) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [X42: $i,X41: $i] :
( ~ p7(X41,X42)
| p7(f15(X41),f15(X42)) )
| ~ p7(f16(c22),f16(c21))
| p7(f15(f16(c22)),f15(f16(c21))) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
p7(f15(f16(c22)),f15(f16(c21))),
inference(unit_resolution,[status(thm)],[44,41,31]) ).
tff(46,plain,
^ [X4: $i] :
refl(
( ( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) )
<=> ( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [X4: $i] :
( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) )
<=> ! [X4: $i] :
( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [X4: $i] :
( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) )
<=> ! [X4: $i] :
( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
^ [X4: $i] :
rewrite(
( ( p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4)))
| ~ p19(X4) )
<=> ( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [X4: $i] :
( p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4)))
| ~ p19(X4) )
<=> ! [X4: $i] :
( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [X4: $i] :
( p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4)))
| ~ p19(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18_27) ).
tff(52,plain,
! [X4: $i] :
( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X4: $i] :
( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [X4: $i] :
( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X4: $i] :
( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( p19(c22)
<=> p19(c22) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
p19(c22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c22_is_p19_2) ).
tff(58,plain,
p19(c22),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
( ( ~ ! [X4: $i] :
( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) )
| ~ p19(c22)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22))) )
<=> ( ~ ! [X4: $i] :
( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) )
| ~ p19(c22)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ! [X4: $i] :
( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) )
| ~ p19(c22)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22))) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [X4: $i] :
( ~ p19(X4)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X4))) )
| ~ p19(c22)
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22))) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22))),
inference(unit_resolution,[status(thm)],[61,58,55]) ).
tff(63,plain,
^ [X6: $i,X7: $i,X5: $i,X8: $i] :
refl(
( ( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) )
<=> ( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) )
<=> ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) )
<=> ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
^ [X6: $i,X7: $i,X5: $i,X8: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p18(X5,X6)
| ~ p7(X7,X5) )
<=> ( ~ p7(X7,X5)
| p18(X5,X6) ) )),
( ( p18(X5,X6)
| ~ p7(X7,X5)
| ~ p7(X8,X6) )
<=> ( ~ p7(X7,X5)
| p18(X5,X6)
| ~ p7(X8,X6) ) )),
rewrite(
( ( ~ p7(X7,X5)
| p18(X5,X6)
| ~ p7(X8,X6) )
<=> ( ~ p7(X7,X5)
| ~ p7(X8,X6)
| p18(X5,X6) ) )),
( ( p18(X5,X6)
| ~ p7(X7,X5)
| ~ p7(X8,X6) )
<=> ( ~ p7(X7,X5)
| ~ p7(X8,X6)
| p18(X5,X6) ) )),
( ( p18(X5,X6)
| ~ p7(X7,X5)
| ~ p7(X8,X6)
| ~ p18(X7,X8) )
<=> ( ~ p7(X7,X5)
| ~ p7(X8,X6)
| p18(X5,X6)
| ~ p18(X7,X8) ) )),
rewrite(
( ( ~ p7(X7,X5)
| ~ p7(X8,X6)
| p18(X5,X6)
| ~ p18(X7,X8) )
<=> ( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) ) )),
( ( p18(X5,X6)
| ~ p7(X7,X5)
| ~ p7(X8,X6)
| ~ p18(X7,X8) )
<=> ( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p18(X5,X6)
| ~ p7(X7,X5)
| ~ p7(X8,X6)
| ~ p18(X7,X8) )
<=> ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,axiom,
! [X6: $i,X7: $i,X5: $i,X8: $i] :
( p18(X5,X6)
| ~ p7(X7,X5)
| ~ p7(X8,X6)
| ~ p18(X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18_23) ).
tff(69,plain,
! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) ),
inference(modus_ponens,[status(thm)],[71,64]) ).
tff(73,plain,
( ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) )
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22)))
| ~ p7(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21))) )
<=> ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) )
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22)))
| ~ p7(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ( ~ p7(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22)))
| ~ p7(f15(f16(c22)),f15(f16(c21)))
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21))) )
<=> ( p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22)))
| ~ p7(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) )
| ~ p7(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22)))
| ~ p7(f15(f16(c22)),f15(f16(c21)))
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21))) )
<=> ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) )
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22)))
| ~ p7(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21))) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) )
| ~ p7(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22)))
| ~ p7(f15(f16(c22)),f15(f16(c21)))
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21))) )
<=> ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) )
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22)))
| ~ p7(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21))) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) )
| ~ p7(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22)))
| ~ p7(f15(f16(c22)),f15(f16(c21)))
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21))) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
( ~ p7(X7,X5)
| ~ p18(X7,X8)
| ~ p7(X8,X6)
| p18(X5,X6) )
| p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c22)))
| ~ p7(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21))) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21))),
inference(unit_resolution,[status(thm)],[78,72,62,45,9]) ).
tff(80,plain,
( ~ ! [X32: $i] : p7(X32,X32)
| p7(f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
p7(f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))),
inference(unit_resolution,[status(thm)],[80,7]) ).
tff(82,plain,
^ [X4: $i] :
refl(
( ( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
<=> ( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [X4: $i] :
( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
<=> ! [X4: $i] :
( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [X4: $i] :
( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
<=> ! [X4: $i] :
( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
^ [X4: $i] :
rewrite(
( ( p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p19(X4) )
<=> ( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [X4: $i] :
( p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p19(X4) )
<=> ! [X4: $i] :
( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [X4: $i] :
( p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p19(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17_28) ).
tff(88,plain,
! [X4: $i] :
( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [X4: $i] :
( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [X4: $i] :
( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [X4: $i] :
( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( ( ~ ! [X4: $i] :
( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
| ~ p19(c22)
| p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
<=> ( ~ ! [X4: $i] :
( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
| ~ p19(c22)
| p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ~ ! [X4: $i] :
( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
| ~ p19(c22)
| p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [X4: $i] :
( ~ p19(X4)
| p17(f15(f16(X4)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(X4))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
| ~ p19(c22)
| p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))),
inference(unit_resolution,[status(thm)],[94,58,91]) ).
tff(96,plain,
^ [X0: $i,X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) )
<=> ( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) )
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) )
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
^ [X0: $i,X3: $i,X2: $i,X1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p17(X0,X1)
| ~ p7(X2,X0) )
<=> ( ~ p7(X2,X0)
| p17(X0,X1) ) )),
( ( p17(X0,X1)
| ~ p7(X2,X0)
| ~ p7(X3,X1) )
<=> ( ~ p7(X2,X0)
| p17(X0,X1)
| ~ p7(X3,X1) ) )),
rewrite(
( ( ~ p7(X2,X0)
| p17(X0,X1)
| ~ p7(X3,X1) )
<=> ( ~ p7(X3,X1)
| ~ p7(X2,X0)
| p17(X0,X1) ) )),
( ( p17(X0,X1)
| ~ p7(X2,X0)
| ~ p7(X3,X1) )
<=> ( ~ p7(X3,X1)
| ~ p7(X2,X0)
| p17(X0,X1) ) )),
( ( p17(X0,X1)
| ~ p7(X2,X0)
| ~ p7(X3,X1)
| ~ p17(X2,X3) )
<=> ( ~ p7(X3,X1)
| ~ p7(X2,X0)
| p17(X0,X1)
| ~ p17(X2,X3) ) )),
rewrite(
( ( ~ p7(X3,X1)
| ~ p7(X2,X0)
| p17(X0,X1)
| ~ p17(X2,X3) )
<=> ( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) ) )),
( ( p17(X0,X1)
| ~ p7(X2,X0)
| ~ p7(X3,X1)
| ~ p17(X2,X3) )
<=> ( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( p17(X0,X1)
| ~ p7(X2,X0)
| ~ p7(X3,X1)
| ~ p17(X2,X3) )
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,axiom,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( p17(X0,X1)
| ~ p7(X2,X0)
| ~ p7(X3,X1)
| ~ p17(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17_22) ).
tff(102,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) ),
inference(modus_ponens,[status(thm)],[104,97]) ).
tff(106,plain,
( ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) )
| p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21)))
| ~ p7(f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
<=> ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) )
| p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21)))
| ~ p7(f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ( ~ p7(f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21)))
| p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
<=> ( p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21)))
| ~ p7(f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) )
| ~ p7(f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21)))
| p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
<=> ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) )
| p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21)))
| ~ p7(f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) )
| ~ p7(f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21)))
| p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
<=> ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) )
| p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21)))
| ~ p7(f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ) ),
inference(transitivity,[status(thm)],[108,106]) ).
tff(110,plain,
( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) )
| ~ p7(f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21)))
| p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p7(X3,X1)
| ~ p17(X2,X3)
| ~ p7(X2,X0)
| p17(X0,X1) )
| p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p17(f15(f16(c22)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p7(f15(f16(c22)),f15(f16(c21)))
| ~ p7(f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))),
inference(unit_resolution,[status(thm)],[111,105,95,45,81]) ).
tff(113,plain,
^ [X27: $i,X28: $i] :
refl(
( ( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) )
<=> ( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) )
<=> ! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) )
<=> ! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,plain,
^ [X27: $i,X28: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p3(f4(f6(X27)),X28)
| ~ p19(X27) )
<=> ( ~ p19(X27)
| p3(f4(f6(X27)),X28) ) )),
( ( p3(f4(f6(X27)),X28)
| ~ p19(X27)
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27))) )
<=> ( ~ p19(X27)
| p3(f4(f6(X27)),X28)
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27))) ) )),
rewrite(
( ( ~ p19(X27)
| p3(f4(f6(X27)),X28)
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27))) )
<=> ( ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) ) )),
( ( p3(f4(f6(X27)),X28)
| ~ p19(X27)
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27))) )
<=> ( ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) ) )),
( ( p3(f4(f6(X27)),X28)
| ~ p19(X27)
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
<=> ( ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28)
| ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ) )),
rewrite(
( ( ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28)
| ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
<=> ( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) ) )),
( ( p3(f4(f6(X27)),X28)
| ~ p19(X27)
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
<=> ( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) ) )),
inference(bind,[status(th)],]) ).
tff(117,plain,
( ! [X27: $i,X28: $i] :
( p3(f4(f6(X27)),X28)
| ~ p19(X27)
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) )
<=> ! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,axiom,
! [X27: $i,X28: $i] :
( p3(f4(f6(X27)),X28)
| ~ p19(X27)
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_29) ).
tff(119,plain,
! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) ),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) ),
inference(modus_ponens,[status(thm)],[121,114]) ).
tff(123,plain,
( ~ p3(f4(f6(c21)),f4(f6(c22)))
<=> ~ p3(f4(f6(c21)),f4(f6(c22))) ),
inference(rewrite,[status(thm)],]) ).
tff(124,axiom,
~ p3(f4(f6(c21)),f4(f6(c22))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p3_8) ).
tff(125,plain,
~ p3(f4(f6(c21)),f4(f6(c22))),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
( p19(c21)
<=> p19(c21) ),
inference(rewrite,[status(thm)],]) ).
tff(127,axiom,
p19(c21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c21_is_p19_1) ).
tff(128,plain,
p19(c21),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
( ( ~ ! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) )
| p3(f4(f6(c21)),f4(f6(c22)))
| ~ p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p19(c21) )
<=> ( ~ ! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) )
| p3(f4(f6(c21)),f4(f6(c22)))
| ~ p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p19(c21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
( ( ~ p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p19(c21)
| p3(f4(f6(c21)),f4(f6(c22))) )
<=> ( p3(f4(f6(c21)),f4(f6(c22)))
| ~ p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p19(c21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
( ( ~ ! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) )
| ~ p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p19(c21)
| p3(f4(f6(c21)),f4(f6(c22))) )
<=> ( ~ ! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) )
| p3(f4(f6(c21)),f4(f6(c22)))
| ~ p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p19(c21) ) ),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
( ( ~ ! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) )
| ~ p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p19(c21)
| p3(f4(f6(c21)),f4(f6(c22))) )
<=> ( ~ ! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) )
| p3(f4(f6(c21)),f4(f6(c22)))
| ~ p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p19(c21) ) ),
inference(transitivity,[status(thm)],[131,129]) ).
tff(133,plain,
( ~ ! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) )
| ~ p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p19(c21)
| p3(f4(f6(c21)),f4(f6(c22))) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
( ~ ! [X27: $i,X28: $i] :
( ~ p17(f15(f16(X27)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),X28),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(X27)))
| ~ p19(X27)
| p3(f4(f6(X27)),X28) )
| p3(f4(f6(c21)),f4(f6(c22)))
| ~ p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21)))
| ~ p19(c21) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
( ~ p17(f15(f16(c21)),f8(f13(f11(f14(f12(c20)))),f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))
| ~ p18(f9(f10(f13(f11(f14(f12(c20)))),f4(f6(c22))),f10(f13(f11(f14(f12(c20)))),f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))),f15(f16(c21))) ),
inference(unit_resolution,[status(thm)],[134,128,125,122]) ).
tff(136,plain,
$false,
inference(unit_resolution,[status(thm)],[135,112,79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN600-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 05:59:18 EDT 2022
% 0.19/0.33 % CPUTime :
% 0.19/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.33 Usage: tptp [options] [-file:]file
% 0.19/0.33 -h, -? prints this message.
% 0.19/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.33 -m, -model generate model.
% 0.19/0.33 -p, -proof generate proof.
% 0.19/0.33 -c, -core generate unsat core of named formulas.
% 0.19/0.33 -st, -statistics display statistics.
% 0.19/0.33 -t:timeout set timeout (in second).
% 0.19/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.33 -<param>:<value> configuration parameter and value.
% 0.19/0.33 -o:<output-file> file to place output in.
% 3.10/2.22 % SZS status Unsatisfiable
% 3.10/2.22 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------