%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN630-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:39:43 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 32 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 263 ( 0 equ)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 403 ( 192 ~; 188 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 8 con; 0-2 aty)
% Number of variables : 147 ( 133 !; 0 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
tff(p22_type,type,
p22: ( $i * $i ) > $o ).
tff(f12_type,type,
f12: ( $i * $i ) > $i ).
tff(f18_type,type,
f18: ( $i * $i ) > $i ).
tff(f9_type,type,
f9: $i > $i ).
tff(f11_type,type,
f11: $i > $i ).
tff(c29_type,type,
c29: $i ).
tff(f10_type,type,
f10: $i > $i ).
tff(p4_type,type,
p4: ( $i * $i ) > $o ).
tff(f5_type,type,
f5: ( $i * $i ) > $i ).
tff(f7_type,type,
f7: ( $i * $i ) > $i ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(p21_type,type,
p21: ( $i * $i ) > $o ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(f13_type,type,
f13: ( $i * $i ) > $i ).
tff(f14_type,type,
f14: ( $i * $i ) > $i ).
tff(f15_type,type,
f15: ( $i * $i ) > $i ).
tff(f16_type,type,
f16: $i > $i ).
tff(f17_type,type,
f17: $i > $i ).
tff(c25_type,type,
c25: $i ).
tff(c27_type,type,
c27: $i ).
tff(c30_type,type,
c30: $i ).
tff(c28_type,type,
c28: $i ).
tff(c26_type,type,
c26: $i ).
tff(c24_type,type,
c24: $i ).
tff(c23_type,type,
c23: $i ).
tff(1,plain,
^ [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
refl(( ( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) )
<=> ( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) )
<=> ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) )
<=> ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p21(X22,f9(f10(f11(c29)))) )
<=> ( ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23) ) )),
( ( p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p21(X22,f9(f10(f11(c29))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20)) )
<=> ( ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p21(X23,f12(f9(f10(f11(c29))),X20)) ) )),
rewrite(( ( ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p21(X23,f12(f9(f10(f11(c29))),X20)) )
<=> ( ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23) ) )),
( ( p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p21(X22,f9(f10(f11(c29))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20)) )
<=> ( ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23) ) )),
( ( p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p21(X22,f9(f10(f11(c29))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) )
<=> ( ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) ) )),
rewrite(( ( ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) )
<=> ( ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) ) )),
( ( p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p21(X22,f9(f10(f11(c29))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) )
<=> ( ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) ) )),
( ( p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p21(X22,f9(f10(f11(c29))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23)
| ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21))))) )
<=> ( ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23)
| ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21))))) ) )),
rewrite(( ( ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23)
| ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21))))) )
<=> ( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) ) )),
( ( p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p21(X22,f9(f10(f11(c29))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23)
| ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21))))) )
<=> ( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p21(X22,f9(f10(f11(c29))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23)
| ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21))))) )
<=> ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p21(X22,f9(f10(f11(c29))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23)
| ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_34) ).
tff(7,plain,
! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25)))))
<=> p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_30) ).
tff(13,plain,
p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25))))),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27)
<=> p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22_17) ).
tff(16,plain,
p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ~ p4(f5(f7(c23,f8(c24,c25)),c26),c27)
<=> ~ p4(f5(f7(c23,f8(c24,c25)),c26),c27) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
~ p4(f5(f7(c23,f8(c24,c25)),c26),c27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p4_12) ).
tff(19,plain,
~ p4(f5(f7(c23,f8(c24,c25)),c26),c27),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( p21(c27,f12(f9(f10(f11(c29))),c24))
<=> p21(c27,f12(f9(f10(f11(c29))),c24)) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
p21(c27,f12(f9(f10(f11(c29))),c24)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_6) ).
tff(22,plain,
p21(c27,f12(f9(f10(f11(c29))),c24)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( p21(c28,f9(f10(f11(c29))))
<=> p21(c28,f9(f10(f11(c29)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
p21(c28,f9(f10(f11(c29)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_5) ).
tff(25,plain,
p21(c28,f9(f10(f11(c29)))),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ( ~ ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) )
| p4(f5(f7(c23,f8(c24,c25)),c26),c27)
| ~ p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25)))))
| ~ p21(c27,f12(f9(f10(f11(c29))),c24))
| ~ p21(c28,f9(f10(f11(c29))))
| ~ p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27) )
<=> ( ~ ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) )
| p4(f5(f7(c23,f8(c24,c25)),c26),c27)
| ~ p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25)))))
| ~ p21(c27,f12(f9(f10(f11(c29))),c24))
| ~ p21(c28,f9(f10(f11(c29))))
| ~ p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ( ~ p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25)))))
| ~ p21(c27,f12(f9(f10(f11(c29))),c24))
| ~ p21(c28,f9(f10(f11(c29))))
| p4(f5(f7(c23,f8(c24,c25)),c26),c27)
| ~ p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27) )
<=> ( p4(f5(f7(c23,f8(c24,c25)),c26),c27)
| ~ p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25)))))
| ~ p21(c27,f12(f9(f10(f11(c29))),c24))
| ~ p21(c28,f9(f10(f11(c29))))
| ~ p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ( ~ ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) )
| ~ p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25)))))
| ~ p21(c27,f12(f9(f10(f11(c29))),c24))
| ~ p21(c28,f9(f10(f11(c29))))
| p4(f5(f7(c23,f8(c24,c25)),c26),c27)
| ~ p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27) )
<=> ( ~ ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) )
| p4(f5(f7(c23,f8(c24,c25)),c26),c27)
| ~ p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25)))))
| ~ p21(c27,f12(f9(f10(f11(c29))),c24))
| ~ p21(c28,f9(f10(f11(c29))))
| ~ p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) )
| ~ p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25)))))
| ~ p21(c27,f12(f9(f10(f11(c29))),c24))
| ~ p21(c28,f9(f10(f11(c29))))
| p4(f5(f7(c23,f8(c24,c25)),c26),c27)
| ~ p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27) )
<=> ( ~ ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) )
| p4(f5(f7(c23,f8(c24,c25)),c26),c27)
| ~ p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25)))))
| ~ p21(c27,f12(f9(f10(f11(c29))),c24))
| ~ p21(c28,f9(f10(f11(c29))))
| ~ p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) )
| ~ p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25)))))
| ~ p21(c27,f12(f9(f10(f11(c29))),c24))
| ~ p21(c28,f9(f10(f11(c29))))
| p4(f5(f7(c23,f8(c24,c25)),c26),c27)
| ~ p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X24: $i,X19: $i] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23)
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23) )
| p4(f5(f7(c23,f8(c24,c25)),c26),c27)
| ~ p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25)))))
| ~ p21(c27,f12(f9(f10(f11(c29))),c24))
| ~ p21(c28,f9(f10(f11(c29))))
| ~ p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,25,22,19,16,13,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN630-1 : TPTP v9.0.0. Released v2.5.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:38:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
% 0.12/0.41 % E exiting
%------------------------------------------------------------------------------