TSTP Solution File: SYN654-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN654-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 23:56:48 EDT 2022
% Result : Unsatisfiable 0.61s 0.62s
% Output : Proof 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 67
% Syntax : Number of formulae : 123 ( 32 unt; 22 typ; 0 def)
% Number of atoms : 420 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 546 ( 251 ~; 247 |; 0 &)
% ( 48 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 60 ( 10 >; 50 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 12 con; 0-8 aty)
% Number of variables : 622 ( 552 !; 0 ?; 622 :)
% Comments :
%------------------------------------------------------------------------------
tff(p8_type,type,
p8: ( $i * $i ) > $o ).
tff(c23_type,type,
c23: $i ).
tff(f16_type,type,
f16: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(c27_type,type,
c27: $i ).
tff(c22_type,type,
c22: $i ).
tff(c26_type,type,
c26: $i ).
tff(f11_type,type,
f11: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(c33_type,type,
c33: $i ).
tff(c32_type,type,
c32: $i ).
tff(c31_type,type,
c31: $i ).
tff(c30_type,type,
c30: $i ).
tff(c29_type,type,
c29: $i ).
tff(c28_type,type,
c28: $i ).
tff(c25_type,type,
c25: $i ).
tff(c24_type,type,
c24: $i ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(f14_type,type,
f14: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(f15_type,type,
f15: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(f17_type,type,
f17: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(f18_type,type,
f18: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(f19_type,type,
f19: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(p21_type,type,
p21: ( $i * $i ) > $o ).
tff(1,plain,
^ [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
refl(
( ( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) )
<=> ( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) )
<=> ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) )
<=> ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
rewrite(
( ( p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43)))
| ~ p21(f11(X38,X39,X36,X42,X43,X40),X41) )
<=> ( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43)))
| ~ p21(f11(X38,X39,X36,X42,X43,X40),X41) )
<=> ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43)))
| ~ p21(f11(X38,X39,X36,X42,X43,X40),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_48) ).
tff(7,plain,
! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( p21(f11(c24,c25,c26,c22,c27,c28),f11(c29,c30,c31,c23,c32,c33))
<=> p21(f11(c24,c25,c26,c22,c27,c28),f11(c29,c30,c31,c23,c32,c33)) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
p21(f11(c24,c25,c26,c22,c27,c28),f11(c29,c30,c31,c23,c32,c33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_27) ).
tff(13,plain,
p21(f11(c24,c25,c26,c22,c27,c28),f11(c29,c30,c31,c23,c32,c33)),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) )
| ~ p21(f11(c24,c25,c26,c22,c27,c28),f11(c29,c30,c31,c23,c32,c33))
| p3(f11(c29,c30,c31,c23,c32,c33),f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27))) )
<=> ( ~ ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) )
| ~ p21(f11(c24,c25,c26,c22,c27,c28),f11(c29,c30,c31,c23,c32,c33))
| p3(f11(c29,c30,c31,c23,c32,c33),f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) )
| ~ p21(f11(c24,c25,c26,c22,c27,c28),f11(c29,c30,c31,c23,c32,c33))
| p3(f11(c29,c30,c31,c23,c32,c33),f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27))) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) )
| ~ p21(f11(c24,c25,c26,c22,c27,c28),f11(c29,c30,c31,c23,c32,c33))
| p3(f11(c29,c30,c31,c23,c32,c33),f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27))) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
p3(f11(c29,c30,c31,c23,c32,c33),f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27))),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [X78: $i] :
refl(
( p3(X78,X78)
<=> p3(X78,X78) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [X78: $i] : p3(X78,X78)
<=> ! [X78: $i] : p3(X78,X78) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X78: $i] : p3(X78,X78)
<=> ! [X78: $i] : p3(X78,X78) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [X78: $i] : p3(X78,X78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_7) ).
tff(22,plain,
! [X78: $i] : p3(X78,X78),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [X78: $i] : p3(X78,X78),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X78: $i] : p3(X78,X78),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [X78: $i] : p3(X78,X78)
| p3(f11(c29,c30,c31,c23,c32,c33),f11(c29,c30,c31,c23,c32,c33)) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
p3(f11(c29,c30,c31,c23,c32,c33),f11(c29,c30,c31,c23,c32,c33)),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
^ [X80: $i,X78: $i,X79: $i] :
refl(
( ( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) )
<=> ( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X80: $i,X78: $i,X79: $i] :
( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) )
<=> ! [X80: $i,X78: $i,X79: $i] :
( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X80: $i,X78: $i,X79: $i] :
( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) )
<=> ! [X80: $i,X78: $i,X79: $i] :
( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [X80: $i,X78: $i,X79: $i] :
trans(
monotonicity(
rewrite(
( ( p3(X79,X80)
| ~ p3(X78,X79) )
<=> ( ~ p3(X78,X79)
| p3(X79,X80) ) )),
( ( p3(X79,X80)
| ~ p3(X78,X79)
| ~ p3(X78,X80) )
<=> ( ~ p3(X78,X79)
| p3(X79,X80)
| ~ p3(X78,X80) ) )),
rewrite(
( ( ~ p3(X78,X79)
| p3(X79,X80)
| ~ p3(X78,X80) )
<=> ( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) ) )),
( ( p3(X79,X80)
| ~ p3(X78,X79)
| ~ p3(X78,X80) )
<=> ( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X80: $i,X78: $i,X79: $i] :
( p3(X79,X80)
| ~ p3(X78,X79)
| ~ p3(X78,X80) )
<=> ! [X80: $i,X78: $i,X79: $i] :
( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [X80: $i,X78: $i,X79: $i] :
( p3(X79,X80)
| ~ p3(X78,X79)
| ~ p3(X78,X80) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_22) ).
tff(33,plain,
! [X80: $i,X78: $i,X79: $i] :
( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [X80: $i,X78: $i,X79: $i] :
( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [X80: $i,X78: $i,X79: $i] :
( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X80: $i,X78: $i,X79: $i] :
( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [X80: $i,X78: $i,X79: $i] :
( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) )
| ~ p3(f11(c29,c30,c31,c23,c32,c33),f11(c29,c30,c31,c23,c32,c33))
| ~ p3(f11(c29,c30,c31,c23,c32,c33),f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)))
| p3(f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)),f11(c29,c30,c31,c23,c32,c33)) )
<=> ( ~ ! [X80: $i,X78: $i,X79: $i] :
( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) )
| ~ p3(f11(c29,c30,c31,c23,c32,c33),f11(c29,c30,c31,c23,c32,c33))
| ~ p3(f11(c29,c30,c31,c23,c32,c33),f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)))
| p3(f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)),f11(c29,c30,c31,c23,c32,c33)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [X80: $i,X78: $i,X79: $i] :
( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) )
| ~ p3(f11(c29,c30,c31,c23,c32,c33),f11(c29,c30,c31,c23,c32,c33))
| ~ p3(f11(c29,c30,c31,c23,c32,c33),f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)))
| p3(f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)),f11(c29,c30,c31,c23,c32,c33)) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [X80: $i,X78: $i,X79: $i] :
( ~ p3(X78,X80)
| ~ p3(X78,X79)
| p3(X79,X80) )
| ~ p3(f11(c29,c30,c31,c23,c32,c33),f11(c29,c30,c31,c23,c32,c33))
| ~ p3(f11(c29,c30,c31,c23,c32,c33),f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)))
| p3(f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)),f11(c29,c30,c31,c23,c32,c33)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
p3(f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)),f11(c29,c30,c31,c23,c32,c33)),
inference(unit_resolution,[status(thm)],[39,36,26,17]) ).
tff(41,plain,
^ [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
refl(
( ( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) )
<=> ( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) )
<=> ! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) )
<=> ! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
^ [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
rewrite(
( ( p8(X8,X13)
| ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4)) )
<=> ( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( p8(X8,X13)
| ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4)) )
<=> ! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( p8(X8,X13)
| ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_31) ).
tff(47,plain,
! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) )
| ~ p3(f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)),f11(c29,c30,c31,c23,c32,c33))
| p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23) )
<=> ( ~ ! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) )
| ~ p3(f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)),f11(c29,c30,c31,c23,c32,c33))
| p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ~ ! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) )
| ~ p3(f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)),f11(c29,c30,c31,c23,c32,c33))
| p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
( ~ ! [X9: $i,X14: $i,X12: $i,X11: $i,X13: $i,X6: $i,X4: $i,X3: $i,X10: $i,X7: $i,X5: $i,X8: $i] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p8(X8,X13) )
| ~ p3(f11(f19(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f18(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f17(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f15(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),f14(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)),f11(c29,c30,c31,c23,c32,c33))
| p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23),
inference(unit_resolution,[status(thm)],[53,50,40]) ).
tff(55,plain,
^ [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
refl(
( ( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) )
<=> ( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) )
<=> ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) )
<=> ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
^ [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
rewrite(
( ( p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43))
| ~ p21(f11(X38,X39,X36,X42,X43,X40),X41) )
<=> ( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43))
| ~ p21(f11(X38,X39,X36,X42,X43,X40),X41) )
<=> ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,axiom,
! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43))
| ~ p21(f11(X38,X39,X36,X42,X43,X40),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_36) ).
tff(61,plain,
! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
( ( ~ ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) )
| ~ p21(f11(c24,c25,c26,c22,c27,c28),f11(c29,c30,c31,c23,c32,c33))
| p8(c22,f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)) )
<=> ( ~ ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) )
| ~ p21(f11(c24,c25,c26,c22,c27,c28),f11(c29,c30,c31,c23,c32,c33))
| p8(c22,f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ~ ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) )
| ~ p21(f11(c24,c25,c26,c22,c27,c28),f11(c29,c30,c31,c23,c32,c33))
| p8(c22,f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
( ~ ! [X43: $i,X39: $i,X42: $i,X38: $i,X37: $i,X41: $i,X36: $i,X40: $i] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p8(X42,f16(X37,X38,X39,X40,X41,X36,X42,X43)) )
| ~ p21(f11(c24,c25,c26,c22,c27,c28),f11(c29,c30,c31,c23,c32,c33))
| p8(c22,f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
p8(c22,f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27)),
inference(unit_resolution,[status(thm)],[67,13,64]) ).
tff(69,plain,
^ [X158: $i] :
refl(
( p8(X158,X158)
<=> p8(X158,X158) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [X158: $i] : p8(X158,X158)
<=> ! [X158: $i] : p8(X158,X158) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [X158: $i] : p8(X158,X158)
<=> ! [X158: $i] : p8(X158,X158) ),
inference(rewrite,[status(thm)],]) ).
tff(72,axiom,
! [X158: $i] : p8(X158,X158),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_3) ).
tff(73,plain,
! [X158: $i] : p8(X158,X158),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [X158: $i] : p8(X158,X158),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [X158: $i] : p8(X158,X158),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
( ~ ! [X158: $i] : p8(X158,X158)
| p8(c22,c22) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
p8(c22,c22),
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
^ [X159: $i,X158: $i,X160: $i] :
refl(
( ( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
<=> ( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
<=> ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
<=> ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
^ [X159: $i,X158: $i,X160: $i] :
trans(
monotonicity(
rewrite(
( ( p8(X159,X160)
| ~ p8(X158,X159) )
<=> ( ~ p8(X158,X159)
| p8(X159,X160) ) )),
( ( p8(X159,X160)
| ~ p8(X158,X159)
| ~ p8(X158,X160) )
<=> ( ~ p8(X158,X159)
| p8(X159,X160)
| ~ p8(X158,X160) ) )),
rewrite(
( ( ~ p8(X158,X159)
| p8(X159,X160)
| ~ p8(X158,X160) )
<=> ( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) ) )),
( ( p8(X159,X160)
| ~ p8(X158,X159)
| ~ p8(X158,X160) )
<=> ( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [X159: $i,X158: $i,X160: $i] :
( p8(X159,X160)
| ~ p8(X158,X159)
| ~ p8(X158,X160) )
<=> ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [X159: $i,X158: $i,X160: $i] :
( p8(X159,X160)
| ~ p8(X158,X159)
| ~ p8(X158,X160) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_18) ).
tff(84,plain,
! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) ),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
( ( ~ ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
| ~ p8(c22,c22)
| ~ p8(c22,f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27))
| p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22) )
<=> ( ~ ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
| ~ p8(c22,c22)
| ~ p8(c22,f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27))
| p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ~ ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
| ~ p8(c22,c22)
| ~ p8(c22,f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27))
| p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
| ~ p8(c22,c22)
| ~ p8(c22,f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27))
| p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22),
inference(unit_resolution,[status(thm)],[90,87,77,68]) ).
tff(92,plain,
( ~ p8(c22,c23)
<=> ~ p8(c22,c23) ),
inference(rewrite,[status(thm)],]) ).
tff(93,axiom,
~ p8(c22,c23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p8_10) ).
tff(94,plain,
~ p8(c22,c23),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
( ( ~ ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
| p8(c22,c23)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23) )
<=> ( ~ ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
| p8(c22,c23)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ( ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22)
| p8(c22,c23) )
<=> ( p8(c22,c23)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ( ~ ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22)
| p8(c22,c23) )
<=> ( ~ ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
| p8(c22,c23)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23) ) ),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
( ( ~ ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22)
| p8(c22,c23) )
<=> ( ~ ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
| p8(c22,c23)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23) ) ),
inference(transitivity,[status(thm)],[97,95]) ).
tff(99,plain,
( ~ ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22)
| p8(c22,c23) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
( ~ ! [X159: $i,X158: $i,X160: $i] :
( ~ p8(X158,X160)
| ~ p8(X158,X159)
| p8(X159,X160) )
| p8(c22,c23)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c22)
| ~ p8(f16(c25,c24,c25,c28,f11(c29,c30,c31,c23,c32,c33),c26,c22,c27),c23) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
$false,
inference(unit_resolution,[status(thm)],[100,94,87,91,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN654-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 06:38:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.61/0.62 % SZS status Unsatisfiable
% 0.61/0.62 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------