TSTP Solution File: SYN719-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN719-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 23:57:04 EDT 2022
% Result : Unsatisfiable 0.20s 0.55s
% Output : Proof 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 74
% Syntax : Number of formulae : 120 ( 32 unt; 36 typ; 0 def)
% Number of atoms : 476 ( 0 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 677 ( 317 ~; 311 |; 0 &)
% ( 49 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 32 ( 32 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 21 >; 21 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 15 con; 0-2 aty)
% Number of variables : 221 ( 201 !; 0 ?; 221 :)
% Comments :
%------------------------------------------------------------------------------
tff(p70_type,type,
p70: ( $i * $i ) > $o ).
tff(f38_type,type,
f38: ( $i * $i ) > $i ).
tff(f40_type,type,
f40: ( $i * $i ) > $i ).
tff(c81_type,type,
c81: $i ).
tff(f42_type,type,
f42: ( $i * $i ) > $i ).
tff(c85_type,type,
c85: $i ).
tff(f44_type,type,
f44: ( $i * $i ) > $i ).
tff(f46_type,type,
f46: ( $i * $i ) > $i ).
tff(c79_type,type,
c79: $i ).
tff(c87_type,type,
c87: $i ).
tff(f30_type,type,
f30: ( $i * $i ) > $i ).
tff(f32_type,type,
f32: ( $i * $i ) > $i ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(c76_type,type,
c76: $i ).
tff(c75_type,type,
c75: $i ).
tff(c89_type,type,
c89: $i ).
tff(c88_type,type,
c88: $i ).
tff(p69_type,type,
p69: ( $i * $i ) > $o ).
tff(f36_type,type,
f36: ( $i * $i ) > $i ).
tff(c86_type,type,
c86: $i ).
tff(p14_type,type,
p14: ( $i * $i ) > $o ).
tff(f23_type,type,
f23: ( $i * $i ) > $i ).
tff(f26_type,type,
f26: ( $i * $i ) > $i ).
tff(c84_type,type,
c84: $i ).
tff(p68_type,type,
p68: ( $i * $i ) > $o ).
tff(f19_type,type,
f19: ( $i * $i ) > $i ).
tff(f21_type,type,
f21: ( $i * $i ) > $i ).
tff(c77_type,type,
c77: $i ).
tff(c83_type,type,
c83: $i ).
tff(p67_type,type,
p67: ( $i * $i ) > $o ).
tff(c82_type,type,
c82: $i ).
tff(f16_type,type,
f16: ( $i * $i ) > $i ).
tff(c80_type,type,
c80: $i ).
tff(p66_type,type,
p66: ( $i * $i ) > $o ).
tff(f12_type,type,
f12: ( $i * $i ) > $i ).
tff(c78_type,type,
c78: $i ).
tff(1,plain,
^ [X13: $i] :
refl(
( p14(X13,X13)
<=> p14(X13,X13) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X13: $i] : p14(X13,X13)
<=> ! [X13: $i] : p14(X13,X13) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X13: $i] : p14(X13,X13)
<=> ! [X13: $i] : p14(X13,X13) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X13: $i] : p14(X13,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_38) ).
tff(5,plain,
! [X13: $i] : p14(X13,X13),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X13: $i] : p14(X13,X13),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X13: $i] : p14(X13,X13),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X13: $i] : p14(X13,X13)
| p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X20: $i] :
refl(
( p14(f23(f26(c84,c85),X20),X20)
<=> p14(f23(f26(c84,c85),X20),X20) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X20: $i] : p14(f23(f26(c84,c85),X20),X20)
<=> ! [X20: $i] : p14(f23(f26(c84,c85),X20),X20) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X20: $i] : p14(f23(f26(c84,c85),X20),X20)
<=> ! [X20: $i] : p14(f23(f26(c84,c85),X20),X20) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X20: $i] : p14(f23(f26(c84,c85),X20),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_45) ).
tff(14,plain,
! [X20: $i] : p14(f23(f26(c84,c85),X20),X20),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X20: $i] : p14(f23(f26(c84,c85),X20),X20),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X20: $i] : p14(f23(f26(c84,c85),X20),X20),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X20: $i] : p14(f23(f26(c84,c85),X20),X20)
| p14(f23(f26(c84,c85),c81),c81) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
p14(f23(f26(c84,c85),c81),c81),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X14: $i,X13: $i,X15: $i] :
refl(
( ( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) )
<=> ( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) )
<=> ! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) )
<=> ! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [X14: $i,X13: $i,X15: $i] :
trans(
monotonicity(
rewrite(
( ( p14(X14,X15)
| ~ p14(X13,X14) )
<=> ( ~ p14(X13,X14)
| p14(X14,X15) ) )),
( ( p14(X14,X15)
| ~ p14(X13,X14)
| ~ p14(X13,X15) )
<=> ( ~ p14(X13,X14)
| p14(X14,X15)
| ~ p14(X13,X15) ) )),
rewrite(
( ( ~ p14(X13,X14)
| p14(X14,X15)
| ~ p14(X13,X15) )
<=> ( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) ) )),
( ( p14(X14,X15)
| ~ p14(X13,X14)
| ~ p14(X13,X15) )
<=> ( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [X14: $i,X13: $i,X15: $i] :
( p14(X14,X15)
| ~ p14(X13,X14)
| ~ p14(X13,X15) )
<=> ! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [X14: $i,X13: $i,X15: $i] :
( p14(X14,X15)
| ~ p14(X13,X14)
| ~ p14(X13,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_90) ).
tff(25,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) )
| ~ p14(f23(f26(c84,c85),c81),c81)
| p14(c81,f23(f26(c84,c85),c81))
| ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)) )
<=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) )
| ~ p14(f23(f26(c84,c85),c81),c81)
| p14(c81,f23(f26(c84,c85),c81))
| ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81))
| ~ p14(f23(f26(c84,c85),c81),c81)
| p14(c81,f23(f26(c84,c85),c81)) )
<=> ( ~ p14(f23(f26(c84,c85),c81),c81)
| p14(c81,f23(f26(c84,c85),c81))
| ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) )
| ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81))
| ~ p14(f23(f26(c84,c85),c81),c81)
| p14(c81,f23(f26(c84,c85),c81)) )
<=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) )
| ~ p14(f23(f26(c84,c85),c81),c81)
| p14(c81,f23(f26(c84,c85),c81))
| ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) )
| ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81))
| ~ p14(f23(f26(c84,c85),c81),c81)
| p14(c81,f23(f26(c84,c85),c81)) )
<=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) )
| ~ p14(f23(f26(c84,c85),c81),c81)
| p14(c81,f23(f26(c84,c85),c81))
| ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) )
| ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81))
| ~ p14(f23(f26(c84,c85),c81),c81)
| p14(c81,f23(f26(c84,c85),c81)) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p14(X13,X15)
| ~ p14(X13,X14)
| p14(X14,X15) )
| ~ p14(f23(f26(c84,c85),c81),c81)
| p14(c81,f23(f26(c84,c85),c81))
| ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
p14(c81,f23(f26(c84,c85),c81)),
inference(unit_resolution,[status(thm)],[34,28,18,9]) ).
tff(36,plain,
^ [X222: $i,X224: $i,X221: $i,X223: $i] :
refl(
( ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) )
<=> ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) )
<=> ! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) )
<=> ! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
^ [X222: $i,X224: $i,X221: $i,X223: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p68(f19(f21(c83,c77),X221),X222)
| ~ p67(f16(c80,X224),c82) )
<=> ( ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ) )),
( ( p68(f19(f21(c83,c77),X221),X222)
| ~ p67(f16(c80,X224),c82)
| ~ p66(f12(c78,c77),X221) )
<=> ( ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222)
| ~ p66(f12(c78,c77),X221) ) )),
rewrite(
( ( ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222)
| ~ p66(f12(c78,c77),X221) )
<=> ( ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ) )),
( ( p68(f19(f21(c83,c77),X221),X222)
| ~ p67(f16(c80,X224),c82)
| ~ p66(f12(c78,c77),X221) )
<=> ( ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ) )),
( ( p68(f19(f21(c83,c77),X221),X222)
| ~ p67(f16(c80,X224),c82)
| ~ p66(f12(c78,c77),X221)
| ~ p14(X222,f23(f26(c84,X223),X224)) )
<=> ( ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222)
| ~ p14(X222,f23(f26(c84,X223),X224)) ) )),
rewrite(
( ( ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222)
| ~ p14(X222,f23(f26(c84,X223),X224)) )
<=> ( ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ) )),
( ( p68(f19(f21(c83,c77),X221),X222)
| ~ p67(f16(c80,X224),c82)
| ~ p66(f12(c78,c77),X221)
| ~ p14(X222,f23(f26(c84,X223),X224)) )
<=> ( ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ) )),
( ( p68(f19(f21(c83,c77),X221),X222)
| ~ p67(f16(c80,X224),c82)
| ~ p66(f12(c78,c77),X221)
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76)))) )
<=> ( ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222)
| ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76)))) ) )),
rewrite(
( ( ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222)
| ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76)))) )
<=> ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ) )),
( ( p68(f19(f21(c83,c77),X221),X222)
| ~ p67(f16(c80,X224),c82)
| ~ p66(f12(c78,c77),X221)
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76)))) )
<=> ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X222: $i,X224: $i,X221: $i,X223: $i] :
( p68(f19(f21(c83,c77),X221),X222)
| ~ p67(f16(c80,X224),c82)
| ~ p66(f12(c78,c77),X221)
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76)))) )
<=> ! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X222: $i,X224: $i,X221: $i,X223: $i] :
( p68(f19(f21(c83,c77),X221),X222)
| ~ p67(f16(c80,X224),c82)
| ~ p66(f12(c78,c77),X221)
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p68_126) ).
tff(42,plain,
! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ~ p68(f19(f21(c83,c77),c79),c81)
<=> ~ p68(f19(f21(c83,c77),c79),c81) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
~ p68(f19(f21(c83,c77),c79),c81),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p68_46) ).
tff(48,plain,
~ p68(f19(f21(c83,c77),c79),c81),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( p67(f16(c80,c81),c82)
<=> p67(f16(c80,c81),c82) ),
inference(rewrite,[status(thm)],]) ).
tff(50,axiom,
p67(f16(c80,c81),c82),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p67_42) ).
tff(51,plain,
p67(f16(c80,c81),c82),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( p66(f12(c78,c77),c79)
<=> p66(f12(c78,c77),c79) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
p66(f12(c78,c77),c79),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p66_41) ).
tff(54,plain,
p66(f12(c78,c77),c79),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) )
| p68(f19(f21(c83,c77),c79),c81)
| ~ p67(f16(c80,c81),c82)
| ~ p14(c81,f23(f26(c84,c85),c81))
| ~ p66(f12(c78,c77),c79)
| ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) )
<=> ( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) )
| p68(f19(f21(c83,c77),c79),c81)
| ~ p67(f16(c80,c81),c82)
| ~ p14(c81,f23(f26(c84,c85),c81))
| ~ p66(f12(c78,c77),c79)
| ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ( ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(c81,f23(f26(c84,c85),c81))
| ~ p66(f12(c78,c77),c79)
| ~ p67(f16(c80,c81),c82)
| p68(f19(f21(c83,c77),c79),c81) )
<=> ( p68(f19(f21(c83,c77),c79),c81)
| ~ p67(f16(c80,c81),c82)
| ~ p14(c81,f23(f26(c84,c85),c81))
| ~ p66(f12(c78,c77),c79)
| ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) )
| ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(c81,f23(f26(c84,c85),c81))
| ~ p66(f12(c78,c77),c79)
| ~ p67(f16(c80,c81),c82)
| p68(f19(f21(c83,c77),c79),c81) )
<=> ( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) )
| p68(f19(f21(c83,c77),c79),c81)
| ~ p67(f16(c80,c81),c82)
| ~ p14(c81,f23(f26(c84,c85),c81))
| ~ p66(f12(c78,c77),c79)
| ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) )
| ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(c81,f23(f26(c84,c85),c81))
| ~ p66(f12(c78,c77),c79)
| ~ p67(f16(c80,c81),c82)
| p68(f19(f21(c83,c77),c79),c81) )
<=> ( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) )
| p68(f19(f21(c83,c77),c79),c81)
| ~ p67(f16(c80,c81),c82)
| ~ p14(c81,f23(f26(c84,c85),c81))
| ~ p66(f12(c78,c77),c79)
| ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
inference(transitivity,[status(thm)],[57,55]) ).
tff(59,plain,
( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) )
| ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(c81,f23(f26(c84,c85),c81))
| ~ p66(f12(c78,c77),c79)
| ~ p67(f16(c80,c81),c82)
| p68(f19(f21(c83,c77),c79),c81) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p14(X222,f23(f26(c84,X223),X224))
| ~ p66(f12(c78,c77),X221)
| ~ p67(f16(c80,X224),c82)
| p68(f19(f21(c83,c77),X221),X222) )
| p68(f19(f21(c83,c77),c79),c81)
| ~ p67(f16(c80,c81),c82)
| ~ p14(c81,f23(f26(c84,c85),c81))
| ~ p66(f12(c78,c77),c79)
| ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))),
inference(unit_resolution,[status(thm)],[60,54,51,48,45,35]) ).
tff(62,plain,
^ [X230: $i,X229: $i] :
refl(
( ( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) )
<=> ( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) )
<=> ! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) )
<=> ! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,axiom,
! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p69_52) ).
tff(66,plain,
! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
( ( ~ ! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) )
| ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81)))
| p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) )
<=> ( ~ ! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) )
| ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81)))
| p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))) )
<=> ( ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81)))
| p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( ~ ! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) )
| p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))) )
<=> ( ~ ! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) )
| ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81)))
| p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ( ~ ! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) )
| p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))) )
<=> ( ~ ! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) )
| ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81)))
| p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,plain,
( ~ ! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) )
| p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
| ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
( ~ ! [X230: $i,X229: $i] :
( p69(f36(c86,X229),X230)
| ~ p70(X230,X229) )
| ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81)))
| p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),
inference(unit_resolution,[status(thm)],[74,68,61]) ).
tff(76,plain,
^ [X242: $i,X243: $i] :
refl(
( p70(f30(c88,X242),f38(c85,X243))
<=> p70(f30(c88,X242),f38(c85,X243)) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243))
<=> ! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243)) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243))
<=> ! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243)) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p70_43) ).
tff(80,plain,
! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243)),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243)),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243)),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
( ~ ! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243))
| p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
$false,
inference(unit_resolution,[status(thm)],[83,82,75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN719-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 06:53:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.55 % SZS status Unsatisfiable
% 0.20/0.55 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------