TSTP Solution File: SYN659-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN659-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 23:56:49 EDT 2022
% Result : Unsatisfiable 1.72s 1.33s
% Output : Proof 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 75
% Syntax : Number of formulae : 148 ( 43 unt; 16 typ; 0 def)
% Number of atoms : 773 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1110 ( 518 ~; 514 |; 0 &)
% ( 78 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 49 ( 49 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 9 >; 6 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 419 ( 382 !; 0 ?; 419 :)
% Comments :
%------------------------------------------------------------------------------
tff(p24_type,type,
p24: ( $i * $i ) > $o ).
tff(f13_type,type,
f13: ( $i * $i ) > $i ).
tff(c33_type,type,
c33: $i ).
tff(c32_type,type,
c32: $i ).
tff(f15_type,type,
f15: ( $i * $i ) > $i ).
tff(c41_type,type,
c41: $i ).
tff(c40_type,type,
c40: $i ).
tff(f8_type,type,
f8: $i > $i ).
tff(c28_type,type,
c28: $i ).
tff(p14_type,type,
p14: ( $i * $i ) > $o ).
tff(c29_type,type,
c29: $i ).
tff(p7_type,type,
p7: ( $i * $i ) > $o ).
tff(p12_type,type,
p12: ( $i * $i ) > $o ).
tff(f17_type,type,
f17: $i > $i ).
tff(c39_type,type,
c39: $i ).
tff(f16_type,type,
f16: $i > $i ).
tff(1,plain,
^ [X87: $i] :
refl(
( p7(X87,X87)
<=> p7(X87,X87) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X87: $i] : p7(X87,X87)
<=> ! [X87: $i] : p7(X87,X87) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X87: $i] : p7(X87,X87)
<=> ! [X87: $i] : p7(X87,X87) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X87: $i] : p7(X87,X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_3) ).
tff(5,plain,
! [X87: $i] : p7(X87,X87),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X87: $i] : p7(X87,X87),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X87: $i] : p7(X87,X87),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X87: $i] : p7(X87,X87)
| p7(f8(c28),f8(c28)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p7(f8(c28),f8(c28)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X87: $i,X88: $i,X89: $i] :
refl(
( ( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) )
<=> ( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) )
<=> ! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) )
<=> ! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X87: $i,X88: $i,X89: $i] :
trans(
monotonicity(
rewrite(
( ( p7(X88,X89)
| ~ p7(X87,X88) )
<=> ( ~ p7(X87,X88)
| p7(X88,X89) ) )),
( ( p7(X88,X89)
| ~ p7(X87,X88)
| ~ p7(X87,X89) )
<=> ( ~ p7(X87,X88)
| p7(X88,X89)
| ~ p7(X87,X89) ) )),
rewrite(
( ( ~ p7(X87,X88)
| p7(X88,X89)
| ~ p7(X87,X89) )
<=> ( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) ) )),
( ( p7(X88,X89)
| ~ p7(X87,X88)
| ~ p7(X87,X89) )
<=> ( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X87: $i,X88: $i,X89: $i] :
( p7(X88,X89)
| ~ p7(X87,X88)
| ~ p7(X87,X89) )
<=> ! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X87: $i,X88: $i,X89: $i] :
( p7(X88,X89)
| ~ p7(X87,X88)
| ~ p7(X87,X89) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_31) ).
tff(16,plain,
! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( p7(f8(c28),c29)
<=> p7(f8(c28),c29) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
p7(f8(c28),c29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_13) ).
tff(22,plain,
p7(f8(c28),c29),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) )
| ~ p7(f8(c28),c29)
| ~ p7(f8(c28),f8(c28))
| p7(c29,f8(c28)) )
<=> ( ~ ! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) )
| ~ p7(f8(c28),c29)
| ~ p7(f8(c28),f8(c28))
| p7(c29,f8(c28)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ p7(f8(c28),f8(c28))
| ~ p7(f8(c28),c29)
| p7(c29,f8(c28)) )
<=> ( ~ p7(f8(c28),c29)
| ~ p7(f8(c28),f8(c28))
| p7(c29,f8(c28)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) )
| ~ p7(f8(c28),f8(c28))
| ~ p7(f8(c28),c29)
| p7(c29,f8(c28)) )
<=> ( ~ ! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) )
| ~ p7(f8(c28),c29)
| ~ p7(f8(c28),f8(c28))
| p7(c29,f8(c28)) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) )
| ~ p7(f8(c28),f8(c28))
| ~ p7(f8(c28),c29)
| p7(c29,f8(c28)) )
<=> ( ~ ! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) )
| ~ p7(f8(c28),c29)
| ~ p7(f8(c28),f8(c28))
| p7(c29,f8(c28)) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) )
| ~ p7(f8(c28),f8(c28))
| ~ p7(f8(c28),c29)
| p7(c29,f8(c28)) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [X87: $i,X88: $i,X89: $i] :
( ~ p7(X87,X89)
| ~ p7(X87,X88)
| p7(X88,X89) )
| ~ p7(f8(c28),c29)
| ~ p7(f8(c28),f8(c28))
| p7(c29,f8(c28)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
p7(c29,f8(c28)),
inference(unit_resolution,[status(thm)],[28,22,19,9]) ).
tff(30,plain,
^ [X14: $i,X13: $i,X15: $i] :
refl(
( ( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) )
<=> ( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) )
<=> ! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) )
<=> ! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
^ [X14: $i,X13: $i,X15: $i] :
trans(
monotonicity(
rewrite(
( ( p12(X14,X15)
| ~ p12(X13,X14) )
<=> ( ~ p12(X13,X14)
| p12(X14,X15) ) )),
( ( p12(X14,X15)
| ~ p12(X13,X14)
| ~ p12(X13,X15) )
<=> ( ~ p12(X13,X14)
| p12(X14,X15)
| ~ p12(X13,X15) ) )),
rewrite(
( ( ~ p12(X13,X14)
| p12(X14,X15)
| ~ p12(X13,X15) )
<=> ( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) ) )),
( ( p12(X14,X15)
| ~ p12(X13,X14)
| ~ p12(X13,X15) )
<=> ( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [X14: $i,X13: $i,X15: $i] :
( p12(X14,X15)
| ~ p12(X13,X14)
| ~ p12(X13,X15) )
<=> ! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [X14: $i,X13: $i,X15: $i] :
( p12(X14,X15)
| ~ p12(X13,X14)
| ~ p12(X13,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_38) ).
tff(36,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( p12(f13(f16(c39),f17(c39)),f13(c40,c41))
<=> p12(f13(f16(c39),f17(c39)),f13(c40,c41)) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
p12(f13(f16(c39),f17(c39)),f13(c40,c41)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_29) ).
tff(42,plain,
p12(f13(f16(c39),f17(c39)),f13(c40,c41)),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
( ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p12(f13(c40,c41),f13(c40,c41)) )
<=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p12(f13(c40,c41),f13(c40,c41)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p12(f13(c40,c41),f13(c40,c41)) )
<=> ( ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p12(f13(c40,c41),f13(c40,c41)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p12(f13(c40,c41),f13(c40,c41)) )
<=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p12(f13(c40,c41),f13(c40,c41)) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p12(f13(c40,c41),f13(c40,c41)) )
<=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p12(f13(c40,c41),f13(c40,c41)) ) ),
inference(transitivity,[status(thm)],[45,43]) ).
tff(47,plain,
( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p12(f13(c40,c41),f13(c40,c41)) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p12(X13,X15)
| ~ p12(X13,X14)
| p12(X14,X15) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p12(f13(c40,c41),f13(c40,c41)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
p12(f13(c40,c41),f13(c40,c41)),
inference(unit_resolution,[status(thm)],[48,42,39]) ).
tff(50,plain,
^ [X25: $i,X23: $i,X26: $i,X24: $i] :
refl(
( ( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
<=> ( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
<=> ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
<=> ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
^ [X25: $i,X23: $i,X26: $i,X24: $i] :
trans(
monotonicity(
rewrite(
( ( p14(f15(X23,X24),f15(X25,X26))
| ~ p12(X24,X26) )
<=> ( ~ p12(X24,X26)
| p14(f15(X23,X24),f15(X25,X26)) ) )),
( ( p14(f15(X23,X24),f15(X25,X26))
| ~ p12(X24,X26)
| ~ p7(X23,X25) )
<=> ( ~ p12(X24,X26)
| p14(f15(X23,X24),f15(X25,X26))
| ~ p7(X23,X25) ) )),
rewrite(
( ( ~ p12(X24,X26)
| p14(f15(X23,X24),f15(X25,X26))
| ~ p7(X23,X25) )
<=> ( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) ) )),
( ( p14(f15(X23,X24),f15(X25,X26))
| ~ p12(X24,X26)
| ~ p7(X23,X25) )
<=> ( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( p14(f15(X23,X24),f15(X25,X26))
| ~ p12(X24,X26)
| ~ p7(X23,X25) )
<=> ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,axiom,
! [X25: $i,X23: $i,X26: $i,X24: $i] :
( p14(f15(X23,X24),f15(X25,X26))
| ~ p12(X24,X26)
| ~ p7(X23,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_45) ).
tff(56,plain,
! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
| ~ p12(f13(c40,c41),f13(c40,c41))
| ~ p7(c29,f8(c28))
| p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) )
<=> ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
| ~ p12(f13(c40,c41),f13(c40,c41))
| ~ p7(c29,f8(c28))
| p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
| ~ p12(f13(c40,c41),f13(c40,c41))
| ~ p7(c29,f8(c28))
| p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
| ~ p12(f13(c40,c41),f13(c40,c41))
| ~ p7(c29,f8(c28))
| p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))),
inference(unit_resolution,[status(thm)],[62,59,49,29]) ).
tff(64,plain,
^ [X13: $i] :
refl(
( p12(X13,X13)
<=> p12(X13,X13) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [X13: $i] : p12(X13,X13)
<=> ! [X13: $i] : p12(X13,X13) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [X13: $i] : p12(X13,X13)
<=> ! [X13: $i] : p12(X13,X13) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
! [X13: $i] : p12(X13,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_10) ).
tff(68,plain,
! [X13: $i] : p12(X13,X13),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [X13: $i] : p12(X13,X13),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [X13: $i] : p12(X13,X13),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [X13: $i] : p12(X13,X13)
| p12(f13(c32,c33),f13(c32,c33)) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
p12(f13(c32,c33),f13(c32,c33)),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
^ [X67: $i,X68: $i,X70: $i,X69: $i] :
refl(
( ( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
<=> ( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
<=> ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
<=> ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
^ [X67: $i,X68: $i,X70: $i,X69: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p24(X67,X68)
| ~ p14(X70,X67) )
<=> ( ~ p14(X70,X67)
| p24(X67,X68) ) )),
( ( p24(X67,X68)
| ~ p14(X70,X67)
| ~ p24(X70,X69) )
<=> ( ~ p14(X70,X67)
| p24(X67,X68)
| ~ p24(X70,X69) ) )),
rewrite(
( ( ~ p14(X70,X67)
| p24(X67,X68)
| ~ p24(X70,X69) )
<=> ( ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) ) )),
( ( p24(X67,X68)
| ~ p14(X70,X67)
| ~ p24(X70,X69) )
<=> ( ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) ) )),
( ( p24(X67,X68)
| ~ p14(X70,X67)
| ~ p24(X70,X69)
| ~ p12(X69,X68) )
<=> ( ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68)
| ~ p12(X69,X68) ) )),
rewrite(
( ( ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68)
| ~ p12(X69,X68) )
<=> ( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) ) )),
( ( p24(X67,X68)
| ~ p14(X70,X67)
| ~ p24(X70,X69)
| ~ p12(X69,X68) )
<=> ( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) ) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( p24(X67,X68)
| ~ p14(X70,X67)
| ~ p24(X70,X69)
| ~ p12(X69,X68) )
<=> ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,axiom,
! [X67: $i,X68: $i,X70: $i,X69: $i] :
( p24(X67,X68)
| ~ p14(X70,X67)
| ~ p24(X70,X69)
| ~ p12(X69,X68) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24_41) ).
tff(79,plain,
! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) ),
inference(modus_ponens,[status(thm)],[81,74]) ).
tff(83,plain,
( p24(f15(c29,f13(c40,c41)),f13(c32,c33))
<=> p24(f15(c29,f13(c40,c41)),f13(c32,c33)) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
p24(f15(c29,f13(c40,c41)),f13(c32,c33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24_27) ).
tff(85,plain,
p24(f15(c29,f13(c40,c41)),f13(c32,c33)),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
| ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
| ~ p12(f13(c32,c33),f13(c32,c33))
| p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
| ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) )
<=> ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
| ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
| ~ p12(f13(c32,c33),f13(c32,c33))
| p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
| ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( ~ p12(f13(c32,c33),f13(c32,c33))
| ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
| ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41)))
| p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33)) )
<=> ( ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
| ~ p12(f13(c32,c33),f13(c32,c33))
| p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
| ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
| ~ p12(f13(c32,c33),f13(c32,c33))
| ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
| ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41)))
| p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33)) )
<=> ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
| ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
| ~ p12(f13(c32,c33),f13(c32,c33))
| p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
| ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
| ~ p12(f13(c32,c33),f13(c32,c33))
| ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
| ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41)))
| p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33)) )
<=> ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
| ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
| ~ p12(f13(c32,c33),f13(c32,c33))
| p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
| ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ) ),
inference(transitivity,[status(thm)],[88,86]) ).
tff(90,plain,
( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
| ~ p12(f13(c32,c33),f13(c32,c33))
| ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
| ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41)))
| p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33)) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
| ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
| ~ p12(f13(c32,c33),f13(c32,c33))
| p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
| ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33)),
inference(unit_resolution,[status(thm)],[91,85,82,72,63]) ).
tff(93,plain,
( ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
| ~ p7(c29,f8(c28)) )
<=> ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
| ~ p7(c29,f8(c28)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ( ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| ~ p7(c29,f8(c28))
| p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) )
<=> ( ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
| ~ p7(c29,f8(c28)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| ~ p7(c29,f8(c28))
| p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) )
<=> ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
| ~ p7(c29,f8(c28)) ) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| ~ p7(c29,f8(c28))
| p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) )
<=> ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
| ~ p7(c29,f8(c28)) ) ),
inference(transitivity,[status(thm)],[95,93]) ).
tff(97,plain,
( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| ~ p7(c29,f8(c28))
| p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
( ~ p12(X24,X26)
| ~ p7(X23,X25)
| p14(f15(X23,X24),f15(X25,X26)) )
| ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
| p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
| ~ p7(c29,f8(c28)) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))),
inference(unit_resolution,[status(thm)],[98,42,59,29]) ).
tff(100,plain,
^ [X20: $i] :
refl(
( p14(X20,X20)
<=> p14(X20,X20) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [X20: $i] : p14(X20,X20)
<=> ! [X20: $i] : p14(X20,X20) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [X20: $i] : p14(X20,X20)
<=> ! [X20: $i] : p14(X20,X20) ),
inference(rewrite,[status(thm)],]) ).
tff(103,axiom,
! [X20: $i] : p14(X20,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_9) ).
tff(104,plain,
! [X20: $i] : p14(X20,X20),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [X20: $i] : p14(X20,X20),
inference(skolemize,[status(sab)],[104]) ).
tff(106,plain,
! [X20: $i] : p14(X20,X20),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
( ~ ! [X20: $i] : p14(X20,X20)
| p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39)))),
inference(unit_resolution,[status(thm)],[107,106]) ).
tff(109,plain,
^ [X22: $i,X21: $i,X20: $i] :
refl(
( ( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) )
<=> ( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) ) )),
inference(bind,[status(th)],]) ).
tff(110,plain,
( ! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) )
<=> ! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,plain,
( ! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) )
<=> ! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
^ [X22: $i,X21: $i,X20: $i] :
trans(
monotonicity(
rewrite(
( ( p14(X21,X22)
| ~ p14(X20,X21) )
<=> ( ~ p14(X20,X21)
| p14(X21,X22) ) )),
( ( p14(X21,X22)
| ~ p14(X20,X21)
| ~ p14(X20,X22) )
<=> ( ~ p14(X20,X21)
| p14(X21,X22)
| ~ p14(X20,X22) ) )),
rewrite(
( ( ~ p14(X20,X21)
| p14(X21,X22)
| ~ p14(X20,X22) )
<=> ( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) ) )),
( ( p14(X21,X22)
| ~ p14(X20,X21)
| ~ p14(X20,X22) )
<=> ( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) ) )),
inference(bind,[status(th)],]) ).
tff(113,plain,
( ! [X22: $i,X21: $i,X20: $i] :
( p14(X21,X22)
| ~ p14(X20,X21)
| ~ p14(X20,X22) )
<=> ! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) ) ),
inference(quant_intro,[status(thm)],[112]) ).
tff(114,axiom,
! [X22: $i,X21: $i,X20: $i] :
( p14(X21,X22)
| ~ p14(X20,X21)
| ~ p14(X20,X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_37) ).
tff(115,plain,
! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) ),
inference(modus_ponens,[status(thm)],[115,111]) ).
tff(117,plain,
! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) ),
inference(skolemize,[status(sab)],[116]) ).
tff(118,plain,
! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) ),
inference(modus_ponens,[status(thm)],[117,110]) ).
tff(119,plain,
( ( ~ ! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) )
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
| p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) )
<=> ( ~ ! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) )
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
| p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
( ( ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
| p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39)))) )
<=> ( ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
| p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( ( ~ ! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) )
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
| p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39)))) )
<=> ( ~ ! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) )
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
| p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) ) ),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( ( ~ ! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) )
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
| p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39)))) )
<=> ( ~ ! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) )
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
| p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) ) ),
inference(transitivity,[status(thm)],[121,119]) ).
tff(123,plain,
( ~ ! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) )
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
| p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(124,plain,
( ~ ! [X22: $i,X21: $i,X20: $i] :
( ~ p14(X20,X22)
| ~ p14(X20,X21)
| p14(X21,X22) )
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
| p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
| ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39)))),
inference(unit_resolution,[status(thm)],[124,118,108,99]) ).
tff(126,plain,
( ~ p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33))
<=> ~ p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33)) ),
inference(rewrite,[status(thm)],]) ).
tff(127,axiom,
~ p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p24_39) ).
tff(128,plain,
~ p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33)),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
( ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
| ~ p12(f13(c32,c33),f13(c32,c33))
| ~ p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
| ~ p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
| p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33)) )
<=> ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
| ~ p12(f13(c32,c33),f13(c32,c33))
| ~ p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
| ~ p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
| p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
| ~ p12(f13(c32,c33),f13(c32,c33))
| ~ p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
| ~ p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
| p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33)) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
( ~ p12(X69,X68)
| ~ p24(X70,X69)
| ~ p14(X70,X67)
| p24(X67,X68) )
| ~ p12(f13(c32,c33),f13(c32,c33))
| ~ p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
| ~ p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
| p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33)) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
$false,
inference(unit_resolution,[status(thm)],[131,128,82,72,125,92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN659-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 06:24:38 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 1.72/1.33 % SZS status Unsatisfiable
% 1.72/1.33 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------