TSTP Solution File: SYN647-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN647-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 23:56:46 EDT 2022
% Result : Unsatisfiable 0.20s 0.54s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 81
% Syntax : Number of formulae : 146 ( 38 unt; 20 typ; 0 def)
% Number of atoms : 730 ( 0 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 1065 ( 501 ~; 496 |; 0 &)
% ( 68 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 28 ( 7 avg)
% Number of FOOLs : 40 ( 40 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 16 >; 7 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-2 aty)
% Number of variables : 292 ( 268 !; 0 ?; 292 :)
% Comments :
%------------------------------------------------------------------------------
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(f13_type,type,
f13: $i > $i ).
tff(f11_type,type,
f11: $i > $i ).
tff(c25_type,type,
c25: $i ).
tff(f5_type,type,
f5: ( $i * $i ) > $i ).
tff(f6_type,type,
f6: ( $i * $i ) > $i ).
tff(f7_type,type,
f7: $i > $i ).
tff(f9_type,type,
f9: $i > $i ).
tff(f8_type,type,
f8: $i > $i ).
tff(c24_type,type,
c24: $i ).
tff(p4_type,type,
p4: ( $i * $i ) > $o ).
tff(f15_type,type,
f15: $i > $i ).
tff(p10_type,type,
p10: ( $i * $i ) > $o ).
tff(c22_type,type,
c22: $i ).
tff(c23_type,type,
c23: $i ).
tff(p20_type,type,
p20: ( $i * $i ) > $o ).
tff(f14_type,type,
f14: $i > $i ).
tff(p21_type,type,
p21: ( $i * $i ) > $o ).
tff(f17_type,type,
f17: $i > $i ).
tff(f12_type,type,
f12: $i > $i ).
tff(1,plain,
( p10(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),c25)
<=> p10(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),c25) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
p10(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),c25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_44) ).
tff(3,plain,
p10(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),c25),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X52: $i,X51: $i] :
refl(
( ( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) )
<=> ( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X52: $i,X51: $i] :
( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) )
<=> ! [X52: $i,X51: $i] :
( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X52: $i,X51: $i] :
( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) )
<=> ! [X52: $i,X51: $i] :
( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [X52: $i,X51: $i] :
rewrite(
( ( p4(f11(X51),f11(X52))
| ~ p10(X51,X52) )
<=> ( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [X52: $i,X51: $i] :
( p4(f11(X51),f11(X52))
| ~ p10(X51,X52) )
<=> ! [X52: $i,X51: $i] :
( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X52: $i,X51: $i] :
( p4(f11(X51),f11(X52))
| ~ p10(X51,X52) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_16) ).
tff(10,plain,
! [X52: $i,X51: $i] :
( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X52: $i,X51: $i] :
( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X52: $i,X51: $i] :
( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X52: $i,X51: $i] :
( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X52: $i,X51: $i] :
( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) )
| ~ p10(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),c25)
| p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25)) )
<=> ( ~ ! [X52: $i,X51: $i] :
( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) )
| ~ p10(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),c25)
| p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [X52: $i,X51: $i] :
( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) )
| ~ p10(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),c25)
| p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25)) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [X52: $i,X51: $i] :
( ~ p10(X51,X52)
| p4(f11(X51),f11(X52)) )
| ~ p10(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),c25)
| p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25)),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [X49: $i,X50: $i,X48: $i] :
refl(
( ( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
<=> ( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
<=> ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
<=> ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [X49: $i,X50: $i,X48: $i] :
trans(
monotonicity(
rewrite(
( ( p4(X49,X50)
| ~ p4(X48,X49) )
<=> ( ~ p4(X48,X49)
| p4(X49,X50) ) )),
( ( p4(X49,X50)
| ~ p4(X48,X49)
| ~ p4(X48,X50) )
<=> ( ~ p4(X48,X49)
| p4(X49,X50)
| ~ p4(X48,X50) ) )),
rewrite(
( ( ~ p4(X48,X49)
| p4(X49,X50)
| ~ p4(X48,X50) )
<=> ( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) ) )),
( ( p4(X49,X50)
| ~ p4(X48,X49)
| ~ p4(X48,X50) )
<=> ( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X49: $i,X50: $i,X48: $i] :
( p4(X49,X50)
| ~ p4(X48,X49)
| ~ p4(X48,X50) )
<=> ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [X49: $i,X50: $i,X48: $i] :
( p4(X49,X50)
| ~ p4(X48,X49)
| ~ p4(X48,X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_26) ).
tff(24,plain,
! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
| ~ p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25))
| p4(f11(c25),f11(c25)) )
<=> ( ~ ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
| ~ p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25))
| p4(f11(c25),f11(c25)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( ~ p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25))
| ~ p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25))
| p4(f11(c25),f11(c25)) )
<=> ( ~ p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25))
| p4(f11(c25),f11(c25)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
| ~ p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25))
| ~ p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25))
| p4(f11(c25),f11(c25)) )
<=> ( ~ ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
| ~ p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25))
| p4(f11(c25),f11(c25)) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
| ~ p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25))
| ~ p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25))
| p4(f11(c25),f11(c25)) )
<=> ( ~ ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
| ~ p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25))
| p4(f11(c25),f11(c25)) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
| ~ p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25))
| ~ p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25))
| p4(f11(c25),f11(c25)) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
| ~ p4(f11(f15(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),f11(c25))
| p4(f11(c25),f11(c25)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
p4(f11(c25),f11(c25)),
inference(unit_resolution,[status(thm)],[33,27,17]) ).
tff(35,plain,
( p4(f11(c25),f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))
<=> p4(f11(c25),f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
p4(f11(c25),f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_41) ).
tff(37,plain,
p4(f11(c25),f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ( ~ ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
| ~ p4(f11(c25),f11(c25))
| ~ p4(f11(c25),f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))
| p4(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))),f11(c25)) )
<=> ( ~ ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
| ~ p4(f11(c25),f11(c25))
| ~ p4(f11(c25),f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))
| p4(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))),f11(c25)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
| ~ p4(f11(c25),f11(c25))
| ~ p4(f11(c25),f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))
| p4(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))),f11(c25)) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [X49: $i,X50: $i,X48: $i] :
( ~ p4(X48,X50)
| ~ p4(X48,X49)
| p4(X49,X50) )
| ~ p4(f11(c25),f11(c25))
| ~ p4(f11(c25),f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))
| p4(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))),f11(c25)) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
p4(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))),f11(c25)),
inference(unit_resolution,[status(thm)],[40,27,37,34]) ).
tff(42,plain,
^ [X22: $i,X21: $i] :
refl(
( ( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) )
<=> ( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) )
<=> ! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) )
<=> ! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
^ [X22: $i,X21: $i] :
rewrite(
( ( p2(f13(X21),f13(X22))
| ~ p4(X21,X22) )
<=> ( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [X22: $i,X21: $i] :
( p2(f13(X21),f13(X22))
| ~ p4(X21,X22) )
<=> ! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,axiom,
! [X22: $i,X21: $i] :
( p2(f13(X21),f13(X22))
| ~ p4(X21,X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_20) ).
tff(48,plain,
! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) ),
inference(modus_ponens,[status(thm)],[50,43]) ).
tff(52,plain,
( ( ~ ! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) )
| ~ p4(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))),f11(c25))
| p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c25))) )
<=> ( ~ ! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) )
| ~ p4(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))),f11(c25))
| p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c25))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ~ ! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) )
| ~ p4(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))),f11(c25))
| p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c25))) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) )
| ~ p4(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))),f11(c25))
| p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c25))) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c25))),
inference(unit_resolution,[status(thm)],[54,51,41]) ).
tff(56,plain,
( ( ~ ! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) )
| ~ p4(f11(c25),f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))
| p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))) )
<=> ( ~ ! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) )
| ~ p4(f11(c25),f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))
| p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) )
| ~ p4(f11(c25),f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))
| p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [X22: $i,X21: $i] :
( ~ p4(X21,X22)
| p2(f13(X21),f13(X22)) )
| ~ p4(f11(c25),f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))
| p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),
inference(unit_resolution,[status(thm)],[58,51,37]) ).
tff(60,plain,
( p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
<=> p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(61,axiom,
p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_36) ).
tff(62,plain,
p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
^ [X17: $i,X16: $i,X18: $i] :
refl(
( ( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
<=> ( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
<=> ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
<=> ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
^ [X17: $i,X16: $i,X18: $i] :
trans(
monotonicity(
rewrite(
( ( p2(X17,X18)
| ~ p2(X16,X17) )
<=> ( ~ p2(X16,X17)
| p2(X17,X18) ) )),
( ( p2(X17,X18)
| ~ p2(X16,X17)
| ~ p2(X16,X18) )
<=> ( ~ p2(X16,X17)
| p2(X17,X18)
| ~ p2(X16,X18) ) )),
rewrite(
( ( ~ p2(X16,X17)
| p2(X17,X18)
| ~ p2(X16,X18) )
<=> ( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) ) )),
( ( p2(X17,X18)
| ~ p2(X16,X17)
| ~ p2(X16,X18) )
<=> ( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [X17: $i,X16: $i,X18: $i] :
( p2(X17,X18)
| ~ p2(X16,X17)
| ~ p2(X16,X18) )
<=> ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,axiom,
! [X17: $i,X16: $i,X18: $i] :
( p2(X17,X18)
| ~ p2(X16,X17)
| ~ p2(X16,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_28) ).
tff(69,plain,
! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) ),
inference(modus_ponens,[status(thm)],[71,64]) ).
tff(73,plain,
( ( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
| ~ p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))))
| p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))) )
<=> ( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
| ~ p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))))
| p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ( ~ p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))))
| ~ p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
| p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))) )
<=> ( ~ p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
| ~ p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))))
| p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))))
| ~ p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
| p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))) )
<=> ( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
| ~ p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))))
| p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))))
| ~ p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
| p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))) )
<=> ( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
| ~ p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))))
| p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))))
| ~ p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
| p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
| ~ p2(f13(f11(c25)),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))))
| p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24))))))))))))))))))))))))))),
inference(unit_resolution,[status(thm)],[78,72,62,59]) ).
tff(80,plain,
( p2(f13(f11(c23)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
<=> p2(f13(f11(c23)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(81,axiom,
p2(f13(f11(c23)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_35) ).
tff(82,plain,
p2(f13(f11(c23)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( p2(f13(f11(c23)),f13(f11(c22)))
<=> p2(f13(f11(c23)),f13(f11(c22))) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
p2(f13(f11(c23)),f13(f11(c22))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_14) ).
tff(85,plain,
p2(f13(f11(c23)),f13(f11(c22))),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f11(c23)),f13(f11(c22)))
| ~ p2(f13(f11(c23)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
| p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f11(c22))) )
<=> ( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f11(c23)),f13(f11(c22)))
| ~ p2(f13(f11(c23)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
| p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f11(c22))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f11(c23)),f13(f11(c22)))
| ~ p2(f13(f11(c23)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
| p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f11(c22))) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f11(c23)),f13(f11(c22)))
| ~ p2(f13(f11(c23)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))))
| p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f11(c22))) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f11(c22))),
inference(unit_resolution,[status(thm)],[88,85,72,82]) ).
tff(90,plain,
( ( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f11(c22)))
| ~ p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))))
| p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c22))) )
<=> ( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f11(c22)))
| ~ p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))))
| p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c22))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f11(c22)))
| ~ p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))))
| p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c22))) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f11(c22)))
| ~ p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))))
| p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c22))) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c22))),
inference(unit_resolution,[status(thm)],[92,72,89,79]) ).
tff(94,plain,
^ [X39: $i,X40: $i] :
refl(
( ( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) )
<=> ( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) ) )),
inference(bind,[status(th)],]) ).
tff(95,plain,
( ! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) )
<=> ! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) )
<=> ! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
^ [X39: $i,X40: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p21(f17(X39),f17(X40))
| ~ p2(f12(f11(X39)),f7(c24)) )
<=> ( ~ p2(f12(f11(X39)),f7(c24))
| p21(f17(X39),f17(X40)) ) )),
( ( p21(f17(X39),f17(X40))
| ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24)) )
<=> ( ~ p2(f12(f11(X39)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p2(f12(f11(X40)),f7(c24)) ) )),
rewrite(
( ( ~ p2(f12(f11(X39)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p2(f12(f11(X40)),f7(c24)) )
<=> ( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40)) ) )),
( ( p21(f17(X39),f17(X40))
| ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24)) )
<=> ( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40)) ) )),
( ( p21(f17(X39),f17(X40))
| ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| ~ p2(f13(f11(X39)),f13(f11(X40))) )
<=> ( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p2(f13(f11(X39)),f13(f11(X40))) ) )),
rewrite(
( ( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p2(f13(f11(X39)),f13(f11(X40))) )
<=> ( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p2(f13(f11(X39)),f13(f11(X40))) ) )),
( ( p21(f17(X39),f17(X40))
| ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| ~ p2(f13(f11(X39)),f13(f11(X40))) )
<=> ( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p2(f13(f11(X39)),f13(f11(X40))) ) )),
( ( p21(f17(X39),f17(X40))
| ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| ~ p2(f13(f11(X39)),f13(f11(X40)))
| ~ p20(f14(f11(X39)),f14(f11(X40))) )
<=> ( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p2(f13(f11(X39)),f13(f11(X40)))
| ~ p20(f14(f11(X39)),f14(f11(X40))) ) )),
rewrite(
( ( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p2(f13(f11(X39)),f13(f11(X40)))
| ~ p20(f14(f11(X39)),f14(f11(X40))) )
<=> ( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) ) )),
( ( p21(f17(X39),f17(X40))
| ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| ~ p2(f13(f11(X39)),f13(f11(X40)))
| ~ p20(f14(f11(X39)),f14(f11(X40))) )
<=> ( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [X39: $i,X40: $i] :
( p21(f17(X39),f17(X40))
| ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| ~ p2(f13(f11(X39)),f13(f11(X40)))
| ~ p20(f14(f11(X39)),f14(f11(X40))) )
<=> ! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,axiom,
! [X39: $i,X40: $i] :
( p21(f17(X39),f17(X40))
| ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| ~ p2(f13(f11(X39)),f13(f11(X40)))
| ~ p20(f14(f11(X39)),f14(f11(X40))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_40) ).
tff(100,plain,
! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) ),
inference(modus_ponens,[status(thm)],[102,95]) ).
tff(104,plain,
( p20(f14(f11(c25)),f14(f11(c22)))
<=> p20(f14(f11(c25)),f14(f11(c22))) ),
inference(rewrite,[status(thm)],]) ).
tff(105,axiom,
p20(f14(f11(c25)),f14(f11(c22))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20_12) ).
tff(106,plain,
p20(f14(f11(c25)),f14(f11(c22))),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
( p2(f12(f11(c25)),f7(c24))
<=> p2(f12(f11(c25)),f7(c24)) ),
inference(rewrite,[status(thm)],]) ).
tff(108,axiom,
p2(f12(f11(c25)),f7(c24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_10) ).
tff(109,plain,
p2(f12(f11(c25)),f7(c24)),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
( p2(f12(f11(c22)),f7(c24))
<=> p2(f12(f11(c22)),f7(c24)) ),
inference(rewrite,[status(thm)],]) ).
tff(111,axiom,
p2(f12(f11(c22)),f7(c24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_9) ).
tff(112,plain,
p2(f12(f11(c22)),f7(c24)),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
( ~ p21(f17(c25),f17(c22))
<=> ~ p21(f17(c25),f17(c22)) ),
inference(rewrite,[status(thm)],]) ).
tff(114,axiom,
~ p21(f17(c25),f17(c22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p21_7) ).
tff(115,plain,
~ p21(f17(c25),f17(c22)),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
( ( ~ ! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) )
| p21(f17(c25),f17(c22))
| ~ p2(f12(f11(c22)),f7(c24))
| ~ p2(f12(f11(c25)),f7(c24))
| ~ p20(f14(f11(c25)),f14(f11(c22)))
| ~ p2(f13(f11(c25)),f13(f11(c22))) )
<=> ( ~ ! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) )
| p21(f17(c25),f17(c22))
| ~ p2(f12(f11(c22)),f7(c24))
| ~ p2(f12(f11(c25)),f7(c24))
| ~ p20(f14(f11(c25)),f14(f11(c22)))
| ~ p2(f13(f11(c25)),f13(f11(c22))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ( ~ p2(f12(f11(c25)),f7(c24))
| ~ p2(f12(f11(c22)),f7(c24))
| p21(f17(c25),f17(c22))
| ~ p20(f14(f11(c25)),f14(f11(c22)))
| ~ p2(f13(f11(c25)),f13(f11(c22))) )
<=> ( p21(f17(c25),f17(c22))
| ~ p2(f12(f11(c22)),f7(c24))
| ~ p2(f12(f11(c25)),f7(c24))
| ~ p20(f14(f11(c25)),f14(f11(c22)))
| ~ p2(f13(f11(c25)),f13(f11(c22))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ( ~ ! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) )
| ~ p2(f12(f11(c25)),f7(c24))
| ~ p2(f12(f11(c22)),f7(c24))
| p21(f17(c25),f17(c22))
| ~ p20(f14(f11(c25)),f14(f11(c22)))
| ~ p2(f13(f11(c25)),f13(f11(c22))) )
<=> ( ~ ! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) )
| p21(f17(c25),f17(c22))
| ~ p2(f12(f11(c22)),f7(c24))
| ~ p2(f12(f11(c25)),f7(c24))
| ~ p20(f14(f11(c25)),f14(f11(c22)))
| ~ p2(f13(f11(c25)),f13(f11(c22))) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ( ~ ! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) )
| ~ p2(f12(f11(c25)),f7(c24))
| ~ p2(f12(f11(c22)),f7(c24))
| p21(f17(c25),f17(c22))
| ~ p20(f14(f11(c25)),f14(f11(c22)))
| ~ p2(f13(f11(c25)),f13(f11(c22))) )
<=> ( ~ ! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) )
| p21(f17(c25),f17(c22))
| ~ p2(f12(f11(c22)),f7(c24))
| ~ p2(f12(f11(c25)),f7(c24))
| ~ p20(f14(f11(c25)),f14(f11(c22)))
| ~ p2(f13(f11(c25)),f13(f11(c22))) ) ),
inference(transitivity,[status(thm)],[118,116]) ).
tff(120,plain,
( ~ ! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) )
| ~ p2(f12(f11(c25)),f7(c24))
| ~ p2(f12(f11(c22)),f7(c24))
| p21(f17(c25),f17(c22))
| ~ p20(f14(f11(c25)),f14(f11(c22)))
| ~ p2(f13(f11(c25)),f13(f11(c22))) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
( ~ ! [X39: $i,X40: $i] :
( ~ p2(f12(f11(X39)),f7(c24))
| ~ p2(f12(f11(X40)),f7(c24))
| p21(f17(X39),f17(X40))
| ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40))) )
| p21(f17(c25),f17(c22))
| ~ p2(f12(f11(c22)),f7(c24))
| ~ p2(f12(f11(c25)),f7(c24))
| ~ p20(f14(f11(c25)),f14(f11(c22)))
| ~ p2(f13(f11(c25)),f13(f11(c22))) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
~ p2(f13(f11(c25)),f13(f11(c22))),
inference(unit_resolution,[status(thm)],[121,115,112,109,106,103]) ).
tff(123,plain,
( ( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c22)))
| ~ p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c25)))
| p2(f13(f11(c25)),f13(f11(c22))) )
<=> ( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c22)))
| ~ p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c25)))
| p2(f13(f11(c25)),f13(f11(c22))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c22)))
| ~ p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c25)))
| p2(f13(f11(c25)),f13(f11(c22))) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
( ~ ! [X17: $i,X16: $i,X18: $i] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) )
| ~ p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c22)))
| ~ p2(f13(f5(f7(c24),f6(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f7(f9(f9(f9(f8(f8(f9(f9(f9(f9(f8(f9(f9(f8(f8(f8(f9(f8(f9(f9(f9(f8(f8(c24)))))))))))))))))))))))))),f13(f11(c25)))
| p2(f13(f11(c25)),f13(f11(c22))) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
$false,
inference(unit_resolution,[status(thm)],[125,72,122,93,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN647-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 06:33:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.54 % SZS status Unsatisfiable
% 0.20/0.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------