%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN588-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:38 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 23 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 136 ( 64 ~; 60 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(p7_type,type,
p7: ( $i * $i ) > $o ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(f9_type,type,
f9: ( $i * $i ) > $i ).
tff(f10_type,type,
f10: ( $i * $i ) > $i ).
tff(c22_type,type,
c22: $i ).
tff(f11_type,type,
f11: $i > $i ).
tff(f3_type,type,
f3: $i > $i ).
tff(f4_type,type,
f4: $i > $i ).
tff(f5_type,type,
f5: $i > $i ).
tff(c17_type,type,
c17: $i ).
tff(c24_type,type,
c24: $i ).
tff(c25_type,type,
c25: $i ).
tff(c23_type,type,
c23: $i ).
tff(f12_type,type,
f12: $i > $i ).
tff(c19_type,type,
c19: $i ).
tff(c21_type,type,
c21: $i ).
tff(c18_type,type,
c18: $i ).
tff(c20_type,type,
c20: $i ).
tff(1,plain,
( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
<=> ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p7_26) ).
tff(3,plain,
~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))))
<=> p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_25) ).
tff(6,plain,
p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
<=> p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_24) ).
tff(9,plain,
p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X25: $i,X27: $i,X26: $i] :
refl(( ( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) )
<=> ( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) )
<=> ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) )
<=> ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [X25: $i,X27: $i,X26: $i] :
trans(monotonicity(rewrite(( ( p7(X26,X27)
| ~ p7(X25,X26) )
<=> ( p7(X26,X27)
| ~ p7(X25,X26) ) )),
( ( p7(X26,X27)
| ~ p7(X25,X26)
| ~ p7(X25,X27) )
<=> ( p7(X26,X27)
| ~ p7(X25,X26)
| ~ p7(X25,X27) ) )),
rewrite(( ( p7(X26,X27)
| ~ p7(X25,X26)
| ~ p7(X25,X27) )
<=> ( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ) )),
( ( p7(X26,X27)
| ~ p7(X25,X26)
| ~ p7(X25,X27) )
<=> ( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X26)
| ~ p7(X25,X27) )
<=> ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X26)
| ~ p7(X25,X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_14) ).
tff(16,plain,
! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) )
| p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) )
<=> ( ~ ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) )
| p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) )
| p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [X25: $i,X27: $i,X26: $i] :
( p7(X26,X27)
| ~ p7(X25,X27)
| ~ p7(X25,X26) )
| p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
| ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN588-1 : TPTP v9.0.0. Released v2.5.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:37:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39 % SZS output start Proof
% See solution above
% 0.21/0.39 % E exiting
%------------------------------------------------------------------------------