%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN567-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:39:35 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 24
% Syntax : Number of formulae : 49 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 253 ( 0 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 263 ( 76 ~; 162 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-1 aty)
% Number of variables : 61 ( 54 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
tff(p5_type,type,
p5: ( $i * $i ) > $o ).
tff(c9_type,type,
c9: $i ).
tff(f8_type,type,
f8: $i > $i ).
tff(f6_type,type,
f6: $i > $i ).
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(f3_type,type,
f3: $i > $i ).
tff(f7_type,type,
f7: $i > $i ).
tff(f4_type,type,
f4: $i > $i ).
tff(c10_type,type,
c10: $i ).
tff(1,plain,
^ [X17: $i] :
refl(( p5(f8(f6(X17)),X17)
<=> p5(f8(f6(X17)),X17) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X17: $i] : p5(f8(f6(X17)),X17)
<=> ! [X17: $i] : p5(f8(f6(X17)),X17) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X17: $i] : p5(f8(f6(X17)),X17)
<=> ! [X17: $i] : p5(f8(f6(X17)),X17) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X17: $i] : p5(f8(f6(X17)),X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_3) ).
tff(5,plain,
! [X17: $i] : p5(f8(f6(X17)),X17),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X17: $i] : p5(f8(f6(X17)),X17),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X17: $i] : p5(f8(f6(X17)),X17),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X17: $i] : p5(f8(f6(X17)),X17)
| p5(f8(f6(c9)),c9) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
p5(f8(f6(c9)),c9),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X3: $i] :
refl(( ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) )
<=> ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) )
<=> ! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) )
<=> ! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [X3: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10))))) )
<=> ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10))))) ) )),
( ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10)))))) )
<=> ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10)))))) ) )),
rewrite(( ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10)))))) )
<=> ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10)))))) ) )),
( ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10)))))) )
<=> ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10)))))) ) )),
( ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) )
<=> ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) ) )),
rewrite(( ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) )
<=> ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) ) )),
( ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) )
<=> ( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) )
<=> ! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_19) ).
tff(16,plain,
! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ~ p2(f6(c9),f3(f7(f7(f7(f4(c10))))))
<=> ~ p2(f6(c9),f3(f7(f7(f7(f4(c10)))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
~ p2(f6(c9),f3(f7(f7(f7(f4(c10)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_12) ).
tff(22,plain,
~ p2(f6(c9),f3(f7(f7(f7(f4(c10)))))),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ~ p2(f6(c9),f3(f7(f7(f4(c10)))))
<=> ~ p2(f6(c9),f3(f7(f7(f4(c10))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
~ p2(f6(c9),f3(f7(f7(f4(c10))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_6) ).
tff(25,plain,
~ p2(f6(c9),f3(f7(f7(f4(c10))))),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ~ p2(f6(c9),f3(f7(f4(c10))))
<=> ~ p2(f6(c9),f3(f7(f4(c10)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
~ p2(f6(c9),f3(f7(f4(c10)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_5) ).
tff(28,plain,
~ p2(f6(c9),f3(f7(f4(c10)))),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ~ p2(f6(c9),f3(f4(c10)))
<=> ~ p2(f6(c9),f3(f4(c10))) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
~ p2(f6(c9),f3(f4(c10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_4) ).
tff(31,plain,
~ p2(f6(c9),f3(f4(c10))),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ( ~ ! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) )
| p2(f6(c9),f3(f4(c10)))
| p2(f6(c9),f3(f7(f4(c10))))
| p2(f6(c9),f3(f7(f7(f4(c10)))))
| p2(f6(c9),f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(f6(c9))),f6(c9)) )
<=> ( ~ ! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) )
| p2(f6(c9),f3(f4(c10)))
| p2(f6(c9),f3(f7(f4(c10))))
| p2(f6(c9),f3(f7(f7(f4(c10)))))
| p2(f6(c9),f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(f6(c9))),f6(c9)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) )
| p2(f6(c9),f3(f4(c10)))
| p2(f6(c9),f3(f7(f4(c10))))
| p2(f6(c9),f3(f7(f7(f4(c10)))))
| p2(f6(c9),f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(f6(c9))),f6(c9)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [X3: $i] :
( p2(X3,f3(f4(c10)))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(X3)),X3) )
| p2(f6(c9),f3(f4(c10)))
| p2(f6(c9),f3(f7(f4(c10))))
| p2(f6(c9),f3(f7(f7(f4(c10)))))
| p2(f6(c9),f3(f7(f7(f7(f4(c10))))))
| ~ p2(f6(f8(f6(c9))),f6(c9)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
~ p2(f6(f8(f6(c9))),f6(c9)),
inference(unit_resolution,[status(thm)],[34,31,28,25,22,19]) ).
tff(36,plain,
^ [X9: $i,X8: $i] :
refl(( ( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) )
<=> ( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [X9: $i,X8: $i] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) )
<=> ! [X9: $i,X8: $i] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X9: $i,X8: $i] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) )
<=> ! [X9: $i,X8: $i] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
^ [X9: $i,X8: $i] :
rewrite(( ( p2(f6(X8),f6(X9))
| ~ p5(X8,X9) )
<=> ( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [X9: $i,X8: $i] :
( p2(f6(X8),f6(X9))
| ~ p5(X8,X9) )
<=> ! [X9: $i,X8: $i] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X9: $i,X8: $i] :
( p2(f6(X8),f6(X9))
| ~ p5(X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_10) ).
tff(42,plain,
! [X9: $i,X8: $i] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X9: $i,X8: $i] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X9: $i,X8: $i] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X9: $i,X8: $i] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [X9: $i,X8: $i] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) )
| ~ p5(f8(f6(c9)),c9)
| p2(f6(f8(f6(c9))),f6(c9)) )
<=> ( ~ ! [X9: $i,X8: $i] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) )
| ~ p5(f8(f6(c9)),c9)
| p2(f6(f8(f6(c9))),f6(c9)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [X9: $i,X8: $i] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) )
| ~ p5(f8(f6(c9)),c9)
| p2(f6(f8(f6(c9))),f6(c9)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [X9: $i,X8: $i] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) )
| ~ p5(f8(f6(c9)),c9)
| p2(f6(f8(f6(c9))),f6(c9)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,45,35,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN567-1 : TPTP v9.0.0. Released v2.5.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:37:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------