%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN711-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:39:53 AM UTC 2025
% Result : Unsatisfiable 0.69s 0.85s
% Output : Proof 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 39 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 175 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 238 ( 111 ~; 107 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 11 ( 4 avg)
% Number of FOOLs : 9 ( 9 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 : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 87 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
tff(p42_type,type,
p42: ( $i * $i ) > $o ).
tff(f13_type,type,
f13: $i > $i ).
tff(f14_type,type,
f14: ( $i * $i ) > $i ).
tff(f11_type,type,
f11: $i > $i ).
tff(f15_type,type,
f15: $i > $i ).
tff(f12_type,type,
f12: $i > $i ).
tff(c49_type,type,
c49: $i ).
tff(f10_type,type,
f10: $i > $i ).
tff(f16_type,type,
f16: $i > $i ).
tff(f7_type,type,
f7: $i > $i ).
tff(c46_type,type,
c46: $i ).
tff(p41_type,type,
p41: ( $i * $i ) > $o ).
tff(c62_type,type,
c62: $i ).
tff(1,plain,
( p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
<=> p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p41_80) ).
tff(3,plain,
p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X73: $i,X74: $i] :
refl(( ( ~ p41(X73,X74)
| p42(X73,X74) )
<=> ( ~ p41(X73,X74)
| p42(X73,X74) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X73: $i,X74: $i] :
( ~ p41(X73,X74)
| p42(X73,X74) )
<=> ! [X73: $i,X74: $i] :
( ~ p41(X73,X74)
| p42(X73,X74) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X73: $i,X74: $i] :
( ~ p41(X73,X74)
| p42(X73,X74) )
<=> ! [X73: $i,X74: $i] :
( ~ p41(X73,X74)
| p42(X73,X74) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [X73: $i,X74: $i] :
rewrite(( ( p42(X73,X74)
| ~ p41(X73,X74) )
<=> ( ~ p41(X73,X74)
| p42(X73,X74) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X73: $i,X74: $i] :
( p42(X73,X74)
| ~ p41(X73,X74) )
<=> ! [X73: $i,X74: $i] :
( ~ p41(X73,X74)
| p42(X73,X74) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X73: $i,X74: $i] :
( p42(X73,X74)
| ~ p41(X73,X74) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p42_26) ).
tff(10,plain,
! [X73: $i,X74: $i] :
( ~ p41(X73,X74)
| p42(X73,X74) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X73: $i,X74: $i] :
( ~ p41(X73,X74)
| p42(X73,X74) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X73: $i,X74: $i] :
( ~ p41(X73,X74)
| p42(X73,X74) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X73: $i,X74: $i] :
( ~ p41(X73,X74)
| p42(X73,X74) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X73: $i,X74: $i] :
( ~ p41(X73,X74)
| p42(X73,X74) )
| ~ p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
| p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) )
<=> ( ~ ! [X73: $i,X74: $i] :
( ~ p41(X73,X74)
| p42(X73,X74) )
| ~ p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
| p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [X73: $i,X74: $i] :
( ~ p41(X73,X74)
| p42(X73,X74) )
| ~ p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
| p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X73: $i,X74: $i] :
( ~ p41(X73,X74)
| p42(X73,X74) )
| ~ p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
| p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( ~ p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
<=> ~ p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
~ p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p42_78) ).
tff(20,plain,
~ p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) )
<=> ! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) )
<=> ! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
^ [X76: $i,X75: $i,X77: $i] :
trans(monotonicity(rewrite(( ( p42(X75,X76)
| ~ p42(X75,X77) )
<=> ( ~ p42(X75,X77)
| p42(X75,X76) ) )),
( ( p42(X75,X76)
| ~ p42(X75,X77)
| ~ p42(X77,X76) )
<=> ( ~ p42(X75,X77)
| p42(X75,X76)
| ~ p42(X77,X76) ) )),
rewrite(( ( ~ p42(X75,X77)
| p42(X75,X76)
| ~ p42(X77,X76) )
<=> ( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) ) )),
( ( p42(X75,X76)
| ~ p42(X75,X77)
| ~ p42(X77,X76) )
<=> ( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [X76: $i,X75: $i,X77: $i] :
( p42(X75,X76)
| ~ p42(X75,X77)
| ~ p42(X77,X76) )
<=> ! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,axiom,
! [X76: $i,X75: $i,X77: $i] :
( p42(X75,X76)
| ~ p42(X75,X77)
| ~ p42(X77,X76) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p42_47) ).
tff(26,plain,
! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
( p42(f16(c62),f16(f7(c46)))
<=> p42(f16(c62),f16(f7(c46))) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
p42(f16(c62),f16(f7(c46))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p42_25) ).
tff(32,plain,
p42(f16(c62),f16(f7(c46))),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ( ~ ! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) )
| p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
| ~ p42(f16(c62),f16(f7(c46)))
| ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) )
<=> ( ~ ! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) )
| p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
| ~ p42(f16(c62),f16(f7(c46)))
| ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
| ~ p42(f16(c62),f16(f7(c46)))
| p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) )
<=> ( p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
| ~ p42(f16(c62),f16(f7(c46)))
| ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ( ~ ! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) )
| ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
| ~ p42(f16(c62),f16(f7(c46)))
| p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) )
<=> ( ~ ! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) )
| p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
| ~ p42(f16(c62),f16(f7(c46)))
| ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ~ ! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) )
| ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
| ~ p42(f16(c62),f16(f7(c46)))
| p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) )
<=> ( ~ ! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) )
| p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
| ~ p42(f16(c62),f16(f7(c46)))
| ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
( ~ ! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) )
| ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
| ~ p42(f16(c62),f16(f7(c46)))
| p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [X76: $i,X75: $i,X77: $i] :
( ~ p42(X77,X76)
| ~ p42(X75,X77)
| p42(X75,X76) )
| p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
| ~ p42(f16(c62),f16(f7(c46)))
| ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,32,29,20,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN711-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n010.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 12:42:27 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.69/0.85 % SZS status Unsatisfiable
% 0.69/0.85 % SZS output start Proof
% See solution above
% 0.69/0.86 % E exiting
%------------------------------------------------------------------------------