%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO334^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 : Wed Feb 25 09:53:58 AM UTC 2026
% Result : Theorem 1.70s 1.42s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 197 ( 100 equ; 0 cnn)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 628 ( 43 ~; 30 |; 44 &; 484 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 80 ( 80 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 196 ( 0 ^; 156 !; 40 ?; 196 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
c: $tType ).
thf(type_def_7,type,
b: $tType ).
thf(type_def_8,type,
a: $tType ).
thf(func_def_0,type,
c: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
a: $tType ).
thf(func_def_3,type,
c_starc: c > c > c ).
thf(func_def_4,type,
c_starb: b > b > b ).
thf(func_def_5,type,
c_stara: a > a > a ).
thf(func_def_9,type,
sK0: b > c ).
thf(func_def_10,type,
sK1: a > b ).
thf(func_def_11,type,
sK2: a > c ).
thf(func_def_12,type,
sK3: b > a ).
thf(func_def_13,type,
sK4: b ).
thf(func_def_14,type,
sK5: c > $o ).
thf(func_def_15,type,
sK6: b ).
thf(func_def_18,type,
ph8:
!>[X0: $tType] : X0 ).
thf(f248,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f247,f14]) ).
thf(f14,plain,
( ( sK5 @ ( sK0 @ ( c_starb @ sK4 @ sK6 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X3: a,X4: b > $o,X5: a] :
( ( $true
= ( X4 @ ( c_starb @ ( sK1 @ X3 ) @ ( sK1 @ X5 ) ) ) )
| ( $true
!= ( X4 @ ( sK1 @ ( c_stara @ X3 @ X5 ) ) ) ) )
& ! [X6: b,X8: b > $o] :
( ( $true
!= ( X8 @ ( sK1 @ ( sK3 @ X6 ) ) ) )
| ( $true
= ( X8 @ X6 ) ) )
& ! [X9: c > $o,X10: a] :
( ( $true
= ( X9 @ ( sK2 @ X10 ) ) )
| ( $true
!= ( X9 @ ( sK0 @ ( sK1 @ X10 ) ) ) ) )
& ! [X11: a,X12: c > $o,X13: a] :
( ( ( X12 @ ( sK2 @ ( c_stara @ X11 @ X13 ) ) )
!= $true )
| ( $true
= ( X12 @ ( c_starc @ ( sK2 @ X11 ) @ ( sK2 @ X13 ) ) ) ) )
& ( ( sK5 @ ( sK0 @ ( c_starb @ sK4 @ sK6 ) ) )
= $true )
& ( $true
!= ( sK5 @ ( c_starc @ ( sK0 @ sK4 ) @ ( sK0 @ sK6 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: b > c,X1: a > b,X2: a > c] :
( ! [X3: a,X4: b > $o,X5: a] :
( ( $true
= ( X4 @ ( c_starb @ ( X1 @ X3 ) @ ( X1 @ X5 ) ) ) )
| ( $true
!= ( X4 @ ( X1 @ ( c_stara @ X3 @ X5 ) ) ) ) )
& ! [X6: b] :
? [X7: a] :
! [X8: b > $o] :
( ( $true
!= ( X8 @ ( X1 @ X7 ) ) )
| ( $true
= ( X8 @ X6 ) ) )
& ! [X9: c > $o,X10: a] :
( ( ( X9 @ ( X2 @ X10 ) )
= $true )
| ( ( X9 @ ( X0 @ ( X1 @ X10 ) ) )
!= $true ) )
& ! [X11: a,X12: c > $o,X13: a] :
( ( $true
!= ( X12 @ ( X2 @ ( c_stara @ X11 @ X13 ) ) ) )
| ( $true
= ( X12 @ ( c_starc @ ( X2 @ X11 ) @ ( X2 @ X13 ) ) ) ) )
& ? [X14: b,X15: c > $o,X16: b] :
( ( $true
= ( X15 @ ( X0 @ ( c_starb @ X14 @ X16 ) ) ) )
& ( ( X15 @ ( c_starc @ ( X0 @ X14 ) @ ( X0 @ X16 ) ) )
!= $true ) ) )
=> ( ! [X5: a,X4: b > $o,X3: a] :
( ( $true
= ( X4 @ ( c_starb @ ( sK1 @ X3 ) @ ( sK1 @ X5 ) ) ) )
| ( $true
!= ( X4 @ ( sK1 @ ( c_stara @ X3 @ X5 ) ) ) ) )
& ! [X6: b] :
? [X7: a] :
! [X8: b > $o] :
( ( $true
!= ( X8 @ ( sK1 @ X7 ) ) )
| ( $true
= ( X8 @ X6 ) ) )
& ! [X10: a,X9: c > $o] :
( ( $true
= ( X9 @ ( sK2 @ X10 ) ) )
| ( $true
!= ( X9 @ ( sK0 @ ( sK1 @ X10 ) ) ) ) )
& ! [X13: a,X12: c > $o,X11: a] :
( ( ( X12 @ ( sK2 @ ( c_stara @ X11 @ X13 ) ) )
!= $true )
| ( $true
= ( X12 @ ( c_starc @ ( sK2 @ X11 ) @ ( sK2 @ X13 ) ) ) ) )
& ? [X16: b,X15: c > $o,X14: b] :
( ( ( X15 @ ( sK0 @ ( c_starb @ X14 @ X16 ) ) )
= $true )
& ( $true
!= ( X15 @ ( c_starc @ ( sK0 @ X14 ) @ ( sK0 @ X16 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X6: b] :
( ? [X7: a] :
! [X8: b > $o] :
( ( $true
!= ( X8 @ ( sK1 @ X7 ) ) )
| ( $true
= ( X8 @ X6 ) ) )
=> ! [X8: b > $o] :
( ( $true
!= ( X8 @ ( sK1 @ ( sK3 @ X6 ) ) ) )
| ( $true
= ( X8 @ X6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X16: b,X15: c > $o,X14: b] :
( ( ( X15 @ ( sK0 @ ( c_starb @ X14 @ X16 ) ) )
= $true )
& ( $true
!= ( X15 @ ( c_starc @ ( sK0 @ X14 ) @ ( sK0 @ X16 ) ) ) ) )
=> ( ( ( sK5 @ ( sK0 @ ( c_starb @ sK4 @ sK6 ) ) )
= $true )
& ( $true
!= ( sK5 @ ( c_starc @ ( sK0 @ sK4 ) @ ( sK0 @ sK6 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: b > c,X1: a > b,X2: a > c] :
( ! [X3: a,X4: b > $o,X5: a] :
( ( $true
= ( X4 @ ( c_starb @ ( X1 @ X3 ) @ ( X1 @ X5 ) ) ) )
| ( $true
!= ( X4 @ ( X1 @ ( c_stara @ X3 @ X5 ) ) ) ) )
& ! [X6: b] :
? [X7: a] :
! [X8: b > $o] :
( ( $true
!= ( X8 @ ( X1 @ X7 ) ) )
| ( $true
= ( X8 @ X6 ) ) )
& ! [X9: c > $o,X10: a] :
( ( ( X9 @ ( X2 @ X10 ) )
= $true )
| ( ( X9 @ ( X0 @ ( X1 @ X10 ) ) )
!= $true ) )
& ! [X11: a,X12: c > $o,X13: a] :
( ( $true
!= ( X12 @ ( X2 @ ( c_stara @ X11 @ X13 ) ) ) )
| ( $true
= ( X12 @ ( c_starc @ ( X2 @ X11 ) @ ( X2 @ X13 ) ) ) ) )
& ? [X14: b,X15: c > $o,X16: b] :
( ( $true
= ( X15 @ ( X0 @ ( c_starb @ X14 @ X16 ) ) ) )
& ( ( X15 @ ( c_starc @ ( X0 @ X14 ) @ ( X0 @ X16 ) ) )
!= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: b > c,X1: a > b,X2: a > c] :
( ! [X13: a,X12: b > $o,X11: a] :
( ( $true
= ( X12 @ ( c_starb @ ( X1 @ X13 ) @ ( X1 @ X11 ) ) ) )
| ( $true
!= ( X12 @ ( X1 @ ( c_stara @ X13 @ X11 ) ) ) ) )
& ! [X5: b] :
? [X6: a] :
! [X7: b > $o] :
( ( $true
!= ( X7 @ ( X1 @ X6 ) ) )
| ( ( X7 @ X5 )
= $true ) )
& ! [X4: c > $o,X3: a] :
( ( $true
= ( X4 @ ( X2 @ X3 ) ) )
| ( $true
!= ( X4 @ ( X0 @ ( X1 @ X3 ) ) ) ) )
& ! [X9: a,X8: c > $o,X10: a] :
( ( ( X8 @ ( X2 @ ( c_stara @ X9 @ X10 ) ) )
!= $true )
| ( $true
= ( X8 @ ( c_starc @ ( X2 @ X9 ) @ ( X2 @ X10 ) ) ) ) )
& ? [X15: b,X14: c > $o,X16: b] :
( ( $true
= ( X14 @ ( X0 @ ( c_starb @ X15 @ X16 ) ) ) )
& ( $true
!= ( X14 @ ( c_starc @ ( X0 @ X15 ) @ ( X0 @ X16 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: b > c,X1: a > b,X2: a > c] :
( ? [X15: b,X14: c > $o,X16: b] :
( ( $true
= ( X14 @ ( X0 @ ( c_starb @ X15 @ X16 ) ) ) )
& ( $true
!= ( X14 @ ( c_starc @ ( X0 @ X15 ) @ ( X0 @ X16 ) ) ) ) )
& ! [X9: a,X8: c > $o,X10: a] :
( ( ( X8 @ ( X2 @ ( c_stara @ X9 @ X10 ) ) )
!= $true )
| ( $true
= ( X8 @ ( c_starc @ ( X2 @ X9 ) @ ( X2 @ X10 ) ) ) ) )
& ! [X5: b] :
? [X6: a] :
! [X7: b > $o] :
( ( $true
!= ( X7 @ ( X1 @ X6 ) ) )
| ( ( X7 @ X5 )
= $true ) )
& ! [X4: c > $o,X3: a] :
( ( $true
= ( X4 @ ( X2 @ X3 ) ) )
| ( $true
!= ( X4 @ ( X0 @ ( X1 @ X3 ) ) ) ) )
& ! [X13: a,X12: b > $o,X11: a] :
( ( $true
= ( X12 @ ( c_starb @ ( X1 @ X13 ) @ ( X1 @ X11 ) ) ) )
| ( $true
!= ( X12 @ ( X1 @ ( c_stara @ X13 @ X11 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: b > c,X1: a > b,X2: a > c] :
( ( ! [X8: c > $o,X9: a,X10: a] :
( ( ( X8 @ ( X2 @ ( c_stara @ X9 @ X10 ) ) )
= $true )
=> ( $true
= ( X8 @ ( c_starc @ ( X2 @ X9 ) @ ( X2 @ X10 ) ) ) ) )
& ! [X5: b] :
? [X6: a] :
! [X7: b > $o] :
( ( $true
= ( X7 @ ( X1 @ X6 ) ) )
=> ( ( X7 @ X5 )
= $true ) )
& ! [X4: c > $o,X3: a] :
( ( $true
= ( X4 @ ( X0 @ ( X1 @ X3 ) ) ) )
=> ( $true
= ( X4 @ ( X2 @ X3 ) ) ) )
& ! [X12: b > $o,X11: a,X13: a] :
( ( $true
= ( X12 @ ( X1 @ ( c_stara @ X13 @ X11 ) ) ) )
=> ( $true
= ( X12 @ ( c_starb @ ( X1 @ X13 ) @ ( X1 @ X11 ) ) ) ) ) )
=> ! [X16: b,X14: c > $o,X15: b] :
( ( $true
= ( X14 @ ( X0 @ ( c_starb @ X15 @ X16 ) ) ) )
=> ( $true
= ( X14 @ ( c_starc @ ( X0 @ X15 ) @ ( X0 @ X16 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: b > c,X1: a > b,X2: a > c] :
( ( ! [X3: a,X4: c > $o] :
( ( X4 @ ( X0 @ ( X1 @ X3 ) ) )
=> ( X4 @ ( X2 @ X3 ) ) )
& ! [X5: b] :
? [X6: a] :
! [X7: b > $o] :
( ( X7 @ ( X1 @ X6 ) )
=> ( X7 @ X5 ) )
& ! [X8: c > $o,X9: a,X10: a] :
( ( X8 @ ( X2 @ ( c_stara @ X9 @ X10 ) ) )
=> ( X8 @ ( c_starc @ ( X2 @ X9 ) @ ( X2 @ X10 ) ) ) )
& ! [X11: a,X12: b > $o,X13: a] :
( ( X12 @ ( X1 @ ( c_stara @ X13 @ X11 ) ) )
=> ( X12 @ ( c_starb @ ( X1 @ X13 ) @ ( X1 @ X11 ) ) ) ) )
=> ! [X14: c > $o,X15: b,X16: b] :
( ( X14 @ ( X0 @ ( c_starb @ X15 @ X16 ) ) )
=> ( X14 @ ( c_starc @ ( X0 @ X15 ) @ ( X0 @ X16 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: b > c,X0: a > b,X1: a > c] :
( ( ! [X3: a,X4: c > $o] :
( ( X4 @ ( X2 @ ( X0 @ X3 ) ) )
=> ( X4 @ ( X1 @ X3 ) ) )
& ! [X5: b] :
? [X3: a] :
! [X4: b > $o] :
( ( X4 @ ( X0 @ X3 ) )
=> ( X4 @ X5 ) )
& ! [X4: c > $o,X3: a,X5: a] :
( ( X4 @ ( X1 @ ( c_stara @ X3 @ X5 ) ) )
=> ( X4 @ ( c_starc @ ( X1 @ X3 ) @ ( X1 @ X5 ) ) ) )
& ! [X5: a,X4: b > $o,X3: a] :
( ( X4 @ ( X0 @ ( c_stara @ X3 @ X5 ) ) )
=> ( X4 @ ( c_starb @ ( X0 @ X3 ) @ ( X0 @ X5 ) ) ) ) )
=> ! [X4: c > $o,X3: b,X5: b] :
( ( X4 @ ( X2 @ ( c_starb @ X3 @ X5 ) ) )
=> ( X4 @ ( c_starc @ ( X2 @ X3 ) @ ( X2 @ X5 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: b > c,X0: a > b,X1: a > c] :
( ( ! [X3: a,X4: c > $o] :
( ( X4 @ ( X2 @ ( X0 @ X3 ) ) )
=> ( X4 @ ( X1 @ X3 ) ) )
& ! [X5: b] :
? [X3: a] :
! [X4: b > $o] :
( ( X4 @ ( X0 @ X3 ) )
=> ( X4 @ X5 ) )
& ! [X4: c > $o,X3: a,X5: a] :
( ( X4 @ ( X1 @ ( c_stara @ X3 @ X5 ) ) )
=> ( X4 @ ( c_starc @ ( X1 @ X3 ) @ ( X1 @ X5 ) ) ) )
& ! [X5: a,X4: b > $o,X3: a] :
( ( X4 @ ( X0 @ ( c_stara @ X3 @ X5 ) ) )
=> ( X4 @ ( c_starb @ ( X0 @ X3 ) @ ( X0 @ X5 ) ) ) ) )
=> ! [X4: c > $o,X3: b,X5: b] :
( ( X4 @ ( X2 @ ( c_starb @ X3 @ X5 ) ) )
=> ( X4 @ ( c_starc @ ( X2 @ X3 ) @ ( X2 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.glNrkzU4u6/DTF2THF_7826.p',cTHM270_INST) ).
thf(f247,plain,
( ( sK5 @ ( sK0 @ ( c_starb @ sK4 @ sK6 ) ) )
!= $true ),
inference(superposition,[status(thm)],[f13,f220]) ).
thf(f220,plain,
! [X0: b,X1: b] :
( ( c_starc @ ( sK0 @ X0 ) @ ( sK0 @ X1 ) )
= ( sK0 @ ( c_starb @ X0 @ X1 ) ) ),
inference(forward_demodulation,[status(thm)],[f213,f76]) ).
thf(f76,plain,
! [X0: b] :
( ( sK0 @ X0 )
= ( sK2 @ ( sK3 @ X0 ) ) ),
inference(superposition,[status(thm)],[f53,f20]) ).
thf(f20,plain,
! [X0: b] :
( ( sK1 @ ( sK3 @ X0 ) )
= X0 ),
inference(leibniz_equality_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X8: b > $o,X6: b] :
( ( $true
!= ( X8 @ ( sK1 @ ( sK3 @ X6 ) ) ) )
| ( $true
= ( X8 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f53,plain,
! [X0: a] :
( ( sK2 @ X0 )
= ( sK0 @ ( sK1 @ X0 ) ) ),
inference(leibniz_equality_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X10: a,X9: c > $o] :
( ( $true
!= ( X9 @ ( sK0 @ ( sK1 @ X10 ) ) ) )
| ( $true
= ( X9 @ ( sK2 @ X10 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f213,plain,
! [X0: b,X1: b] :
( ( c_starc @ ( sK2 @ ( sK3 @ X0 ) ) @ ( sK0 @ X1 ) )
= ( sK0 @ ( c_starb @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f145,f20]) ).
thf(f145,plain,
! [X0: a,X1: b] :
( ( sK0 @ ( c_starb @ ( sK1 @ X0 ) @ X1 ) )
= ( c_starc @ ( sK2 @ X0 ) @ ( sK0 @ X1 ) ) ),
inference(forward_demodulation,[status(thm)],[f142,f120]) ).
thf(f120,plain,
! [X0: b,X1: a] :
( ( c_starc @ ( sK2 @ X1 ) @ ( sK0 @ X0 ) )
= ( sK2 @ ( c_stara @ X1 @ ( sK3 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f66,f76]) ).
thf(f66,plain,
! [X0: a,X1: a] :
( ( sK2 @ ( c_stara @ X0 @ X1 ) )
= ( c_starc @ ( sK2 @ X0 ) @ ( sK2 @ X1 ) ) ),
inference(leibniz_equality_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X11: a,X12: c > $o,X13: a] :
( ( $true
= ( X12 @ ( c_starc @ ( sK2 @ X11 ) @ ( sK2 @ X13 ) ) ) )
| ( ( X12 @ ( sK2 @ ( c_stara @ X11 @ X13 ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f142,plain,
! [X0: a,X1: b] :
( ( sK0 @ ( c_starb @ ( sK1 @ X0 ) @ X1 ) )
= ( sK2 @ ( c_stara @ X0 @ ( sK3 @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f53,f135]) ).
thf(f135,plain,
! [X0: b,X1: a] :
( ( c_starb @ ( sK1 @ X1 ) @ X0 )
= ( sK1 @ ( c_stara @ X1 @ ( sK3 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f79,f20]) ).
thf(f79,plain,
! [X0: a,X1: a] :
( ( c_starb @ ( sK1 @ X0 ) @ ( sK1 @ X1 ) )
= ( sK1 @ ( c_stara @ X0 @ X1 ) ) ),
inference(leibniz_equality_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X3: a,X4: b > $o,X5: a] :
( ( $true
= ( X4 @ ( c_starb @ ( sK1 @ X3 ) @ ( sK1 @ X5 ) ) ) )
| ( $true
!= ( X4 @ ( sK1 @ ( c_stara @ X3 @ X5 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f13,plain,
( $true
!= ( sK5 @ ( c_starc @ ( sK0 @ sK4 ) @ ( sK0 @ sK6 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO334^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n009.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 14:28:55 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.40 ---- Original DTF file ---
% 0.16/0.40 thf(spec,logic,$$dhol).
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 % File : SYO334^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.40 % Domain : Syntactic
% 0.16/0.40 % Problem : TPS problem from BASIC-HO-THMS
% 0.16/0.40 % Version : Especial.
% 0.16/0.40 % English :
% 0.16/0.40
% 0.16/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.40 % Source : [Bro09]
% 0.16/0.40 % Names : tps_1076 [Bro09]
% 0.16/0.40
% 0.16/0.40 % Status : Theorem
% 0.16/0.40 % Rating : 0.58 v9.1.0, 0.50 v8.2.0, 0.55 v8.1.0, 0.50 v7.4.0, 0.56 v7.3.0, 0.60 v7.2.0, 0.62 v7.1.0, 0.71 v7.0.0, 0.75 v6.4.0, 0.86 v6.3.0, 0.83 v6.2.0, 1.00 v6.1.0, 0.83 v6.0.0, 0.67 v5.5.0, 0.80 v5.4.0, 1.00 v5.0.0, 0.75 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.16/0.40 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.16/0.40 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.16/0.40 % Maximal formula atoms : 0 ( 0 avg)
% 0.16/0.40 % Number of connectives : 44 ( 0 ~; 0 |; 3 &; 35 @)
% 0.16/0.40 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.16/0.40 % Maximal formula depth : 16 ( 16 avg)
% 0.16/0.40 % Number of types : 4 ( 3 usr)
% 0.16/0.40 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.16/0.40 % Number of symbols : 3 ( 3 usr; 0 con; 2-2 aty)
% 0.16/0.40 % Number of variables : 17 ( 0 ^; 16 !; 1 ?; 17 :)
% 0.16/0.40 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.40
% 0.16/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 thf(c_type,type,
% 0.16/0.40 c: $tType ).
% 0.16/0.40
% 0.16/0.40 thf(b_type,type,
% 0.16/0.40 b: $tType ).
% 0.16/0.40
% 0.16/0.40 thf(a_type,type,
% 0.16/0.40 a: $tType ).
% 0.16/0.40
% 0.16/0.40 thf(c_starc,type,
% 0.16/0.40 c_starc: c > c > c ).
% 0.16/0.40
% 0.16/0.40 thf(c_starb,type,
% 0.16/0.40 c_starb: b > b > b ).
% 0.16/0.40
% 0.16/0.40 thf(c_stara,type,
% 0.16/0.40 c_stara: a > a > a ).
% 0.16/0.40
% 0.16/0.40 thf(cTHM270_INST,conjecture,
% 0.16/0.40 ! [Xf: a > b,Xg: a > c,Xh: b > c] :
% 0.16/0.40 ( ( ! [Xx: a,Xq: c > $o] :
% 0.16/0.40 ( ( Xq @ ( Xh @ ( Xf @ Xx ) ) )
% 0.16/0.40 => ( Xq @ ( Xg @ Xx ) ) )
% 0.16/0.40 & ! [Xy: b] :
% 0.16/0.40 ? [Xx: a] :
% 0.16/0.40 ! [Xq: b > $o] :
% 0.16/0.40 ( ( Xq @ ( Xf @ Xx ) )
% 0.16/0.40 => ( Xq @ Xy ) )
% 0.16/0.40 & ! [Xx: a,Xy: a,Xq: b > $o] :
% 0.16/0.40 ( ( Xq @ ( Xf @ ( c_stara @ Xx @ Xy ) ) )
% 0.16/0.40 => ( Xq @ ( c_starb @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) ) )
% 0.16/0.40 & ! [Xx: a,Xy: a,Xq: c > $o] :
% 0.16/0.40 ( ( Xq @ ( Xg @ ( c_stara @ Xx @ Xy ) ) )
% 0.16/0.40 => ( Xq @ ( c_starc @ ( Xg @ Xx ) @ ( Xg @ Xy ) ) ) ) )
% 0.16/0.40 => ! [Xx: b,Xy: b,Xq: c > $o] :
% 0.16/0.40 ( ( Xq @ ( Xh @ ( c_starb @ Xx @ Xy ) ) )
% 0.16/0.40 => ( Xq @ ( c_starc @ ( Xh @ Xx ) @ ( Xh @ Xy ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 ------------------------
% 1.58/1.36 ---- Embedded in THF ---
% 1.58/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.58/1.36 %%% Generated on Tue Feb 24 14:28:56 EST 2026
% 1.58/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.58/1.36 %%% Logic specification used:
% 1.58/1.36 %%% thf(spec, logic, $$dhol).
% 1.58/1.36
% 1.58/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.glNrkzU4u6/DTF2DTF7826.p
% See solution above
% 1.58/1.36 ------------------------
% 1.58/1.37 ---- Cleaned THF ---
% 1.58/1.37 thf(c_type,type,
% 1.58/1.37 c: $tType ).
% 1.58/1.37
% 1.58/1.37 thf(b_type,type,
% 1.58/1.37 b: $tType ).
% 1.58/1.37
% 1.58/1.37 thf(a_type,type,
% 1.58/1.37 a: $tType ).
% 1.58/1.37
% 1.58/1.37 thf(c_starc,type,
% 1.58/1.37 c_starc: c > c > c ).
% 1.58/1.37
% 1.58/1.37 thf(c_starb,type,
% 1.58/1.37 c_starb: b > b > b ).
% 1.58/1.37
% 1.58/1.37 thf(c_stara,type,
% 1.58/1.37 c_stara: a > a > a ).
% 1.58/1.37
% 1.58/1.37 thf(cTHM270_INST,conjecture,
% 1.58/1.37 ! [Xf: a > b,Xg: a > c,Xh: b > c] :
% 1.58/1.37 ( ( ! [Xx: a,Xq: c > $o] :
% 1.58/1.37 ( ( Xq @ ( Xh @ ( Xf @ Xx ) ) )
% 1.58/1.37 => ( Xq @ ( Xg @ Xx ) ) )
% 1.58/1.37 & ! [Xy: b] :
% 1.58/1.37 ? [Xx: a] :
% 1.58/1.37 ! [Xq: b > $o] :
% 1.58/1.37 ( ( Xq @ ( Xf @ Xx ) )
% 1.58/1.37 => ( Xq @ Xy ) )
% 1.58/1.37 & ! [Xx: a,Xy: a,Xq: b > $o] :
% 1.58/1.37 ( ( Xq @ ( Xf @ ( c_stara @ Xx @ Xy ) ) )
% 1.58/1.37 => ( Xq @ ( c_starb @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) ) )
% 1.58/1.37 & ! [Xx: a,Xy: a,Xq: c > $o] :
% 1.58/1.37 ( ( Xq @ ( Xg @ ( c_stara @ Xx @ Xy ) ) )
% 1.58/1.37 => ( Xq @ ( c_starc @ ( Xg @ Xx ) @ ( Xg @ Xy ) ) ) ) )
% 1.58/1.37 => ! [Xx: b,Xy: b,Xq: c > $o] :
% 1.58/1.37 ( ( Xq @ ( Xh @ ( c_starb @ Xx @ Xy ) ) )
% 1.58/1.37 => ( Xq @ ( c_starc @ ( Xh @ Xx ) @ ( Xh @ Xy ) ) ) ) ) ).
% 1.58/1.37 ------------------------
% 1.58/1.39 % (7929)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7826 for (2999ds/18Mi)
% 1.58/1.39 % (7927)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_7826 for (2999ds/2Mi)
% 1.58/1.39 % (7923)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7826 for (2999ds/183Mi)
% 1.58/1.39 % (7925)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_7826 for (2999ds/27Mi)
% 1.58/1.39 % (7928)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_7826 for (2999ds/275Mi)
% 1.58/1.39 % (7924)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_7826 for (2999ds/4Mi)
% 1.58/1.39 % (7927)Instruction limit reached!
% 1.58/1.39 % (7927)------------------------------
% 1.58/1.39 % (7927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.39 % (7927)Termination reason: Unknown
% 1.58/1.39 % (7927)Termination phase: Property scanning
% 1.58/1.39
% 1.58/1.39 % (7927)Memory used [KB]: 1023
% 1.58/1.39 % (7927)Time elapsed: 0.003 s
% 1.58/1.39 % (7927)Instructions burned: 2 (million)
% 1.58/1.39 % (7927)------------------------------
% 1.58/1.39 % (7927)------------------------------
% 1.58/1.39 % (7926)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7826 for (2999ds/2Mi)
% 1.58/1.39 % (7924)Instruction limit reached!
% 1.58/1.39 % (7924)------------------------------
% 1.58/1.39 % (7924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.39 % (7924)Termination reason: Unknown
% 1.58/1.39 % (7924)Termination phase: Saturation
% 1.58/1.39
% 1.58/1.39 % (7924)Memory used [KB]: 5500
% 1.58/1.39 % (7924)Time elapsed: 0.004 s
% 1.58/1.39 % (7924)Instructions burned: 4 (million)
% 1.58/1.39 % (7924)------------------------------
% 1.58/1.39 % (7924)------------------------------
% 1.58/1.39 % (7926)Instruction limit reached!
% 1.58/1.39 % (7926)------------------------------
% 1.58/1.39 % (7926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.39 % (7925)Refutation not found, incomplete strategy
% 1.58/1.39 % (7925)------------------------------
% 1.58/1.39 % (7925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.39 % (7925)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.39
% 1.58/1.39
% 1.58/1.39 % (7925)Memory used [KB]: 5500
% 1.58/1.39 % (7925)Time elapsed: 0.005 s
% 1.58/1.39 % (7925)Instructions burned: 4 (million)
% 1.58/1.39 % (7925)------------------------------
% 1.58/1.39 % (7925)------------------------------
% 1.58/1.39 % (7926)Termination reason: Unknown
% 1.58/1.39 % (7926)Termination phase: Preprocessing 3
% 1.58/1.39
% 1.58/1.39 % (7926)Memory used [KB]: 1023
% 1.58/1.39 % (7926)Time elapsed: 0.003 s
% 1.58/1.39 % (7926)Instructions burned: 2 (million)
% 1.58/1.39 % (7926)------------------------------
% 1.58/1.39 % (7926)------------------------------
% 1.70/1.40 % (7929)Instruction limit reached!
% 1.70/1.40 % (7929)------------------------------
% 1.70/1.40 % (7929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.40 % (7929)Termination reason: Unknown
% 1.70/1.40 % (7929)Termination phase: Saturation
% 1.70/1.40
% 1.70/1.40 % (7929)Memory used [KB]: 5628
% 1.70/1.40 % (7929)Time elapsed: 0.012 s
% 1.70/1.40 % (7929)Instructions burned: 18 (million)
% 1.70/1.40 % (7929)------------------------------
% 1.70/1.40 % (7929)------------------------------
% 1.70/1.41 % (7930)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7826 for (2999ds/3Mi)
% 1.70/1.41 % (7931)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_7826 for (2999ds/37Mi)
% 1.70/1.41 % (7933)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7826 for (2999ds/3Mi)
% 1.70/1.41 % (7930)Instruction limit reached!
% 1.70/1.41 % (7930)------------------------------
% 1.70/1.41 % (7930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.41 % (7930)Termination reason: Unknown
% 1.70/1.41 % (7930)Termination phase: Saturation
% 1.70/1.41
% 1.70/1.41 % (7930)Memory used [KB]: 5500
% 1.70/1.41 % (7930)Time elapsed: 0.004 s
% 1.70/1.41 % (7930)Instructions burned: 4 (million)
% 1.70/1.41 % (7930)------------------------------
% 1.70/1.41 % (7930)------------------------------
% 1.70/1.41 % (7932)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_7826 for (2999ds/15Mi)
% 1.70/1.41 % (7933)Instruction limit reached!
% 1.70/1.41 % (7933)------------------------------
% 1.70/1.41 % (7933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.41 % (7933)Termination reason: Unknown
% 1.70/1.41 % (7933)Termination phase: Saturation
% 1.70/1.41
% 1.70/1.41 % (7933)Memory used [KB]: 5500
% 1.70/1.41 % (7933)Time elapsed: 0.004 s
% 1.70/1.41 % (7933)Instructions burned: 4 (million)
% 1.70/1.41 % (7933)------------------------------
% 1.70/1.41 % (7933)------------------------------
% 1.70/1.41 % (7928)First to succeed.
% 1.70/1.42 % (7928)Refutation found. Thanks to Tanya!
% 1.70/1.42 % SZS status Theorem for DTF2THF_7826
% 1.70/1.42 % SZS output start Proof for DTF2THF_7826
% 1.70/1.42 thf(type_def_5, type, c: $tType).
% 1.70/1.42 thf(type_def_7, type, b: $tType).
% 1.70/1.42 thf(type_def_8, type, a: $tType).
% 1.70/1.42 thf(func_def_0, type, c: $tType).
% 1.70/1.42 thf(func_def_1, type, b: $tType).
% 1.70/1.42 thf(func_def_2, type, a: $tType).
% 1.70/1.42 thf(func_def_3, type, c_starc: c > c > c).
% 1.70/1.42 thf(func_def_4, type, c_starb: b > b > b).
% 1.70/1.42 thf(func_def_5, type, c_stara: a > a > a).
% 1.70/1.42 thf(func_def_9, type, sK0: b > c).
% 1.70/1.42 thf(func_def_10, type, sK1: a > b).
% 1.70/1.42 thf(func_def_11, type, sK2: a > c).
% 1.70/1.42 thf(func_def_12, type, sK3: b > a).
% 1.70/1.42 thf(func_def_13, type, sK4: b).
% 1.70/1.42 thf(func_def_14, type, sK5: c > $o).
% 1.70/1.42 thf(func_def_15, type, sK6: b).
% 1.70/1.42 thf(func_def_18, type, ph8: !>[X0: $tType]:(X0)).
% 1.70/1.42 thf(f248,plain,(
% 1.70/1.42 $false),
% 1.70/1.42 inference(subsumption_resolution,[status(thm)],[f247,f14])).
% 1.70/1.42 thf(f14,plain,(
% 1.70/1.42 ((sK5 @ (sK0 @ (c_starb @ sK4 @ sK6))) = $true)),
% 1.70/1.42 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.42 thf(f12,plain,(
% 1.70/1.42 ! [X3 : a,X4 : b > $o,X5 : a] : (($true = (X4 @ (c_starb @ (sK1 @ X3) @ (sK1 @ X5)))) | ($true != (X4 @ (sK1 @ (c_stara @ X3 @ X5))))) & ! [X6 : b] : ! [X8 : b > $o] : (($true != (X8 @ (sK1 @ (sK3 @ X6)))) | ($true = (X8 @ X6))) & ! [X9 : c > $o,X10 : a] : (($true = (X9 @ (sK2 @ X10))) | ($true != (X9 @ (sK0 @ (sK1 @ X10))))) & ! [X11 : a,X12 : c > $o,X13 : a] : (((X12 @ (sK2 @ (c_stara @ X11 @ X13))) != $true) | ($true = (X12 @ (c_starc @ (sK2 @ X11) @ (sK2 @ X13))))) & (((sK5 @ (sK0 @ (c_starb @ sK4 @ sK6))) = $true) & ($true != (sK5 @ (c_starc @ (sK0 @ sK4) @ (sK0 @ sK6)))))),
% 1.70/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f8,f11,f10,f9])).
% 1.70/1.42 thf(f9,plain,(
% 1.70/1.42 ? [X0 : b > c,X1 : a > b,X2 : a > c] : (! [X3 : a,X4 : b > $o,X5 : a] : (($true = (X4 @ (c_starb @ (X1 @ X3) @ (X1 @ X5)))) | ($true != (X4 @ (X1 @ (c_stara @ X3 @ X5))))) & ! [X6 : b] : ? [X7 : a] : ! [X8 : b > $o] : (($true != (X8 @ (X1 @ X7))) | ($true = (X8 @ X6))) & ! [X9 : c > $o,X10 : a] : (((X9 @ (X2 @ X10)) = $true) | ((X9 @ (X0 @ (X1 @ X10))) != $true)) & ! [X11 : a,X12 : c > $o,X13 : a] : (($true != (X12 @ (X2 @ (c_stara @ X11 @ X13)))) | ($true = (X12 @ (c_starc @ (X2 @ X11) @ (X2 @ X13))))) & ? [X14 : b,X15 : c > $o,X16 : b] : (($true = (X15 @ (X0 @ (c_starb @ X14 @ X16)))) & ((X15 @ (c_starc @ (X0 @ X14) @ (X0 @ X16))) != $true))) => (! [X5 : a,X4 : b > $o,X3 : a] : (($true = (X4 @ (c_starb @ (sK1 @ X3) @ (sK1 @ X5)))) | ($true != (X4 @ (sK1 @ (c_stara @ X3 @ X5))))) & ! [X6 : b] : ? [X7 : a] : ! [X8 : b > $o] : (($true != (X8 @ (sK1 @ X7))) | ($true = (X8 @ X6))) & ! [X10 : a,X9 : c > $o] : (($true = (X9 @ (sK2 @ X10))) | ($true != (X9 @ (sK0 @ (sK1 @ X10))))) & ! [X13 : a,X12 : c > $o,X11 : a] : (((X12 @ (sK2 @ (c_stara @ X11 @ X13))) != $true) | ($true = (X12 @ (c_starc @ (sK2 @ X11) @ (sK2 @ X13))))) & ? [X16 : b,X15 : c > $o,X14 : b] : (((X15 @ (sK0 @ (c_starb @ X14 @ X16))) = $true) & ($true != (X15 @ (c_starc @ (sK0 @ X14) @ (sK0 @ X16))))))),
% 1.70/1.42 introduced(definition,[],[choice_axiom])).
% 1.70/1.42 thf(f10,plain,(
% 1.70/1.42 ! [X6 : b] : (? [X7 : a] : ! [X8 : b > $o] : (($true != (X8 @ (sK1 @ X7))) | ($true = (X8 @ X6))) => ! [X8 : b > $o] : (($true != (X8 @ (sK1 @ (sK3 @ X6)))) | ($true = (X8 @ X6))))),
% 1.70/1.42 introduced(definition,[],[choice_axiom])).
% 1.70/1.42 thf(f11,plain,(
% 1.70/1.42 ? [X16 : b,X15 : c > $o,X14 : b] : (((X15 @ (sK0 @ (c_starb @ X14 @ X16))) = $true) & ($true != (X15 @ (c_starc @ (sK0 @ X14) @ (sK0 @ X16))))) => (((sK5 @ (sK0 @ (c_starb @ sK4 @ sK6))) = $true) & ($true != (sK5 @ (c_starc @ (sK0 @ sK4) @ (sK0 @ sK6)))))),
% 1.70/1.42 introduced(definition,[],[choice_axiom])).
% 1.70/1.42 thf(f8,plain,(
% 1.70/1.42 ? [X0 : b > c,X1 : a > b,X2 : a > c] : (! [X3 : a,X4 : b > $o,X5 : a] : (($true = (X4 @ (c_starb @ (X1 @ X3) @ (X1 @ X5)))) | ($true != (X4 @ (X1 @ (c_stara @ X3 @ X5))))) & ! [X6 : b] : ? [X7 : a] : ! [X8 : b > $o] : (($true != (X8 @ (X1 @ X7))) | ($true = (X8 @ X6))) & ! [X9 : c > $o,X10 : a] : (((X9 @ (X2 @ X10)) = $true) | ((X9 @ (X0 @ (X1 @ X10))) != $true)) & ! [X11 : a,X12 : c > $o,X13 : a] : (($true != (X12 @ (X2 @ (c_stara @ X11 @ X13)))) | ($true = (X12 @ (c_starc @ (X2 @ X11) @ (X2 @ X13))))) & ? [X14 : b,X15 : c > $o,X16 : b] : (($true = (X15 @ (X0 @ (c_starb @ X14 @ X16)))) & ((X15 @ (c_starc @ (X0 @ X14) @ (X0 @ X16))) != $true)))),
% 1.70/1.42 inference(rectify,[status(thm)],[f7])).
% 1.70/1.42 thf(f7,plain,(
% 1.70/1.42 ? [X0 : b > c,X1 : a > b,X2 : a > c] : (! [X13 : a,X12 : b > $o,X11 : a] : (($true = (X12 @ (c_starb @ (X1 @ X13) @ (X1 @ X11)))) | ($true != (X12 @ (X1 @ (c_stara @ X13 @ X11))))) & ! [X5 : b] : ? [X6 : a] : ! [X7 : b > $o] : (($true != (X7 @ (X1 @ X6))) | ((X7 @ X5) = $true)) & ! [X4 : c > $o,X3 : a] : (($true = (X4 @ (X2 @ X3))) | ($true != (X4 @ (X0 @ (X1 @ X3))))) & ! [X9 : a,X8 : c > $o,X10 : a] : (((X8 @ (X2 @ (c_stara @ X9 @ X10))) != $true) | ($true = (X8 @ (c_starc @ (X2 @ X9) @ (X2 @ X10))))) & ? [X15 : b,X14 : c > $o,X16 : b] : (($true = (X14 @ (X0 @ (c_starb @ X15 @ X16)))) & ($true != (X14 @ (c_starc @ (X0 @ X15) @ (X0 @ X16))))))),
% 1.70/1.42 inference(flattening,[status(thm)],[f6])).
% 1.70/1.42 thf(f6,plain,(
% 1.70/1.42 ? [X0 : b > c,X1 : a > b,X2 : a > c] : (? [X15 : b,X14 : c > $o,X16 : b] : (($true = (X14 @ (X0 @ (c_starb @ X15 @ X16)))) & ($true != (X14 @ (c_starc @ (X0 @ X15) @ (X0 @ X16))))) & (! [X9 : a,X8 : c > $o,X10 : a] : (((X8 @ (X2 @ (c_stara @ X9 @ X10))) != $true) | ($true = (X8 @ (c_starc @ (X2 @ X9) @ (X2 @ X10))))) & ! [X5 : b] : ? [X6 : a] : ! [X7 : b > $o] : (($true != (X7 @ (X1 @ X6))) | ((X7 @ X5) = $true)) & ! [X4 : c > $o,X3 : a] : (($true = (X4 @ (X2 @ X3))) | ($true != (X4 @ (X0 @ (X1 @ X3))))) & ! [X13 : a,X12 : b > $o,X11 : a] : (($true = (X12 @ (c_starb @ (X1 @ X13) @ (X1 @ X11)))) | ($true != (X12 @ (X1 @ (c_stara @ X13 @ X11)))))))),
% 1.70/1.42 inference(ennf_transformation,[status(thm)],[f5])).
% 1.70/1.42 thf(f5,plain,(
% 1.70/1.42 ~! [X0 : b > c,X1 : a > b,X2 : a > c] : ((! [X8 : c > $o,X9 : a,X10 : a] : (((X8 @ (X2 @ (c_stara @ X9 @ X10))) = $true) => ($true = (X8 @ (c_starc @ (X2 @ X9) @ (X2 @ X10))))) & ! [X5 : b] : ? [X6 : a] : ! [X7 : b > $o] : (($true = (X7 @ (X1 @ X6))) => ((X7 @ X5) = $true)) & ! [X4 : c > $o,X3 : a] : (($true = (X4 @ (X0 @ (X1 @ X3)))) => ($true = (X4 @ (X2 @ X3)))) & ! [X12 : b > $o,X11 : a,X13 : a] : (($true = (X12 @ (X1 @ (c_stara @ X13 @ X11)))) => ($true = (X12 @ (c_starb @ (X1 @ X13) @ (X1 @ X11)))))) => ! [X16 : b,X14 : c > $o,X15 : b] : (($true = (X14 @ (X0 @ (c_starb @ X15 @ X16)))) => ($true = (X14 @ (c_starc @ (X0 @ X15) @ (X0 @ X16))))))),
% 1.70/1.42 inference(fool_elimination,[status(thm)],[f4])).
% 1.70/1.42 thf(f4,plain,(
% 1.70/1.42 ~! [X0 : b > c,X1 : a > b,X2 : a > c] : ((! [X3 : a,X4 : c > $o] : ((X4 @ (X0 @ (X1 @ X3))) => (X4 @ (X2 @ X3))) & ! [X5 : b] : ? [X6 : a] : ! [X7 : b > $o] : ((X7 @ (X1 @ X6)) => (X7 @ X5)) & ! [X8 : c > $o,X9 : a,X10 : a] : ((X8 @ (X2 @ (c_stara @ X9 @ X10))) => (X8 @ (c_starc @ (X2 @ X9) @ (X2 @ X10)))) & ! [X11 : a,X12 : b > $o,X13 : a] : ((X12 @ (X1 @ (c_stara @ X13 @ X11))) => (X12 @ (c_starb @ (X1 @ X13) @ (X1 @ X11))))) => ! [X14 : c > $o,X15 : b,X16 : b] : ((X14 @ (X0 @ (c_starb @ X15 @ X16))) => (X14 @ (c_starc @ (X0 @ X15) @ (X0 @ X16)))))),
% 1.70/1.42 inference(rectify,[status(thm)],[f2])).
% 1.70/1.42 thf(f2,negated_conjecture,(
% 1.70/1.42 ~! [X2 : b > c,X0 : a > b,X1 : a > c] : ((! [X3 : a,X4 : c > $o] : ((X4 @ (X2 @ (X0 @ X3))) => (X4 @ (X1 @ X3))) & ! [X5 : b] : ? [X3 : a] : ! [X4 : b > $o] : ((X4 @ (X0 @ X3)) => (X4 @ X5)) & ! [X4 : c > $o,X3 : a,X5 : a] : ((X4 @ (X1 @ (c_stara @ X3 @ X5))) => (X4 @ (c_starc @ (X1 @ X3) @ (X1 @ X5)))) & ! [X5 : a,X4 : b > $o,X3 : a] : ((X4 @ (X0 @ (c_stara @ X3 @ X5))) => (X4 @ (c_starb @ (X0 @ X3) @ (X0 @ X5))))) => ! [X4 : c > $o,X3 : b,X5 : b] : ((X4 @ (X2 @ (c_starb @ X3 @ X5))) => (X4 @ (c_starc @ (X2 @ X3) @ (X2 @ X5)))))),
% 1.70/1.42 inference(negated_conjecture,[status(cth)],[f1])).
% 1.70/1.42 thf(f1,conjecture,(
% 1.70/1.42 ! [X2 : b > c,X0 : a > b,X1 : a > c] : ((! [X3 : a,X4 : c > $o] : ((X4 @ (X2 @ (X0 @ X3))) => (X4 @ (X1 @ X3))) & ! [X5 : b] : ? [X3 : a] : ! [X4 : b > $o] : ((X4 @ (X0 @ X3)) => (X4 @ X5)) & ! [X4 : c > $o,X3 : a,X5 : a] : ((X4 @ (X1 @ (c_stara @ X3 @ X5))) => (X4 @ (c_starc @ (X1 @ X3) @ (X1 @ X5)))) & ! [X5 : a,X4 : b > $o,X3 : a] : ((X4 @ (X0 @ (c_stara @ X3 @ X5))) => (X4 @ (c_starb @ (X0 @ X3) @ (X0 @ X5))))) => ! [X4 : c > $o,X3 : b,X5 : b] : ((X4 @ (X2 @ (c_starb @ X3 @ X5))) => (X4 @ (c_starc @ (X2 @ X3) @ (X2 @ X5)))))),
% 1.70/1.42 file('/export/starexec/sandbox2/tmp/tmp.glNrkzU4u6/DTF2THF_7826.p',cTHM270_INST)).
% 1.70/1.42 thf(f247,plain,(
% 1.70/1.42 ((sK5 @ (sK0 @ (c_starb @ sK4 @ sK6))) != $true)),
% 1.70/1.42 inference(superposition,[status(thm)],[f13,f220])).
% 1.70/1.42 thf(f220,plain,(
% 1.70/1.42 ( ! [X0 : b,X1 : b] : (((c_starc @ (sK0 @ X0) @ (sK0 @ X1)) = (sK0 @ (c_starb @ X0 @ X1)))) )),
% 1.70/1.42 inference(forward_demodulation,[status(thm)],[f213,f76])).
% 1.70/1.42 thf(f76,plain,(
% 1.70/1.42 ( ! [X0 : b] : (((sK0 @ X0) = (sK2 @ (sK3 @ X0)))) )),
% 1.70/1.42 inference(superposition,[status(thm)],[f53,f20])).
% 1.70/1.42 thf(f20,plain,(
% 1.70/1.42 ( ! [X0 : b] : (((sK1 @ (sK3 @ X0)) = X0)) )),
% 1.70/1.42 inference(leibniz_equality_elimination,[status(thm)],[f17])).
% 1.70/1.42 thf(f17,plain,(
% 1.70/1.42 ( ! [X8 : b > $o,X6 : b] : (($true != (X8 @ (sK1 @ (sK3 @ X6)))) | ($true = (X8 @ X6))) )),
% 1.70/1.42 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.42 thf(f53,plain,(
% 1.70/1.42 ( ! [X0 : a] : (((sK2 @ X0) = (sK0 @ (sK1 @ X0)))) )),
% 1.70/1.42 inference(leibniz_equality_elimination,[status(thm)],[f16])).
% 1.70/1.42 thf(f16,plain,(
% 1.70/1.42 ( ! [X10 : a,X9 : c > $o] : (($true != (X9 @ (sK0 @ (sK1 @ X10)))) | ($true = (X9 @ (sK2 @ X10)))) )),
% 1.70/1.42 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.42 thf(f213,plain,(
% 1.70/1.42 ( ! [X0 : b,X1 : b] : (((c_starc @ (sK2 @ (sK3 @ X0)) @ (sK0 @ X1)) = (sK0 @ (c_starb @ X0 @ X1)))) )),
% 1.70/1.42 inference(superposition,[status(thm)],[f145,f20])).
% 1.70/1.42 thf(f145,plain,(
% 1.70/1.42 ( ! [X0 : a,X1 : b] : (((sK0 @ (c_starb @ (sK1 @ X0) @ X1)) = (c_starc @ (sK2 @ X0) @ (sK0 @ X1)))) )),
% 1.70/1.42 inference(forward_demodulation,[status(thm)],[f142,f120])).
% 1.70/1.42 thf(f120,plain,(
% 1.70/1.42 ( ! [X0 : b,X1 : a] : (((c_starc @ (sK2 @ X1) @ (sK0 @ X0)) = (sK2 @ (c_stara @ X1 @ (sK3 @ X0))))) )),
% 1.70/1.42 inference(superposition,[status(thm)],[f66,f76])).
% 1.70/1.42 thf(f66,plain,(
% 1.70/1.42 ( ! [X0 : a,X1 : a] : (((sK2 @ (c_stara @ X0 @ X1)) = (c_starc @ (sK2 @ X0) @ (sK2 @ X1)))) )),
% 1.70/1.42 inference(leibniz_equality_elimination,[status(thm)],[f15])).
% 1.70/1.42 thf(f15,plain,(
% 1.70/1.42 ( ! [X11 : a,X12 : c > $o,X13 : a] : (($true = (X12 @ (c_starc @ (sK2 @ X11) @ (sK2 @ X13)))) | ((X12 @ (sK2 @ (c_stara @ X11 @ X13))) != $true)) )),
% 1.70/1.42 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.42 thf(f142,plain,(
% 1.70/1.42 ( ! [X0 : a,X1 : b] : (((sK0 @ (c_starb @ (sK1 @ X0) @ X1)) = (sK2 @ (c_stara @ X0 @ (sK3 @ X1))))) )),
% 1.70/1.42 inference(superposition,[status(thm)],[f53,f135])).
% 1.70/1.42 thf(f135,plain,(
% 1.70/1.42 ( ! [X0 : b,X1 : a] : (((c_starb @ (sK1 @ X1) @ X0) = (sK1 @ (c_stara @ X1 @ (sK3 @ X0))))) )),
% 1.70/1.42 inference(superposition,[status(thm)],[f79,f20])).
% 1.70/1.42 thf(f79,plain,(
% 1.70/1.42 ( ! [X0 : a,X1 : a] : (((c_starb @ (sK1 @ X0) @ (sK1 @ X1)) = (sK1 @ (c_stara @ X0 @ X1)))) )),
% 1.70/1.42 inference(leibniz_equality_elimination,[status(thm)],[f18])).
% 1.70/1.42 thf(f18,plain,(
% 1.70/1.42 ( ! [X3 : a,X4 : b > $o,X5 : a] : (($true = (X4 @ (c_starb @ (sK1 @ X3) @ (sK1 @ X5)))) | ($true != (X4 @ (sK1 @ (c_stara @ X3 @ X5))))) )),
% 1.70/1.42 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.42 thf(f13,plain,(
% 1.70/1.42 ($true != (sK5 @ (c_starc @ (sK0 @ sK4) @ (sK0 @ sK6))))),
% 1.70/1.42 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.42 % SZS output end Proof for DTF2THF_7826
% 1.70/1.42 % (7928)------------------------------
% 1.70/1.42 % (7928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.42 % (7928)Termination reason: Refutation
% 1.70/1.42
% 1.70/1.42 % (7928)Memory used [KB]: 5756
% 1.70/1.42 % (7928)Time elapsed: 0.027 s
% 1.70/1.42 % (7928)Instructions burned: 45 (million)
% 1.70/1.42 % (7928)------------------------------
% 1.70/1.42 % (7928)------------------------------
% 1.70/1.42 % (7922)Success in time 0.037 s
%------------------------------------------------------------------------------