TSTP Solution File: SEV053^5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEV053^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.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 : Tue May 21 04:14:22 EDT 2024
% Result : Theorem 0.20s 0.37s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of formulae : 37 ( 6 unt; 16 typ; 0 def)
% Number of atoms : 355 ( 46 equ; 0 cnn)
% Maximal formula atoms : 5 ( 16 avg)
% Number of connectives : 66 ( 25 ~; 16 |; 16 &; 0 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 22 ( 21 >; 1 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 3 con; 0-6 aty)
% Number of variables : 57 ( 0 ^ 47 !; 4 ?; 57 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
cF: b > b ).
thf(func_def_3,type,
cA: b > a ).
thf(func_def_4,type,
cL: a > a > $o ).
thf(func_def_8,type,
sK0: b ).
thf(func_def_10,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_11,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_12,type,
vAND: $o > $o > $o ).
thf(func_def_13,type,
vOR: $o > $o > $o ).
thf(func_def_14,type,
vIMP: $o > $o > $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f70,plain,
$false,
inference(trivial_inequality_removal,[],[f63]) ).
thf(f63,plain,
$true = $false,
inference(superposition,[],[f44,f56]) ).
thf(f56,plain,
! [X0: b] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X0)))) ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f53,plain,
! [X0: b] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X0)))) ) ),
inference(superposition,[],[f52,f13]) ).
thf(f13,plain,
! [X1: b] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X1)),vAPP(b,a,cA,vAPP(b,b,cF,X1))) ),
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,sK0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,sK0)))) )
& ! [X1: b] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X1)),vAPP(b,a,cA,vAPP(b,b,cF,X1))) )
& ! [X2: a,X3: a,X4: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X4) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X3),X4) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X3) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: b] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X0)))) )
=> ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,sK0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,sK0)))) ) ),
introduced(choice_axiom,[]) ).
thf(f9,plain,
( ? [X0: b] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X0)))) )
& ! [X1: b] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X1)),vAPP(b,a,cA,vAPP(b,b,cF,X1))) )
& ! [X2: a,X3: a,X4: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X4) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X3),X4) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X3) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,plain,
( ? [X4: b] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X4)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X4)))) != $true )
& ! [X0: b] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),vAPP(b,a,cA,vAPP(b,b,cF,X0))) )
& ! [X1: a,X2: a,X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X3) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X2) != $true ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
( ? [X4: b] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X4)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X4)))) != $true )
& ! [X0: b] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),vAPP(b,a,cA,vAPP(b,b,cF,X0))) )
& ! [X1: a,X2: a,X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X3) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X2) != $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: b] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),vAPP(b,a,cA,vAPP(b,b,cF,X0))) )
& ! [X1: a,X2: a,X3: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X3) )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X2) = $true ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X3) ) ) )
=> ! [X4: b] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X4)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X4)))) = $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: b] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),vAPP(b,a,cA,vAPP(b,b,cF,X0)))
& ! [X1: a,X2: a,X3: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X3)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X2) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X3) ) )
=> ! [X4: b] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X4)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X4)))) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: b] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X3)),vAPP(b,a,cA,vAPP(b,b,cF,X3)))
& ! [X0: a,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X2)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X0),X1) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X0),X2) ) )
=> ! [X4: b] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X4)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X4)))) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ( ! [X3: b] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X3)),vAPP(b,a,cA,vAPP(b,b,cF,X3)))
& ! [X0: a,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X2)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X0),X1) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X0),X2) ) )
=> ! [X4: b] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X4)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X4)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM89B_pme) ).
thf(f52,plain,
! [X0: b,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,vAPP(b,b,cF,X0))),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),X1) ) ),
inference(trivial_inequality_removal,[],[f48]) ).
thf(f48,plain,
! [X0: b,X1: a] :
( ( $true != $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,vAPP(b,b,cF,X0))),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),X1) ) ),
inference(superposition,[],[f12,f13]) ).
thf(f12,plain,
! [X2: a,X3: a,X4: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X3),X4) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X4) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f44,plain,
$false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,sK0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,sK0)))),
inference(trivial_inequality_removal,[],[f43]) ).
thf(f43,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,sK0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,sK0)))) ) ),
inference(superposition,[],[f14,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f14,plain,
$true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,sK0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,sK0)))),
inference(cnf_transformation,[],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV053^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 19:13:38 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % (8849)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (8855)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.36 % (8856)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.36 % Exception at run slice level
% 0.14/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.37 % (8855)First to succeed.
% 0.14/0.37 % (8855)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-8849"
% 0.14/0.37 % (8850)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37 % (8851)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.37 % (8855)Refutation found. Thanks to Tanya!
% 0.20/0.37 % SZS status Theorem for theBenchmark
% 0.20/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.37 % (8855)------------------------------
% 0.20/0.37 % (8855)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.37 % (8855)Termination reason: Refutation
% 0.20/0.37
% 0.20/0.37 % (8855)Memory used [KB]: 776
% 0.20/0.37 % (8855)Time elapsed: 0.006 s
% 0.20/0.37 % (8855)Instructions burned: 8 (million)
% 0.20/0.37 % (8849)Success in time 0.018 s
%------------------------------------------------------------------------------