TSTP Solution File: SEU957^5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU957^5 : 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 : n005.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 04:07:06 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 31
% Syntax : Number of formulae : 59 ( 11 unt; 17 typ; 0 def)
% Number of atoms : 242 ( 70 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 105 ( 39 ~; 25 |; 14 &; 0 @)
% ( 7 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 77 ( 76 >; 1 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 9 con; 0-6 aty)
% Number of variables : 103 ( 0 ^ 55 !; 42 ?; 103 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_5,type,
sK0: ( b > a ) > b ).
thf(func_def_6,type,
sK1: ( b > a ) > b ).
thf(func_def_7,type,
sK2: a > b ).
thf(func_def_8,type,
sK3: b > a ).
thf(func_def_9,type,
sK4: ( a > $o ) > a ).
thf(func_def_11,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_12,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_13,type,
vAND: $o > $o > $o ).
thf(func_def_14,type,
vOR: $o > $o > $o ).
thf(func_def_15,type,
vIMP: $o > $o > $o ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f90,plain,
$false,
inference(avatar_sat_refutation,[],[f22,f27,f31,f35,f45,f51,f86,f89]) ).
thf(f89,plain,
( ~ spl5_3
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[],[f88]) ).
thf(f88,plain,
( $false
| ~ spl5_3
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f87,plain,
( ( vAPP(sTfun(b,a),b,sK0,sK3) != vAPP(sTfun(b,a),b,sK0,sK3) )
| ~ spl5_3
| ~ spl5_7 ),
inference(superposition,[],[f30,f85]) ).
thf(f85,plain,
( ( vAPP(sTfun(b,a),b,sK1,sK3) = vAPP(sTfun(b,a),b,sK0,sK3) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f83,plain,
( spl5_7
<=> ( vAPP(sTfun(b,a),b,sK1,sK3) = vAPP(sTfun(b,a),b,sK0,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
thf(f30,plain,
( ! [X0: b > a] : ( vAPP(sTfun(b,a),b,sK0,X0) != vAPP(sTfun(b,a),b,sK1,X0) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f29,plain,
( spl5_3
<=> ! [X0: b > a] : ( vAPP(sTfun(b,a),b,sK0,X0) != vAPP(sTfun(b,a),b,sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
thf(f86,plain,
( spl5_7
| ~ spl5_1
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f47,f43,f20,f83]) ).
thf(f20,plain,
( spl5_1
<=> ! [X4: b] : ( vAPP(a,b,sK2,vAPP(b,a,sK3,X4)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
thf(f43,plain,
( spl5_5
<=> ! [X0: b > a] : ( vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK0,X0)) = vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
thf(f47,plain,
( ( vAPP(sTfun(b,a),b,sK1,sK3) = vAPP(sTfun(b,a),b,sK0,sK3) )
| ~ spl5_1
| ~ spl5_5 ),
inference(forward_demodulation,[],[f46,f21]) ).
thf(f21,plain,
( ! [X4: b] : ( vAPP(a,b,sK2,vAPP(b,a,sK3,X4)) = X4 )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f46,plain,
( ( vAPP(sTfun(b,a),b,sK1,sK3) = vAPP(a,b,sK2,vAPP(b,a,sK3,vAPP(sTfun(b,a),b,sK0,sK3))) )
| ~ spl5_1
| ~ spl5_5 ),
inference(superposition,[],[f21,f44]) ).
thf(f44,plain,
( ! [X0: b > a] : ( vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK0,X0)) = vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK1,X0)) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f51,plain,
spl5_6,
inference(avatar_split_clause,[],[f4,f49]) ).
thf(f49,plain,
( spl5_6
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f45,plain,
spl5_5,
inference(avatar_split_clause,[],[f17,f43]) ).
thf(f17,plain,
! [X0: b > a] : ( vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK0,X0)) = vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK1,X0)) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
( ! [X0: b > a] :
( ( vAPP(sTfun(b,a),b,sK0,X0) != vAPP(sTfun(b,a),b,sK1,X0) )
& ( vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK0,X0)) = vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK1,X0)) ) )
& ! [X4: b] : ( vAPP(a,b,sK2,vAPP(b,a,sK3,X4)) = X4 )
& ! [X7: a > $o] :
( ( $true = vAPP(a,$o,X7,vAPP(sTfun(a,$o),a,sK4,X7)) )
| ! [X8: a] : ( $true != vAPP(a,$o,X7,X8) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f13,f12,f11,f10]) ).
thf(f10,plain,
! [X0: b > a] :
( ? [X1: b,X2: b] :
( ( X1 != X2 )
& ( vAPP(b,a,X0,X1) = vAPP(b,a,X0,X2) ) )
=> ( ( vAPP(sTfun(b,a),b,sK0,X0) != vAPP(sTfun(b,a),b,sK1,X0) )
& ( vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK0,X0)) = vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK1,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
( ? [X3: a > b] :
! [X4: b] :
? [X5: a] : ( vAPP(a,b,X3,X5) = X4 )
=> ! [X4: b] :
? [X5: a] : ( vAPP(a,b,sK2,X5) = X4 ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
! [X4: b] :
( ? [X5: a] : ( vAPP(a,b,sK2,X5) = X4 )
=> ( vAPP(a,b,sK2,vAPP(b,a,sK3,X4)) = X4 ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
( ? [X6: ( a > $o ) > a] :
! [X7: a > $o] :
( ( $true = vAPP(a,$o,X7,vAPP(sTfun(a,$o),a,X6,X7)) )
| ! [X8: a] : ( $true != vAPP(a,$o,X7,X8) ) )
=> ! [X7: a > $o] :
( ( $true = vAPP(a,$o,X7,vAPP(sTfun(a,$o),a,sK4,X7)) )
| ! [X8: a] : ( $true != vAPP(a,$o,X7,X8) ) ) ),
introduced(choice_axiom,[]) ).
thf(f9,plain,
( ! [X0: b > a] :
? [X1: b,X2: b] :
( ( X1 != X2 )
& ( vAPP(b,a,X0,X1) = vAPP(b,a,X0,X2) ) )
& ? [X3: a > b] :
! [X4: b] :
? [X5: a] : ( vAPP(a,b,X3,X5) = X4 )
& ? [X6: ( a > $o ) > a] :
! [X7: a > $o] :
( ( $true = vAPP(a,$o,X7,vAPP(sTfun(a,$o),a,X6,X7)) )
| ! [X8: a] : ( $true != vAPP(a,$o,X7,X8) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,plain,
( ! [X6: b > a] :
? [X7: b,X8: b] :
( ( X7 != X8 )
& ( vAPP(b,a,X6,X7) = vAPP(b,a,X6,X8) ) )
& ? [X3: a > b] :
! [X4: b] :
? [X5: a] : ( vAPP(a,b,X3,X5) = X4 )
& ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ( vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,X0,X1)) = $true )
| ! [X2: a] : ( vAPP(a,$o,X1,X2) != $true ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
( ! [X6: b > a] :
? [X7: b,X8: b] :
( ( X7 != X8 )
& ( vAPP(b,a,X6,X7) = vAPP(b,a,X6,X8) ) )
& ? [X3: a > b] :
! [X4: b] :
? [X5: a] : ( vAPP(a,b,X3,X5) = X4 )
& ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ( vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,X0,X1)) = $true )
| ! [X2: a] : ( vAPP(a,$o,X1,X2) != $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ( ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ? [X2: a] : ( vAPP(a,$o,X1,X2) = $true )
=> ( vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,X0,X1)) = $true ) )
=> ( ? [X3: a > b] :
! [X4: b] :
? [X5: a] : ( vAPP(a,b,X3,X5) = X4 )
=> ? [X6: b > a] :
! [X7: b,X8: b] :
( ( vAPP(b,a,X6,X7) = vAPP(b,a,X6,X8) )
=> ( X7 = X8 ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ( ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ? [X2: a] : vAPP(a,$o,X1,X2)
=> vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,X0,X1)) )
=> ( ? [X3: a > b] :
! [X4: b] :
? [X5: a] : ( vAPP(a,b,X3,X5) = X4 )
=> ? [X6: b > a] :
! [X7: b,X8: b] :
( ( vAPP(b,a,X6,X7) = vAPP(b,a,X6,X8) )
=> ( X7 = X8 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ? [X2: a] : vAPP(a,$o,X1,X2)
=> vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,X0,X1)) )
=> ( ? [X3: a > b] :
! [X4: b] :
? [X1: a] : ( vAPP(a,b,X3,X1) = X4 )
=> ? [X5: b > a] :
! [X6: b,X7: b] :
( ( vAPP(b,a,X5,X6) = vAPP(b,a,X5,X7) )
=> ( X6 = X7 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ? [X2: a] : vAPP(a,$o,X1,X2)
=> vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,X0,X1)) )
=> ( ? [X3: a > b] :
! [X4: b] :
? [X1: a] : ( vAPP(a,b,X3,X1) = X4 )
=> ? [X5: b > a] :
! [X6: b,X7: b] :
( ( vAPP(b,a,X5,X6) = vAPP(b,a,X5,X7) )
=> ( X6 = X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM607_pme) ).
thf(f35,plain,
spl5_4,
inference(avatar_split_clause,[],[f15,f33]) ).
thf(f33,plain,
( spl5_4
<=> ! [X7: a > $o,X8: a] :
( ( $true = vAPP(a,$o,X7,vAPP(sTfun(a,$o),a,sK4,X7)) )
| ( $true != vAPP(a,$o,X7,X8) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
thf(f15,plain,
! [X8: a,X7: a > $o] :
( ( $true = vAPP(a,$o,X7,vAPP(sTfun(a,$o),a,sK4,X7)) )
| ( $true != vAPP(a,$o,X7,X8) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f31,plain,
spl5_3,
inference(avatar_split_clause,[],[f18,f29]) ).
thf(f18,plain,
! [X0: b > a] : ( vAPP(sTfun(b,a),b,sK0,X0) != vAPP(sTfun(b,a),b,sK1,X0) ),
inference(cnf_transformation,[],[f14]) ).
thf(f27,plain,
~ spl5_2,
inference(avatar_split_clause,[],[f3,f24]) ).
thf(f24,plain,
( spl5_2
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
thf(f3,plain,
$true != $false,
introduced(fool_axiom,[]) ).
thf(f22,plain,
spl5_1,
inference(avatar_split_clause,[],[f16,f20]) ).
thf(f16,plain,
! [X4: b] : ( vAPP(a,b,sK2,vAPP(b,a,sK3,X4)) = X4 ),
inference(cnf_transformation,[],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SEU957^5 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37 % Computer : n005.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun May 19 18:14:53 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % (27278)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (27281)WARNING: value z3 for option sas not known
% 0.15/0.39 % (27279)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (27280)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (27282)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (27281)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.39 % (27283)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.39 % (27284)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.39 % (27285)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.39 % Exception at run slice level% Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39
% 0.15/0.39 % Exception at run slice levelUser error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % (27285)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39 % (27284)Also succeeded, but the first one will report.
% 0.15/0.39 % (27283)First to succeed.
% 0.15/0.39 % (27285)Also succeeded, but the first one will report.
% 0.15/0.39 % (27281)Also succeeded, but the first one will report.
% 0.15/0.39 % (27283)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-27278"
% 0.15/0.39 % (27283)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39 % (27283)------------------------------
% 0.15/0.39 % (27283)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39 % (27283)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (27283)Memory used [KB]: 790
% 0.15/0.39 % (27283)Time elapsed: 0.006 s
% 0.15/0.39 % (27283)Instructions burned: 7 (million)
% 0.15/0.39 % (27278)Success in time 0.007 s
%------------------------------------------------------------------------------