TSTP Solution File: NUM765^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM765^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n017.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 02:13:19 EDT 2024
% Result : Theorem 0.11s 0.35s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 27
% Syntax : Number of formulae : 93 ( 3 unt; 17 typ; 0 def)
% Number of atoms : 855 ( 117 equ; 0 cnn)
% Maximal formula atoms : 4 ( 11 avg)
% Number of connectives : 234 ( 115 ~; 67 |; 5 &; 0 @)
% ( 4 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 23 >; 1 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 10 con; 0-6 aty)
% Number of variables : 90 ( 0 ^ 84 !; 0 ?; 90 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
frac: $tType ).
thf(func_def_1,type,
x: frac ).
thf(func_def_2,type,
y: frac ).
thf(func_def_3,type,
z: frac ).
thf(func_def_4,type,
u: frac ).
thf(func_def_5,type,
moref: frac > frac > $o ).
thf(func_def_6,type,
eq: frac > frac > $o ).
thf(func_def_8,type,
pf: frac > frac > frac ).
thf(func_def_12,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_13,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_14,type,
vAND: $o > $o > $o ).
thf(func_def_15,type,
vOR: $o > $o > $o ).
thf(func_def_16,type,
vIMP: $o > $o > $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(func_def_18,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f147,plain,
$false,
inference(avatar_sat_refutation,[],[f88,f97,f104,f115,f129,f146]) ).
thf(f146,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f145]) ).
thf(f145,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f142]) ).
thf(f142,plain,
( ( $true != $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[],[f141,f96]) ).
thf(f96,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) = $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f94,plain,
( spl0_4
<=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f141,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f140,plain,
( ( $true != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f139,f83]) ).
thf(f83,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) = $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f81]) ).
thf(f81,plain,
( spl0_1
<=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f139,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) != $true ) ),
inference(trivial_inequality_removal,[],[f138]) ).
thf(f138,plain,
( ( $true != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) != $true ) ),
inference(superposition,[],[f41,f50]) ).
thf(f50,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f40,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
| ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
& ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) ) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) ) ),
inference(flattening,[],[f39]) ).
thf(f39,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
| ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
& ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) ) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) ) ),
inference(ennf_transformation,[],[f30]) ).
thf(f30,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) )
=> ( ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
=> ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) ) )
=> ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ) ),
inference(flattening,[],[f24]) ).
thf(f24,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) )
=> ( ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
=> ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) ) )
=> ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f23,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1)
=> ( ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X1: frac,X2: frac,X3: frac,X4: frac] :
( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X1),X2)
=> ( ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X3),X4)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X3),X4) )
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X2),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz65b) ).
thf(f41,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) != $true,
inference(cnf_transformation,[],[f31]) ).
thf(f31,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) != $true )
& ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) != $true ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f25,plain,
~ ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) != $true )
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) = $true ) ),
inference(flattening,[],[f12]) ).
thf(f12,plain,
~ ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) != $true )
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) = $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,plain,
~ ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u))
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) ),
inference(rectify,[],[f8]) ).
thf(f8,negated_conjecture,
~ ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u))
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) ),
inference(negated_conjecture,[],[f7]) ).
thf(f7,conjecture,
( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u))
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz66) ).
thf(f129,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f128]) ).
thf(f128,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f125]) ).
thf(f125,plain,
( ( $true != $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f124,f96]) ).
thf(f124,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f123]) ).
thf(f123,plain,
( ( $true != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f122,f87]) ).
thf(f87,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f85]) ).
thf(f85,plain,
( spl0_2
<=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f122,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) != $true ) ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f121,plain,
( ( $true != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) != $true ) ),
inference(superposition,[],[f42,f48]) ).
thf(f48,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f38,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) ) ),
inference(flattening,[],[f37]) ).
thf(f37,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f22,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) )
=> ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
=> ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f21,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1)
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X1: frac,X2: frac,X3: frac,X4: frac] :
( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X1),X2)
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X3),X4)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X2),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz56) ).
thf(f42,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) != $true,
inference(cnf_transformation,[],[f31]) ).
thf(f115,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f114]) ).
thf(f114,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f111]) ).
thf(f111,plain,
( ( $true != $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f110,f87]) ).
thf(f110,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) != $true )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f109,plain,
( ( $true != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) != $true )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f108,f92]) ).
thf(f92,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) = $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f90]) ).
thf(f90,plain,
( spl0_3
<=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f108,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) != $true ) ),
inference(trivial_inequality_removal,[],[f107]) ).
thf(f107,plain,
( ( $true != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) != $true ) ),
inference(superposition,[],[f41,f47]) ).
thf(f47,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f36,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
| ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) )
& ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) ) ) ),
inference(flattening,[],[f35]) ).
thf(f35,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
| ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) )
& ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) ) ) ),
inference(ennf_transformation,[],[f29]) ).
thf(f29,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) )
=> ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) ) )
=> ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
=> ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ) ),
inference(flattening,[],[f20]) ).
thf(f20,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) )
=> ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) ) )
=> ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
=> ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f19,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) )
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
! [X1: frac,X2: frac,X3: frac,X4: frac] :
( ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X1),X2)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X1),X2) )
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X3),X4)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X2),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz65a) ).
thf(f104,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f103,f90,f81]) ).
thf(f103,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) != $true ) ),
inference(trivial_inequality_removal,[],[f102]) ).
thf(f102,plain,
( ( $true != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) != $true ) ),
inference(superposition,[],[f41,f46]) ).
thf(f46,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f97,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f44,f94,f90]) ).
thf(f44,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) = $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) = $true ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f33,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) = $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) = $true ) ),
inference(ennf_transformation,[],[f27]) ).
thf(f27,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) != $true )
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) = $true ) ),
inference(flattening,[],[f16]) ).
thf(f16,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) != $true )
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) = $true ) ),
inference(fool_elimination,[],[f15]) ).
thf(f15,plain,
( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(f88,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f43,f85,f81]) ).
thf(f43,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) = $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) = $true ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f32,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) = $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) = $true ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f26,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) != $true )
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) = $true ) ),
inference(flattening,[],[f14]) ).
thf(f14,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) != $true )
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) = $true ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,plain,
( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : NUM765^1 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n017.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 20 03:56:52 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % (7103)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (7105)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.34 % (7107)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.11/0.34 % (7108)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.11/0.34 % (7109)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.11/0.34 % (7106)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.11/0.34 % (7110)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)
% 0.11/0.34 % (7106)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.34 % (7107)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.34 % Exception at run slice level% Exception at run slice level% Exception at run slice level
% 0.11/0.34
% 0.11/0.34 User error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructsFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.34
% 0.11/0.34
% 0.11/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.34 % (7104)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.35 % Exception at run slice level
% 0.11/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.35 % (7106)First to succeed.
% 0.11/0.35 % (7106)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-7103"
% 0.11/0.35 % (7106)Refutation found. Thanks to Tanya!
% 0.11/0.35 % SZS status Theorem for theBenchmark
% 0.11/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.35 % (7106)------------------------------
% 0.11/0.35 % (7106)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.35 % (7106)Termination reason: Refutation
% 0.11/0.35
% 0.11/0.35 % (7106)Memory used [KB]: 852
% 0.11/0.35 % (7106)Time elapsed: 0.009 s
% 0.11/0.35 % (7106)Instructions burned: 15 (million)
% 0.11/0.35 % (7103)Success in time 0.022 s
%------------------------------------------------------------------------------