TSTP Solution File: SEV174^5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEV174^5 : 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 : n006.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 04:14:35 EDT 2024
% Result : Theorem 2.04s 0.64s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 33
% Syntax : Number of formulae : 101 ( 8 unt; 22 typ; 0 def)
% Number of atoms : 1254 ( 312 equ; 0 cnn)
% Maximal formula atoms : 17 ( 15 avg)
% Number of connectives : 383 ( 104 ~; 149 |; 97 &; 0 @)
% ( 5 <=>; 25 =>; 0 <=; 3 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 149 ( 148 >; 1 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 3 con; 0-6 aty)
% Number of variables : 174 ( 0 ^ 111 !; 57 ?; 174 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cP: ( a > $o ) > $o ).
thf(func_def_5,type,
sP0: a > $o ).
thf(func_def_6,type,
sP1: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_7,type,
sP2: ( a > $o ) > $o ).
thf(func_def_8,type,
sP3: $o ).
thf(func_def_9,type,
sK4: a > $o ).
thf(func_def_10,type,
sK5: a > $o ).
thf(func_def_11,type,
sK6: ( a > $o ) > a ).
thf(func_def_12,type,
sK7: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_13,type,
sK8: a > a > $o ).
thf(func_def_14,type,
sK9: a > $o ).
thf(func_def_15,type,
sK10: ( a > $o ) > a ).
thf(func_def_16,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_17,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_18,type,
vAND: $o > $o > $o ).
thf(func_def_19,type,
vOR: $o > $o > $o ).
thf(func_def_20,type,
vIMP: $o > $o > $o ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(func_def_22,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f15483,plain,
$false,
inference(unit_resulting_resolution,[],[f12086,f14145,f41]) ).
thf(f41,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X1),X0) )
| ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK7,X1),X0)) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f25,plain,
! [X0: a > $o,X1: a > $o] :
( ( ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK7,X1),X0)) )
& ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK7,X1),X0)) ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f23,f24]) ).
thf(f24,plain,
! [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( vAPP(a,$o,X0,X2) = $true )
& ( $true = vAPP(a,$o,X1,X2) ) )
=> ( ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK7,X1),X0)) )
& ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK7,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f23,plain,
! [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( vAPP(a,$o,X0,X2) = $true )
& ( $true = vAPP(a,$o,X1,X2) ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X1),X0) ) ),
inference(rectify,[],[f22]) ).
thf(f22,plain,
! [X7: a > $o,X6: a > $o] :
( ? [X8: a] :
( ( $true = vAPP(a,$o,X7,X8) )
& ( $true = vAPP(a,$o,X6,X8) ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X6),X7) ) ),
inference(nnf_transformation,[],[f10]) ).
thf(f10,plain,
! [X7: a > $o,X6: a > $o] :
( ? [X8: a] :
( ( $true = vAPP(a,$o,X7,X8) )
& ( $true = vAPP(a,$o,X6,X8) ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X6),X7) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f14145,plain,
$true != vAPP(a,$o,sK5,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK7,sK4),sK5)),
inference(unit_resulting_resolution,[],[f12089,f12087,f12088,f12401,f46]) ).
thf(f46,plain,
! [X3: a,X4: a > $o,X5: a > $o] :
( ( $true != vAPP(a,$o,X5,X3) )
| ( X4 = X5 )
| ( $true != vAPP(a,$o,X4,X3) )
| ( vAPP(sTfun(a,$o),$o,cP,X5) != $true )
| ( $true != vAPP(sTfun(a,$o),$o,cP,X4) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f33,plain,
( ! [X0: a > $o] :
( ( $true = sP3 )
| ( $true = vAPP(sTfun(a,$o),$o,sP2,X0) )
| ( ! [X2: a] : ( $true != vAPP(a,$o,sK9,X2) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,sK9) ) ) )
& ! [X3: a,X4: a > $o,X5: a > $o] :
( ( X4 = X5 )
| ( $true != vAPP(a,$o,X5,X3) )
| ( $true != vAPP(a,$o,X4,X3) )
| ( vAPP(sTfun(a,$o),$o,cP,X5) != $true )
| ( $true != vAPP(sTfun(a,$o),$o,cP,X4) ) )
& ! [X6: a > $o] :
( ( $true = vAPP(a,$o,X6,vAPP(sTfun(a,$o),a,sK10,X6)) )
| ( vAPP(sTfun(a,$o),$o,cP,X6) != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f30,f32,f31]) ).
thf(f31,plain,
( ? [X1: a > $o] :
( ! [X2: a] : ( $true != vAPP(a,$o,X1,X2) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,X1) ) )
=> ( ! [X2: a] : ( $true != vAPP(a,$o,sK9,X2) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,sK9) ) ) ),
introduced(choice_axiom,[]) ).
thf(f32,plain,
! [X6: a > $o] :
( ? [X7: a] : ( $true = vAPP(a,$o,X6,X7) )
=> ( $true = vAPP(a,$o,X6,vAPP(sTfun(a,$o),a,sK10,X6)) ) ),
introduced(choice_axiom,[]) ).
thf(f30,plain,
( ! [X0: a > $o] :
( ( $true = sP3 )
| ( $true = vAPP(sTfun(a,$o),$o,sP2,X0) )
| ? [X1: a > $o] :
( ! [X2: a] : ( $true != vAPP(a,$o,X1,X2) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,X1) ) ) )
& ! [X3: a,X4: a > $o,X5: a > $o] :
( ( X4 = X5 )
| ( $true != vAPP(a,$o,X5,X3) )
| ( $true != vAPP(a,$o,X4,X3) )
| ( vAPP(sTfun(a,$o),$o,cP,X5) != $true )
| ( $true != vAPP(sTfun(a,$o),$o,cP,X4) ) )
& ! [X6: a > $o] :
( ? [X7: a] : ( $true = vAPP(a,$o,X6,X7) )
| ( vAPP(sTfun(a,$o),$o,cP,X6) != $true ) ) ),
inference(rectify,[],[f13]) ).
thf(f13,plain,
( ! [X5: a > $o] :
( ( $true = sP3 )
| ( $true = vAPP(sTfun(a,$o),$o,sP2,X5) )
| ? [X11: a > $o] :
( ! [X12: a] : ( $true != vAPP(a,$o,X11,X12) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,X11) ) ) )
& ! [X0: a,X1: a > $o,X2: a > $o] :
( ( X1 = X2 )
| ( $true != vAPP(a,$o,X2,X0) )
| ( $true != vAPP(a,$o,X1,X0) )
| ( $true != vAPP(sTfun(a,$o),$o,cP,X2) )
| ( $true != vAPP(sTfun(a,$o),$o,cP,X1) ) )
& ! [X3: a > $o] :
( ? [X4: a] : ( $true = vAPP(a,$o,X3,X4) )
| ( vAPP(sTfun(a,$o),$o,cP,X3) != $true ) ) ),
inference(definition_folding,[],[f8,f12,f11,f10,f9]) ).
thf(f9,plain,
! [X9: a] :
( ( $true = vAPP(a,$o,sP0,X9) )
<=> ? [X10: a > $o] :
( ( $true = vAPP(a,$o,X10,X9) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,X10) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f11,plain,
! [X5: a > $o] :
( ? [X9: a] :
( ( $true = vAPP(a,$o,X5,X9) )
<~> ( $true = vAPP(a,$o,sP0,X9) ) )
| ( $true != vAPP(sTfun(a,$o),$o,sP2,X5) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f12,plain,
( ? [X6: a > $o,X7: a > $o] :
( ( X6 != X7 )
& ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X6),X7) )
& ( vAPP(sTfun(a,$o),$o,cP,X7) = $true )
& ( vAPP(sTfun(a,$o),$o,cP,X6) = $true ) )
| ( $true != sP3 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f8,plain,
( ! [X5: a > $o] :
( ? [X6: a > $o,X7: a > $o] :
( ( X6 != X7 )
& ? [X8: a] :
( ( $true = vAPP(a,$o,X7,X8) )
& ( $true = vAPP(a,$o,X6,X8) ) )
& ( vAPP(sTfun(a,$o),$o,cP,X7) = $true )
& ( vAPP(sTfun(a,$o),$o,cP,X6) = $true ) )
| ? [X9: a] :
( ( $true = vAPP(a,$o,X5,X9) )
<~> ? [X10: a > $o] :
( ( $true = vAPP(a,$o,X10,X9) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,X10) ) ) )
| ? [X11: a > $o] :
( ! [X12: a] : ( $true != vAPP(a,$o,X11,X12) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,X11) ) ) )
& ! [X0: a,X1: a > $o,X2: a > $o] :
( ( X1 = X2 )
| ( $true != vAPP(a,$o,X2,X0) )
| ( $true != vAPP(a,$o,X1,X0) )
| ( $true != vAPP(sTfun(a,$o),$o,cP,X2) )
| ( $true != vAPP(sTfun(a,$o),$o,cP,X1) ) )
& ! [X3: a > $o] :
( ? [X4: a] : ( $true = vAPP(a,$o,X3,X4) )
| ( vAPP(sTfun(a,$o),$o,cP,X3) != $true ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
( ! [X5: a > $o] :
( ? [X6: a > $o,X7: a > $o] :
( ( X6 != X7 )
& ? [X8: a] :
( ( $true = vAPP(a,$o,X7,X8) )
& ( $true = vAPP(a,$o,X6,X8) ) )
& ( vAPP(sTfun(a,$o),$o,cP,X7) = $true )
& ( vAPP(sTfun(a,$o),$o,cP,X6) = $true ) )
| ? [X9: a] :
( ( $true = vAPP(a,$o,X5,X9) )
<~> ? [X10: a > $o] :
( ( $true = vAPP(a,$o,X10,X9) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,X10) ) ) )
| ? [X11: a > $o] :
( ! [X12: a] : ( $true != vAPP(a,$o,X11,X12) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,X11) ) ) )
& ! [X0: a,X1: a > $o,X2: a > $o] :
( ( X1 = X2 )
| ( $true != vAPP(a,$o,X2,X0) )
| ( $true != vAPP(a,$o,X1,X0) )
| ( $true != vAPP(sTfun(a,$o),$o,cP,X2) )
| ( $true != vAPP(sTfun(a,$o),$o,cP,X1) ) )
& ! [X3: a > $o] :
( ? [X4: a] : ( $true = vAPP(a,$o,X3,X4) )
| ( vAPP(sTfun(a,$o),$o,cP,X3) != $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: a,X1: a > $o,X2: a > $o] :
( ( ( $true = vAPP(a,$o,X2,X0) )
& ( $true = vAPP(a,$o,X1,X0) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,X2) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,X1) ) )
=> ( X1 = X2 ) )
& ! [X3: a > $o] :
( ( vAPP(sTfun(a,$o),$o,cP,X3) = $true )
=> ? [X4: a] : ( $true = vAPP(a,$o,X3,X4) ) ) )
=> ? [X5: a > $o] :
( ! [X6: a > $o,X7: a > $o] :
( ( ? [X8: a] :
( ( $true = vAPP(a,$o,X7,X8) )
& ( $true = vAPP(a,$o,X6,X8) ) )
& ( vAPP(sTfun(a,$o),$o,cP,X7) = $true )
& ( vAPP(sTfun(a,$o),$o,cP,X6) = $true ) )
=> ( X6 = X7 ) )
& ! [X9: a] :
( ( $true = vAPP(a,$o,X5,X9) )
<=> ? [X10: a > $o] :
( ( $true = vAPP(a,$o,X10,X9) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,X10) ) ) )
& ! [X11: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,cP,X11) )
=> ? [X12: a] : ( $true = vAPP(a,$o,X11,X12) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: a,X1: a > $o,X2: a > $o] :
( ( vAPP(a,$o,X2,X0)
& vAPP(a,$o,X1,X0)
& vAPP(sTfun(a,$o),$o,cP,X2)
& vAPP(sTfun(a,$o),$o,cP,X1) )
=> ( X1 = X2 ) )
& ! [X3: a > $o] :
( vAPP(sTfun(a,$o),$o,cP,X3)
=> ? [X4: a] : vAPP(a,$o,X3,X4) ) )
=> ? [X5: a > $o] :
( ! [X6: a > $o,X7: a > $o] :
( ( ? [X8: a] :
( vAPP(a,$o,X7,X8)
& vAPP(a,$o,X6,X8) )
& vAPP(sTfun(a,$o),$o,cP,X7)
& vAPP(sTfun(a,$o),$o,cP,X6) )
=> ( X6 = X7 ) )
& ! [X9: a] :
( vAPP(a,$o,X5,X9)
<=> ? [X10: a > $o] :
( vAPP(a,$o,X10,X9)
& vAPP(sTfun(a,$o),$o,cP,X10) ) )
& ! [X11: a > $o] :
( vAPP(sTfun(a,$o),$o,cP,X11)
=> ? [X12: a] : vAPP(a,$o,X11,X12) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X2: a,X0: a > $o,X3: a > $o] :
( ( vAPP(a,$o,X3,X2)
& vAPP(a,$o,X0,X2)
& vAPP(sTfun(a,$o),$o,cP,X3)
& vAPP(sTfun(a,$o),$o,cP,X0) )
=> ( X0 = X3 ) )
& ! [X0: a > $o] :
( vAPP(sTfun(a,$o),$o,cP,X0)
=> ? [X1: a] : vAPP(a,$o,X0,X1) ) )
=> ? [X4: a > $o] :
( ! [X7: a > $o,X8: a > $o] :
( ( ? [X2: a] :
( vAPP(a,$o,X8,X2)
& vAPP(a,$o,X7,X2) )
& vAPP(sTfun(a,$o),$o,cP,X8)
& vAPP(sTfun(a,$o),$o,cP,X7) )
=> ( X7 = X8 ) )
& ! [X2: a] :
( vAPP(a,$o,X4,X2)
<=> ? [X6: a > $o] :
( vAPP(a,$o,X6,X2)
& vAPP(sTfun(a,$o),$o,cP,X6) ) )
& ! [X5: a > $o] :
( vAPP(sTfun(a,$o),$o,cP,X5)
=> ? [X2: a] : vAPP(a,$o,X5,X2) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ( ! [X2: a,X0: a > $o,X3: a > $o] :
( ( vAPP(a,$o,X3,X2)
& vAPP(a,$o,X0,X2)
& vAPP(sTfun(a,$o),$o,cP,X3)
& vAPP(sTfun(a,$o),$o,cP,X0) )
=> ( X0 = X3 ) )
& ! [X0: a > $o] :
( vAPP(sTfun(a,$o),$o,cP,X0)
=> ? [X1: a] : vAPP(a,$o,X0,X1) ) )
=> ? [X4: a > $o] :
( ! [X7: a > $o,X8: a > $o] :
( ( ? [X2: a] :
( vAPP(a,$o,X8,X2)
& vAPP(a,$o,X7,X2) )
& vAPP(sTfun(a,$o),$o,cP,X8)
& vAPP(sTfun(a,$o),$o,cP,X7) )
=> ( X7 = X8 ) )
& ! [X2: a] :
( vAPP(a,$o,X4,X2)
<=> ? [X6: a > $o] :
( vAPP(a,$o,X6,X2)
& vAPP(sTfun(a,$o),$o,cP,X6) ) )
& ! [X5: a > $o] :
( vAPP(sTfun(a,$o),$o,cP,X5)
=> ? [X2: a] : vAPP(a,$o,X5,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM555_pme) ).
thf(f12401,plain,
$true = vAPP(a,$o,sK4,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK7,sK4),sK5)),
inference(trivial_inequality_removal,[],[f12400]) ).
thf(f12400,plain,
( ( $true = $false )
| ( $true = vAPP(a,$o,sK4,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK7,sK4),sK5)) ) ),
inference(forward_demodulation,[],[f12399,f12056]) ).
thf(f12056,plain,
$true = sP3,
inference(trivial_inequality_removal,[],[f12055]) ).
thf(f12055,plain,
( ( $true = $false )
| ( $true = sP3 ) ),
inference(duplicate_literal_removal,[],[f11960]) ).
thf(f11960,plain,
( ( $true = $false )
| ( $true = sP3 )
| ( $true = sP3 ) ),
inference(superposition,[],[f11930,f6979]) ).
thf(f6979,plain,
( ( $false = vAPP(sTfun(a,$o),$o,cP,sK9) )
| ( $true = sP3 ) ),
inference(subsumption_resolution,[],[f6978,f4153]) ).
thf(f4153,plain,
( ( $true = vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,sP0)) )
| ( $true = sP3 )
| ( $false = vAPP(sTfun(a,$o),$o,cP,sK9) ) ),
inference(trivial_inequality_removal,[],[f4120]) ).
thf(f4120,plain,
( ( $true = $false )
| ( $true = vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,sP0)) )
| ( $true = sP3 )
| ( $false = vAPP(sTfun(a,$o),$o,cP,sK9) ) ),
inference(superposition,[],[f4052,f92]) ).
thf(f92,plain,
! [X0: a > $o] :
( ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK10,X0)) )
| ( vAPP(sTfun(a,$o),$o,cP,X0) = $false ) ),
inference(trivial_inequality_removal,[],[f91]) ).
thf(f91,plain,
! [X0: a > $o] :
( ( $true != $true )
| ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK10,X0)) )
| ( vAPP(sTfun(a,$o),$o,cP,X0) = $false ) ),
inference(superposition,[],[f45,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f45,plain,
! [X6: a > $o] :
( ( vAPP(sTfun(a,$o),$o,cP,X6) != $true )
| ( $true = vAPP(a,$o,X6,vAPP(sTfun(a,$o),a,sK10,X6)) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f4052,plain,
! [X0: a] :
( ( $true = vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,sP0)) )
| ( $false = vAPP(a,$o,sK9,X0) )
| ( $true = sP3 ) ),
inference(trivial_inequality_removal,[],[f4047]) ).
thf(f4047,plain,
! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,sP0)) )
| ( $false = vAPP(a,$o,sK9,X0) )
| ( $true = sP3 ) ),
inference(equality_factoring,[],[f3137]) ).
thf(f3137,plain,
! [X0: a > $o,X1: a] :
( ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $true = vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $false = vAPP(a,$o,sK9,X1) )
| ( $true = sP3 ) ),
inference(trivial_inequality_removal,[],[f3134]) ).
thf(f3134,plain,
! [X0: a > $o,X1: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $true = vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $false = vAPP(a,$o,sK9,X1) )
| ( $true = sP3 ) ),
inference(superposition,[],[f38,f84]) ).
thf(f84,plain,
! [X0: a,X1: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,sP2,X1) )
| ( $false = vAPP(a,$o,sK9,X0) )
| ( $true = sP3 ) ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f83,plain,
! [X0: a,X1: a > $o] :
( ( $true != $true )
| ( $true = vAPP(sTfun(a,$o),$o,sP2,X1) )
| ( $true = sP3 )
| ( $false = vAPP(a,$o,sK9,X0) ) ),
inference(superposition,[],[f48,f4]) ).
thf(f48,plain,
! [X2: a,X0: a > $o] :
( ( $true != vAPP(a,$o,sK9,X2) )
| ( $true = vAPP(sTfun(a,$o),$o,sP2,X0) )
| ( $true = sP3 ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f38,plain,
! [X0: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,sP2,X0) )
| ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $true = vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,X0)) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f21,plain,
! [X0: a > $o] :
( ( ( ( $true != vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK6,X0)) ) )
& ( ( $true = vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK6,X0)) ) ) )
| ( $true != vAPP(sTfun(a,$o),$o,sP2,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f19,f20]) ).
thf(f20,plain,
! [X0: a > $o] :
( ? [X1: a] :
( ( ( $true != vAPP(a,$o,sP0,X1) )
| ( vAPP(a,$o,X0,X1) != $true ) )
& ( ( $true = vAPP(a,$o,sP0,X1) )
| ( vAPP(a,$o,X0,X1) = $true ) ) )
=> ( ( ( $true != vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK6,X0)) ) )
& ( ( $true = vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK6,X0)) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f19,plain,
! [X0: a > $o] :
( ? [X1: a] :
( ( ( $true != vAPP(a,$o,sP0,X1) )
| ( vAPP(a,$o,X0,X1) != $true ) )
& ( ( $true = vAPP(a,$o,sP0,X1) )
| ( vAPP(a,$o,X0,X1) = $true ) ) )
| ( $true != vAPP(sTfun(a,$o),$o,sP2,X0) ) ),
inference(rectify,[],[f18]) ).
thf(f18,plain,
! [X5: a > $o] :
( ? [X9: a] :
( ( ( $true != vAPP(a,$o,sP0,X9) )
| ( $true != vAPP(a,$o,X5,X9) ) )
& ( ( $true = vAPP(a,$o,sP0,X9) )
| ( $true = vAPP(a,$o,X5,X9) ) ) )
| ( $true != vAPP(sTfun(a,$o),$o,sP2,X5) ) ),
inference(nnf_transformation,[],[f11]) ).
thf(f6978,plain,
( ( $true != vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,sP0)) )
| ( $true = sP3 )
| ( $false = vAPP(sTfun(a,$o),$o,cP,sK9) ) ),
inference(subsumption_resolution,[],[f6973,f107]) ).
thf(f107,plain,
! [X0: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,sP2,X0) )
| ( $false = vAPP(sTfun(a,$o),$o,cP,sK9) )
| ( $true = sP3 ) ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f100,plain,
! [X0: a > $o] :
( ( $true = $false )
| ( $false = vAPP(sTfun(a,$o),$o,cP,sK9) )
| ( $true = vAPP(sTfun(a,$o),$o,sP2,X0) )
| ( $true = sP3 ) ),
inference(superposition,[],[f92,f84]) ).
thf(f6973,plain,
( ( $true != vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,sP0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sP2,sP0) )
| ( $true = sP3 )
| ( $false = vAPP(sTfun(a,$o),$o,cP,sK9) ) ),
inference(trivial_inequality_removal,[],[f6957]) ).
thf(f6957,plain,
( ( $true != $true )
| ( $true != vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,sP0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sP2,sP0) )
| ( $true = sP3 )
| ( $false = vAPP(sTfun(a,$o),$o,cP,sK9) ) ),
inference(superposition,[],[f39,f4153]) ).
thf(f39,plain,
! [X0: a > $o] :
( ( $true != vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sP2,X0) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f11930,plain,
( ( $true = vAPP(sTfun(a,$o),$o,cP,sK9) )
| ( $true = sP3 ) ),
inference(subsumption_resolution,[],[f11929,f11770]) ).
thf(f11770,plain,
( ( $true = vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,sP0)) )
| ( $true = sP3 )
| ( $true = vAPP(sTfun(a,$o),$o,cP,sK9) ) ),
inference(trivial_inequality_removal,[],[f11767]) ).
thf(f11767,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,sP0)) )
| ( $true = sP3 )
| ( $true = vAPP(sTfun(a,$o),$o,cP,sK9) ) ),
inference(equality_factoring,[],[f3138]) ).
thf(f3138,plain,
! [X0: a > $o] :
( ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $true = vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $true = sP3 )
| ( $true = vAPP(sTfun(a,$o),$o,cP,sK9) ) ),
inference(trivial_inequality_removal,[],[f3133]) ).
thf(f3133,plain,
! [X0: a > $o] :
( ( $true != $true )
| ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $true = vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,X0)) )
| ( $true = sP3 )
| ( $true = vAPP(sTfun(a,$o),$o,cP,sK9) ) ),
inference(superposition,[],[f38,f47]) ).
thf(f47,plain,
! [X0: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,sP2,X0) )
| ( $true = sP3 )
| ( $true = vAPP(sTfun(a,$o),$o,cP,sK9) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f11929,plain,
( ( $true != vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,sP0)) )
| ( $true = sP3 )
| ( $true = vAPP(sTfun(a,$o),$o,cP,sK9) ) ),
inference(subsumption_resolution,[],[f11926,f47]) ).
thf(f11926,plain,
( ( $true != vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,sP0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sP2,sP0) )
| ( $true = sP3 )
| ( $true = vAPP(sTfun(a,$o),$o,cP,sK9) ) ),
inference(trivial_inequality_removal,[],[f11896]) ).
thf(f11896,plain,
( ( $true != $true )
| ( $true != vAPP(a,$o,sP0,vAPP(sTfun(a,$o),a,sK6,sP0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sP2,sP0) )
| ( $true = sP3 )
| ( $true = vAPP(sTfun(a,$o),$o,cP,sK9) ) ),
inference(superposition,[],[f39,f11770]) ).
thf(f12399,plain,
( ( $true = vAPP(a,$o,sK4,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK7,sK4),sK5)) )
| ( $false = sP3 ) ),
inference(trivial_inequality_removal,[],[f12396]) ).
thf(f12396,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,sK4,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK7,sK4),sK5)) )
| ( $false = sP3 ) ),
inference(superposition,[],[f40,f110]) ).
thf(f110,plain,
( ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK4),sK5) )
| ( $false = sP3 ) ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f109,plain,
( ( $true != $true )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK4),sK5) )
| ( $false = sP3 ) ),
inference(superposition,[],[f36,f4]) ).
thf(f36,plain,
( ( $true != sP3 )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK4),sK5) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f17,plain,
( ( ( sK4 != sK5 )
& ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK4),sK5) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,sK5) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,sK4) ) )
| ( $true != sP3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f15,f16]) ).
thf(f16,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( X0 != X1 )
& ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X0),X1) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,X1) )
& ( vAPP(sTfun(a,$o),$o,cP,X0) = $true ) )
=> ( ( sK4 != sK5 )
& ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK4),sK5) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,sK5) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,sK4) ) ) ),
introduced(choice_axiom,[]) ).
thf(f15,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( X0 != X1 )
& ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X0),X1) )
& ( $true = vAPP(sTfun(a,$o),$o,cP,X1) )
& ( vAPP(sTfun(a,$o),$o,cP,X0) = $true ) )
| ( $true != sP3 ) ),
inference(rectify,[],[f14]) ).
thf(f14,plain,
( ? [X6: a > $o,X7: a > $o] :
( ( X6 != X7 )
& ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X6),X7) )
& ( vAPP(sTfun(a,$o),$o,cP,X7) = $true )
& ( vAPP(sTfun(a,$o),$o,cP,X6) = $true ) )
| ( $true != sP3 ) ),
inference(nnf_transformation,[],[f12]) ).
thf(f40,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X1),X0) )
| ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK7,X1),X0)) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f12088,plain,
$true = vAPP(sTfun(a,$o),$o,cP,sK4),
inference(unit_resulting_resolution,[],[f12056,f34]) ).
thf(f34,plain,
( ( $true != sP3 )
| ( $true = vAPP(sTfun(a,$o),$o,cP,sK4) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f12087,plain,
$true = vAPP(sTfun(a,$o),$o,cP,sK5),
inference(unit_resulting_resolution,[],[f12056,f35]) ).
thf(f35,plain,
( ( $true != sP3 )
| ( $true = vAPP(sTfun(a,$o),$o,cP,sK5) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f12089,plain,
sK4 != sK5,
inference(unit_resulting_resolution,[],[f12056,f37]) ).
thf(f37,plain,
( ( sK4 != sK5 )
| ( $true != sP3 ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f12086,plain,
$true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK4),sK5),
inference(unit_resulting_resolution,[],[f12056,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEV174^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 18:47:53 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (21925)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (21928)WARNING: value z3 for option sas not known
% 0.15/0.37 % (21932)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)
% 0.15/0.37 % (21926)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (21932)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.37 % (21927)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (21928)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)
% 0.15/0.37 % (21931)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)
% 0.15/0.37 % Exception at run slice level
% 0.15/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37 % Exception at run slice level
% 0.15/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.38 % (21930)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)
% 0.15/0.38 % (21929)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % Exception at run slice level
% 0.15/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % (21933)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.39 % (21934)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.15/0.39 % (21933)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39 % (21934)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40 % (21935)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.15/0.41 % (21936)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 2.04/0.64 % (21932)First to succeed.
% 2.04/0.64 % (21932)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-21925"
% 2.04/0.64 % (21932)Refutation found. Thanks to Tanya!
% 2.04/0.64 % SZS status Theorem for theBenchmark
% 2.04/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 2.04/0.64 % (21932)------------------------------
% 2.04/0.64 % (21932)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.04/0.64 % (21932)Termination reason: Refutation
% 2.04/0.64
% 2.04/0.64 % (21932)Memory used [KB]: 1757
% 2.04/0.64 % (21932)Time elapsed: 0.268 s
% 2.04/0.64 % (21932)Instructions burned: 990 (million)
% 2.04/0.64 % (21925)Success in time 0.281 s
%------------------------------------------------------------------------------